/**
 *  date : 2021-02-19 09:55:24
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <exception>
#include <forward_list>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ratio>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <system_error>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <valarray>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  T &x() { return first; }
  const T &x() const { return first; }
  U &y() { return second; }
  const U &y() const { return second; }

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}
template <typename T, size_t N>
void mem(T (&a)[N], int c) {
  memset(a, c, sizeof(T) * N);
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<T> reord(const vector<T> &v, const vector<T> &ord) {
  int N = v.size();
  vector<T> ret(N);
  for (int i = 0; i < N; i++) ret[i] = v[ord[i]];
  return ret;
};

template <typename T = int>
vector<T> mkiota(int N) {
  vector<T> ret(N);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
vector<int> mkinv(vector<T> &v, int max_val = -1) {
  if (max_val < (int)v.size()) max_val = v.size() - 1;
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

}  // namespace Nyaan

// bit operation
namespace Nyaan {

__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}

__attribute__((target("bmi"))) inline int lsb(const u64 &a) {
  return _tzcnt_u64(a);
}
__attribute__((target("bmi"))) inline int ctz(const u64 &a) {
  return _tzcnt_u64(a);
}

__attribute__((target("lzcnt"))) inline int msb(const u64 &a) {
  return 63 - _lzcnt_u64(a);
}
__attribute__((target("lzcnt"))) inline int clz64(const u64 &a) {
  return _lzcnt_u64(a);
}

template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  a ^= (gbit(a, i) == b ? 0 : (T(b) << i));
}

constexpr long long PW(int n) { return 1LL << n; }

constexpr long long MSK(int n) { return (1LL << n) - 1; }

}  // namespace Nyaan

// inout
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if (is_signed<T>::value)
    if (t == -Nyaan::inf) res = "-inf";
  if (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if (is_signed<T>::value)
      if (t == -Nyaan::infLL) res = "-inf";
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...)
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define repc(i, a, cond) for (long long i = (a); (cond); i++)
#define enm(i, val, vec)                                  \
  for (long long i = 0; i < (long long)(vec).size(); i++) \
    if (auto& val = vec[i]; false)                        \
      ;                                                   \
    else

#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define inc(...)    \
  char __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }

#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//

#include <immintrin.h>

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
my128_mullo_epu32(const __m128i &a, const __m128i &b) {
  return _mm_mullo_epi32(a, b);
}

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
my128_mulhi_epu32(const __m128i &a, const __m128i &b) {
  __m128i a13 = _mm_shuffle_epi32(a, 0xF5);
  __m128i b13 = _mm_shuffle_epi32(b, 0xF5);
  __m128i prod02 = _mm_mul_epu32(a, b);
  __m128i prod13 = _mm_mul_epu32(a13, b13);
  __m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13),
                                    _mm_unpackhi_epi32(prod02, prod13));
  return prod;
}

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
montgomery_mul_128(const __m128i &a, const __m128i &b, const __m128i &r,
                   const __m128i &m1) {
  return _mm_sub_epi32(
      _mm_add_epi32(my128_mulhi_epu32(a, b), m1),
      my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1));
}

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
montgomery_add_128(const __m128i &a, const __m128i &b, const __m128i &m2,
                   const __m128i &m0) {
  __m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2);
  return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
montgomery_sub_128(const __m128i &a, const __m128i &b, const __m128i &m2,
                   const __m128i &m0) {
  __m128i ret = _mm_sub_epi32(a, b);
  return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
my256_mullo_epu32(const __m256i &a, const __m256i &b) {
  return _mm256_mullo_epi32(a, b);
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
my256_mulhi_epu32(const __m256i &a, const __m256i &b) {
  __m256i a13 = _mm256_shuffle_epi32(a, 0xF5);
  __m256i b13 = _mm256_shuffle_epi32(b, 0xF5);
  __m256i prod02 = _mm256_mul_epu32(a, b);
  __m256i prod13 = _mm256_mul_epu32(a13, b13);
  __m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13),
                                       _mm256_unpackhi_epi32(prod02, prod13));
  return prod;
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
montgomery_mul_256(const __m256i &a, const __m256i &b, const __m256i &r,
                   const __m256i &m1) {
  return _mm256_sub_epi32(
      _mm256_add_epi32(my256_mulhi_epu32(a, b), m1),
      my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1));
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
montgomery_add_256(const __m256i &a, const __m256i &b, const __m256i &m2,
                   const __m256i &m0) {
  __m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2);
  return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
                          ret);
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
montgomery_sub_256(const __m256i &a, const __m256i &b, const __m256i &m2,
                   const __m256i &m0) {
  __m256i ret = _mm256_sub_epi32(a, b);
  return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
                          ret);
}
namespace ntt_inner {
using u64 = uint64_t;
constexpr uint32_t get_pr(uint32_t mod) {
  if (mod == 2) return 1;
  u64 ds[32] = {};
  int idx = 0;
  u64 m = mod - 1;
  for (u64 i = 2; i * i <= m; ++i) {
    if (m % i == 0) {
      ds[idx++] = i;
      while (m % i == 0) m /= i;
    }
  }
  if (m != 1) ds[idx++] = m;

  uint32_t pr = 2;
  while (1) {
    int flg = 1;
    for (int i = 0; i < idx; ++i) {
      u64 a = pr, b = (mod - 1) / ds[i], r = 1;
      while (b) {
        if (b & 1) r = r * a % mod;
        a = a * a % mod;
        b >>= 1;
      }
      if (r == 1) {
        flg = 0;
        break;
      }
    }
    if (flg == 1) break;
    ++pr;
  }
  return pr;
}

constexpr int SZ_FFT_BUF = 1 << 23;
uint32_t _buf1[SZ_FFT_BUF] __attribute__((aligned(64)));
uint32_t _buf2[SZ_FFT_BUF] __attribute__((aligned(64)));
}  // namespace ntt_inner

template <typename mint>
struct NTT {
  static constexpr uint32_t mod = mint::get_mod();
  static constexpr uint32_t pr = ntt_inner::get_pr(mint::get_mod());
  static constexpr int level = __builtin_ctzll(mod - 1);
  mint dw[level], dy[level];
  mint *buf1, *buf2;

  constexpr NTT() {
    setwy(level);
    union raw_cast {
      mint dat;
      uint32_t _;
    };
    buf1 = &(((raw_cast *)(ntt_inner::_buf1))->dat);
    buf2 = &(((raw_cast *)(ntt_inner::_buf2))->dat);
  }

  constexpr void setwy(int k) {
    mint w[level], y[level];
    w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
    y[k - 1] = w[k - 1].inverse();
    for (int i = k - 2; i > 0; --i)
      w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
    dw[0] = dy[0] = w[1] * w[1];
    dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
    for (int i = 3; i < k; ++i) {
      dw[i] = dw[i - 1] * y[i - 2] * w[i];
      dy[i] = dy[i - 1] * w[i - 2] * y[i];
    }
  }

  __attribute__((target("avx2"))) void ntt(mint *a, int n) {
    int k = n ? __builtin_ctz(n) : 0;
    if (k == 0) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    if (k & 1) {
      int v = 1 << (k - 1);
      if (v < 8) {
        for (int j = 0; j < v; ++j) {
          mint ajv = a[j + v];
          a[j + v] = a[j] - ajv;
          a[j] += ajv;
        }
      } else {
        const __m256i m0 = _mm256_set1_epi32(0);
        const __m256i m2 = _mm256_set1_epi32(mod + mod);
        int j0 = 0;
        int j1 = v;
        for (; j0 < v; j0 += 8, j1 += 8) {
          __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
          __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
          __m256i naj = montgomery_add_256(T0, T1, m2, m0);
          __m256i najv = montgomery_sub_256(T0, T1, m2, m0);
          _mm256_storeu_si256((__m256i *)(a + j0), naj);
          _mm256_storeu_si256((__m256i *)(a + j1), najv);
        }
      }
    }
    int u = 1 << (2 + (k & 1));
    int v = 1 << (k - 2 - (k & 1));
    mint one = mint(1);
    mint imag = dw[1];
    while (v) {
      if (v == 1) {
        mint ww = one, xx = one, wx = one;
        for (int jh = 0; jh < u;) {
          ww = xx * xx, wx = ww * xx;
          mint t0 = a[jh + 0], t1 = a[jh + 1] * xx;
          mint t2 = a[jh + 2] * ww, t3 = a[jh + 3] * wx;
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[jh + 0] = t0p2 + t1p3, a[jh + 1] = t0p2 - t1p3;
          a[jh + 2] = t0m2 + t1m3, a[jh + 3] = t0m2 - t1m3;
          xx *= dw[__builtin_ctz((jh += 4))];
        }
      } else if (v == 4) {
        const __m128i m0 = _mm_set1_epi32(0);
        const __m128i m1 = _mm_set1_epi32(mod);
        const __m128i m2 = _mm_set1_epi32(mod + mod);
        const __m128i r = _mm_set1_epi32(mint::r);
        const __m128i Imag = _mm_set1_epi32(imag.a);
        mint ww = one, xx = one, wx = one;
        for (int jh = 0; jh < u;) {
          if (jh == 0) {
            int j0 = 0;
            int j1 = v;
            int j2 = j1 + v;
            int j3 = j2 + v;
            int je = v;
            for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
              const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
              const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
              const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
              const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
              const __m128i T0P2 = montgomery_add_128(T0, T2, m2, m0);
              const __m128i T1P3 = montgomery_add_128(T1, T3, m2, m0);
              const __m128i T0M2 = montgomery_sub_128(T0, T2, m2, m0);
              const __m128i T1M3 = montgomery_mul_128(
                  montgomery_sub_128(T1, T3, m2, m0), Imag, r, m1);
              _mm_storeu_si128((__m128i *)(a + j0),
                               montgomery_add_128(T0P2, T1P3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j1),
                               montgomery_sub_128(T0P2, T1P3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j2),
                               montgomery_add_128(T0M2, T1M3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j3),
                               montgomery_sub_128(T0M2, T1M3, m2, m0));
            }
          } else {
            ww = xx * xx, wx = ww * xx;
            const __m128i WW = _mm_set1_epi32(ww.a);
            const __m128i WX = _mm_set1_epi32(wx.a);
            const __m128i XX = _mm_set1_epi32(xx.a);
            int j0 = jh * v;
            int j1 = j0 + v;
            int j2 = j1 + v;
            int j3 = j2 + v;
            int je = j1;
            for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
              const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
              const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
              const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
              const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
              const __m128i MT1 = montgomery_mul_128(T1, XX, r, m1);
              const __m128i MT2 = montgomery_mul_128(T2, WW, r, m1);
              const __m128i MT3 = montgomery_mul_128(T3, WX, r, m1);
              const __m128i T0P2 = montgomery_add_128(T0, MT2, m2, m0);
              const __m128i T1P3 = montgomery_add_128(MT1, MT3, m2, m0);
              const __m128i T0M2 = montgomery_sub_128(T0, MT2, m2, m0);
              const __m128i T1M3 = montgomery_mul_128(
                  montgomery_sub_128(MT1, MT3, m2, m0), Imag, r, m1);
              _mm_storeu_si128((__m128i *)(a + j0),
                               montgomery_add_128(T0P2, T1P3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j1),
                               montgomery_sub_128(T0P2, T1P3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j2),
                               montgomery_add_128(T0M2, T1M3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j3),
                               montgomery_sub_128(T0M2, T1M3, m2, m0));
            }
          }
          xx *= dw[__builtin_ctz((jh += 4))];
        }
      } else {
        const __m256i m0 = _mm256_set1_epi32(0);
        const __m256i m1 = _mm256_set1_epi32(mod);
        const __m256i m2 = _mm256_set1_epi32(mod + mod);
        const __m256i r = _mm256_set1_epi32(mint::r);
        const __m256i Imag = _mm256_set1_epi32(imag.a);
        mint ww = one, xx = one, wx = one;
        for (int jh = 0; jh < u;) {
          if (jh == 0) {
            int j0 = 0;
            int j1 = v;
            int j2 = j1 + v;
            int j3 = j2 + v;
            int je = v;
            for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
              const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
              const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
              const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
              const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
              const __m256i T0P2 = montgomery_add_256(T0, T2, m2, m0);
              const __m256i T1P3 = montgomery_add_256(T1, T3, m2, m0);
              const __m256i T0M2 = montgomery_sub_256(T0, T2, m2, m0);
              const __m256i T1M3 = montgomery_mul_256(
                  montgomery_sub_256(T1, T3, m2, m0), Imag, r, m1);
              _mm256_storeu_si256((__m256i *)(a + j0),
                                  montgomery_add_256(T0P2, T1P3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j1),
                                  montgomery_sub_256(T0P2, T1P3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j2),
                                  montgomery_add_256(T0M2, T1M3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j3),
                                  montgomery_sub_256(T0M2, T1M3, m2, m0));
            }
          } else {
            ww = xx * xx, wx = ww * xx;
            const __m256i WW = _mm256_set1_epi32(ww.a);
            const __m256i WX = _mm256_set1_epi32(wx.a);
            const __m256i XX = _mm256_set1_epi32(xx.a);
            int j0 = jh * v;
            int j1 = j0 + v;
            int j2 = j1 + v;
            int j3 = j2 + v;
            int je = j1;
            for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
              const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
              const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
              const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
              const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
              const __m256i MT1 = montgomery_mul_256(T1, XX, r, m1);
              const __m256i MT2 = montgomery_mul_256(T2, WW, r, m1);
              const __m256i MT3 = montgomery_mul_256(T3, WX, r, m1);
              const __m256i T0P2 = montgomery_add_256(T0, MT2, m2, m0);
              const __m256i T1P3 = montgomery_add_256(MT1, MT3, m2, m0);
              const __m256i T0M2 = montgomery_sub_256(T0, MT2, m2, m0);
              const __m256i T1M3 = montgomery_mul_256(
                  montgomery_sub_256(MT1, MT3, m2, m0), Imag, r, m1);
              _mm256_storeu_si256((__m256i *)(a + j0),
                                  montgomery_add_256(T0P2, T1P3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j1),
                                  montgomery_sub_256(T0P2, T1P3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j2),
                                  montgomery_add_256(T0M2, T1M3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j3),
                                  montgomery_sub_256(T0M2, T1M3, m2, m0));
            }
          }
          xx *= dw[__builtin_ctz((jh += 4))];
        }
      }
      u <<= 2;
      v >>= 2;
    }
  }

  __attribute__((target("avx2"))) void intt(mint *a, int n,
                                            int normalize = true) {
    int k = n ? __builtin_ctz(n) : 0;
    if (k == 0) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      if (normalize) {
        a[0] *= mint(2).inverse();
        a[1] *= mint(2).inverse();
      }
      return;
    }
    int u = 1 << (k - 2);
    int v = 1;
    mint one = mint(1);
    mint imag = dy[1];
    while (u) {
      if (v == 1) {
        mint ww = one, xx = one, yy = one;
        u <<= 2;
        for (int jh = 0; jh < u;) {
          ww = xx * xx, yy = xx * imag;
          mint t0 = a[jh + 0], t1 = a[jh + 1];
          mint t2 = a[jh + 2], t3 = a[jh + 3];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
          a[jh + 0] = t0p1 + t2p3, a[jh + 2] = (t0p1 - t2p3) * ww;
          a[jh + 1] = t0m1 + t2m3, a[jh + 3] = (t0m1 - t2m3) * ww;
          xx *= dy[__builtin_ctz(jh += 4)];
        }
      } else if (v == 4) {
        const __m128i m0 = _mm_set1_epi32(0);
        const __m128i m1 = _mm_set1_epi32(mod);
        const __m128i m2 = _mm_set1_epi32(mod + mod);
        const __m128i r = _mm_set1_epi32(mint::r);
        const __m128i Imag = _mm_set1_epi32(imag.a);
        mint ww = one, xx = one, yy = one;
        u <<= 2;
        for (int jh = 0; jh < u;) {
          if (jh == 0) {
            int j0 = 0;
            int j1 = v;
            int j2 = v + v;
            int j3 = j2 + v;
            for (; j0 < v; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
              const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
              const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
              const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
              const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
              const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0);
              const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0);
              const __m128i T0M1 = montgomery_sub_128(T0, T1, m2, m0);
              const __m128i T2M3 = montgomery_mul_128(
                  montgomery_sub_128(T2, T3, m2, m0), Imag, r, m1);
              _mm_storeu_si128((__m128i *)(a + j0),
                               montgomery_add_128(T0P1, T2P3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j2),
                               montgomery_sub_128(T0P1, T2P3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j1),
                               montgomery_add_128(T0M1, T2M3, m2, m0));
              _mm_storeu_si128((__m128i *)(a + j3),
                               montgomery_sub_128(T0M1, T2M3, m2, m0));
            }
          } else {
            ww = xx * xx, yy = xx * imag;
            const __m128i WW = _mm_set1_epi32(ww.a);
            const __m128i XX = _mm_set1_epi32(xx.a);
            const __m128i YY = _mm_set1_epi32(yy.a);
            int j0 = jh * v;
            int j1 = j0 + v;
            int j2 = j1 + v;
            int j3 = j2 + v;
            int je = j1;
            for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
              const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
              const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
              const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
              const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
              const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0);
              const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0);
              const __m128i T0M1 = montgomery_mul_128(
                  montgomery_sub_128(T0, T1, m2, m0), XX, r, m1);
              __m128i T2M3 = montgomery_mul_128(
                  montgomery_sub_128(T2, T3, m2, m0), YY, r, m1);
              _mm_storeu_si128((__m128i *)(a + j0),
                               montgomery_add_128(T0P1, T2P3, m2, m0));
              _mm_storeu_si128(
                  (__m128i *)(a + j2),
                  montgomery_mul_128(montgomery_sub_128(T0P1, T2P3, m2, m0), WW,
                                     r, m1));
              _mm_storeu_si128((__m128i *)(a + j1),
                               montgomery_add_128(T0M1, T2M3, m2, m0));
              _mm_storeu_si128(
                  (__m128i *)(a + j3),
                  montgomery_mul_128(montgomery_sub_128(T0M1, T2M3, m2, m0), WW,
                                     r, m1));
            }
          }
          xx *= dy[__builtin_ctz(jh += 4)];
        }
      } else {
        const __m256i m0 = _mm256_set1_epi32(0);
        const __m256i m1 = _mm256_set1_epi32(mod);
        const __m256i m2 = _mm256_set1_epi32(mod + mod);
        const __m256i r = _mm256_set1_epi32(mint::r);
        const __m256i Imag = _mm256_set1_epi32(imag.a);
        mint ww = one, xx = one, yy = one;
        u <<= 2;
        for (int jh = 0; jh < u;) {
          if (jh == 0) {
            int j0 = 0;
            int j1 = v;
            int j2 = v + v;
            int j3 = j2 + v;
            for (; j0 < v; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
              const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
              const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
              const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
              const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
              const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0);
              const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0);
              const __m256i T0M1 = montgomery_sub_256(T0, T1, m2, m0);
              const __m256i T2M3 = montgomery_mul_256(
                  montgomery_sub_256(T2, T3, m2, m0), Imag, r, m1);
              _mm256_storeu_si256((__m256i *)(a + j0),
                                  montgomery_add_256(T0P1, T2P3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j2),
                                  montgomery_sub_256(T0P1, T2P3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j1),
                                  montgomery_add_256(T0M1, T2M3, m2, m0));
              _mm256_storeu_si256((__m256i *)(a + j3),
                                  montgomery_sub_256(T0M1, T2M3, m2, m0));
            }
          } else {
            ww = xx * xx, yy = xx * imag;
            const __m256i WW = _mm256_set1_epi32(ww.a);
            const __m256i XX = _mm256_set1_epi32(xx.a);
            const __m256i YY = _mm256_set1_epi32(yy.a);
            int j0 = jh * v;
            int j1 = j0 + v;
            int j2 = j1 + v;
            int j3 = j2 + v;
            int je = j1;
            for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
              const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
              const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
              const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
              const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
              const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0);
              const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0);
              const __m256i T0M1 = montgomery_mul_256(
                  montgomery_sub_256(T0, T1, m2, m0), XX, r, m1);
              const __m256i T2M3 = montgomery_mul_256(
                  montgomery_sub_256(T2, T3, m2, m0), YY, r, m1);
              _mm256_storeu_si256((__m256i *)(a + j0),
                                  montgomery_add_256(T0P1, T2P3, m2, m0));
              _mm256_storeu_si256(
                  (__m256i *)(a + j2),
                  montgomery_mul_256(montgomery_sub_256(T0P1, T2P3, m2, m0), WW,
                                     r, m1));
              _mm256_storeu_si256((__m256i *)(a + j1),
                                  montgomery_add_256(T0M1, T2M3, m2, m0));
              _mm256_storeu_si256(
                  (__m256i *)(a + j3),
                  montgomery_mul_256(montgomery_sub_256(T0M1, T2M3, m2, m0), WW,
                                     r, m1));
            }
          }
          xx *= dy[__builtin_ctz(jh += 4)];
        }
      }
      u >>= 4;
      v <<= 2;
    }
    if (k & 1) {
      v = 1 << (k - 1);
      if (v < 8) {
        for (int j = 0; j < v; ++j) {
          mint ajv = a[j] - a[j + v];
          a[j] += a[j + v];
          a[j + v] = ajv;
        }
      } else {
        const __m256i m0 = _mm256_set1_epi32(0);
        const __m256i m2 = _mm256_set1_epi32(mod + mod);
        int j0 = 0;
        int j1 = v;
        for (; j0 < v; j0 += 8, j1 += 8) {
          const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
          const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
          __m256i naj = montgomery_add_256(T0, T1, m2, m0);
          __m256i najv = montgomery_sub_256(T0, T1, m2, m0);
          _mm256_storeu_si256((__m256i *)(a + j0), naj);
          _mm256_storeu_si256((__m256i *)(a + j1), najv);
        }
      }
    }
    if (normalize) {
      mint invn = mint(n).inverse();
      for (int i = 0; i < n; i++) a[i] *= invn;
    }
  }

  __attribute__((target("avx2"))) void inplace_multiply(
      int l1, int l2, int zero_padding = true) {
    int l = l1 + l2 - 1;
    int M = 4;
    while (M < l) M <<= 1;
    if (zero_padding) {
      for (int i = l1; i < M; i++) ntt_inner::_buf1[i] = 0;
      for (int i = l2; i < M; i++) ntt_inner::_buf2[i] = 0;
    }
    const __m256i m0 = _mm256_set1_epi32(0);
    const __m256i m1 = _mm256_set1_epi32(mod);
    const __m256i r = _mm256_set1_epi32(mint::r);
    const __m256i N2 = _mm256_set1_epi32(mint::n2);
    for (int i = 0; i < l1; i += 8) {
      __m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
      __m256i b = montgomery_mul_256(a, N2, r, m1);
      _mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), b);
    }
    for (int i = 0; i < l2; i += 8) {
      __m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i));
      __m256i b = montgomery_mul_256(a, N2, r, m1);
      _mm256_storeu_si256((__m256i *)(ntt_inner::_buf2 + i), b);
    }
    ntt(buf1, M);
    ntt(buf2, M);
    for (int i = 0; i < M; i += 8) {
      __m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
      __m256i b = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i));
      __m256i c = montgomery_mul_256(a, b, r, m1);
      _mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), c);
    }
    intt(buf1, M, false);
    const __m256i INVM = _mm256_set1_epi32((mint(M).inverse()).a);
    for (int i = 0; i < l; i += 8) {
      __m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
      __m256i b = montgomery_mul_256(a, INVM, r, m1);
      __m256i c = my256_mulhi_epu32(my256_mullo_epu32(b, r), m1);
      __m256i d = _mm256_and_si256(_mm256_cmpgt_epi32(c, m0), m1);
      __m256i e = _mm256_sub_epi32(d, c);
      _mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), e);
    }
  }

  void ntt(vector<mint> &a) {
    int M = (int)a.size();
    for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
    ntt(buf1, M);
    for (int i = 0; i < M; i++) a[i].a = buf1[i].a;
  }

  void intt(vector<mint> &a) {
    int M = (int)a.size();
    for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
    intt(buf1, M, true);
    for (int i = 0; i < M; i++) a[i].a = buf1[i].a;
  }

  vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
    if (a.size() == 0 && b.size() == 0) return vector<mint>{};
    int l = a.size() + b.size() - 1;
    if (min<int>(a.size(), b.size()) <= 40) {
      vector<mint> s(l);
      for (int i = 0; i < (int)a.size(); ++i)
        for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
      return s;
    }
    assert(l <= ntt_inner::SZ_FFT_BUF);
    int M = 4;
    while (M < l) M <<= 1;
    for (int i = 0; i < (int)a.size(); ++i) buf1[i].a = a[i].a;
    for (int i = (int)a.size(); i < M; ++i) buf1[i].a = 0;
    for (int i = 0; i < (int)b.size(); ++i) buf2[i].a = b[i].a;
    for (int i = (int)b.size(); i < M; ++i) buf2[i].a = 0;
    ntt(buf1, M);
    ntt(buf2, M);
    for (int i = 0; i < M; ++i)
      buf1[i].a = mint::reduce(uint64_t(buf1[i].a) * buf2[i].a);
    intt(buf1, M, false);
    vector<mint> s(l);
    mint invm = mint(M).inverse();
    for (int i = 0; i < l; ++i) s[i] = buf1[i] * invm;
    return s;
  }

  void ntt_doubling(vector<mint> &a) {
    int M = (int)a.size();
    for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
    intt(buf1, M);
    mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
    for (int i = 0; i < M; i++) buf1[i] *= r, r *= zeta;
    ntt(buf1, M);
    a.resize(2 * M);
    for (int i = 0; i < M; i++) a[M + i].a = buf1[i].a;
  }
};

template <typename mint>
struct FormalPowerSeries : vector<mint> {
  using vector<mint>::vector;
  using FPS = FormalPowerSeries;

  FPS &operator+=(const FPS &r) {
    if (r.size() > this->size()) this->resize(r.size());
    for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
    return *this;
  }

  FPS &operator+=(const mint &r) {
    if (this->empty()) this->resize(1);
    (*this)[0] += r;
    return *this;
  }

  FPS &operator-=(const FPS &r) {
    if (r.size() > this->size()) this->resize(r.size());
    for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
    return *this;
  }

  FPS &operator-=(const mint &r) {
    if (this->empty()) this->resize(1);
    (*this)[0] -= r;
    return *this;
  }

  FPS &operator*=(const mint &v) {
    for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
    return *this;
  }

  FPS &operator/=(const FPS &r) {
    if (this->size() < r.size()) {
      this->clear();
      return *this;
    }
    int n = this->size() - r.size() + 1;
    if ((int)r.size() <= 64) {
      FPS f(*this), g(r);
      g.shrink();
      mint coeff = g.back().inverse();
      for (auto &x : g) x *= coeff;
      int deg = (int)f.size() - (int)g.size() + 1;
      int gs = g.size();
      FPS quo(deg);
      for (int i = deg - 1; i >= 0; i--) {
        quo[i] = f[i + gs - 1];
        for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
      }
      *this = quo * coeff;
      this->resize(n, mint(0));
      return *this;
    }
    return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
  }

  FPS &operator%=(const FPS &r) {
    *this -= *this / r * r;
    shrink();
    return *this;
  }

  FPS operator+(const FPS &r) const { return FPS(*this) += r; }
  FPS operator+(const mint &v) const { return FPS(*this) += v; }
  FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
  FPS operator-(const mint &v) const { return FPS(*this) -= v; }
  FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
  FPS operator*(const mint &v) const { return FPS(*this) *= v; }
  FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
  FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
  FPS operator-() const {
    FPS ret(this->size());
    for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
    return ret;
  }

  void shrink() {
    while (this->size() && this->back() == mint(0)) this->pop_back();
  }

  FPS rev() const {
    FPS ret(*this);
    reverse(begin(ret), end(ret));
    return ret;
  }

  FPS dot(FPS r) const {
    FPS ret(min(this->size(), r.size()));
    for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
    return ret;
  }

  FPS pre(int sz) const {
    return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));
  }

  FPS operator>>(int sz) const {
    if ((int)this->size() <= sz) return {};
    FPS ret(*this);
    ret.erase(ret.begin(), ret.begin() + sz);
    return ret;
  }

  FPS operator<<(int sz) const {
    FPS ret(*this);
    ret.insert(ret.begin(), sz, mint(0));
    return ret;
  }

  FPS diff() const {
    const int n = (int)this->size();
    FPS ret(max(0, n - 1));
    mint one(1), coeff(1);
    for (int i = 1; i < n; i++) {
      ret[i - 1] = (*this)[i] * coeff;
      coeff += one;
    }
    return ret;
  }

  FPS integral() const {
    const int n = (int)this->size();
    FPS ret(n + 1);
    ret[0] = mint(0);
    if (n > 0) ret[1] = mint(1);
    auto mod = mint::get_mod();
    for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
    for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
    return ret;
  }

  mint eval(mint x) const {
    mint r = 0, w = 1;
    for (auto &v : *this) r += w * v, w *= x;
    return r;
  }

  FPS log(int deg = -1) const {
    assert((*this)[0] == mint(1));
    if (deg == -1) deg = (int)this->size();
    return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
  }

  FPS pow(int64_t k, int deg = -1) const {
    const int n = (int)this->size();
    if (deg == -1) deg = n;
    for (int i = 0; i < n; i++) {
      if ((*this)[i] != mint(0)) {
        if (i * k > deg) return FPS(deg, mint(0));
        mint rev = mint(1) / (*this)[i];
        FPS ret =
            (((*this * rev) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));
        ret = (ret << (i * k)).pre(deg);
        if ((int)ret.size() < deg) ret.resize(deg, mint(0));
        return ret;
      }
    }
    return FPS(deg, mint(0));
  }

  static void *ntt_ptr;
  static void set_fft();
  FPS &operator*=(const FPS &r);
  void ntt();
  void intt();
  void ntt_doubling();
  static int ntt_pr();
  FPS inv(int deg = -1) const;
  FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;

/**
 * @brief 多項式/形式的冪級数ライブラリ
 * @docs docs/fps/formal-power-series.md
 */

template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
  if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}

template <typename mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(
    const FormalPowerSeries<mint>& r) {
  if (this->empty() || r.empty()) {
    this->clear();
    return *this;
  }
  set_fft();
  auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);
  return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}

template <typename mint>
void FormalPowerSeries<mint>::ntt() {
  set_fft();
  static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}

template <typename mint>
void FormalPowerSeries<mint>::intt() {
  set_fft();
  static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}

template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
  set_fft();
  static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}

template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
  set_fft();
  return static_cast<NTT<mint>*>(ntt_ptr)->pr;
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
  assert((*this)[0] != mint(0));
  if (deg == -1) deg = (int)this->size();
  FormalPowerSeries<mint> res(deg);
  res[0] = {mint(1) / (*this)[0]};
  for (int d = 1; d < deg; d <<= 1) {
    FormalPowerSeries<mint> f(2 * d), g(2 * d);
    for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];
    for (int j = 0; j < d; j++) g[j] = res[j];
    f.ntt();
    g.ntt();
    for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
    f.intt();
    for (int j = 0; j < d; j++) f[j] = 0;
    f.ntt();
    for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
    f.intt();
    for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
  }
  return res.pre(deg);
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
  using fps = FormalPowerSeries<mint>;
  assert((*this).size() == 0 || (*this)[0] == mint(0));
  if (deg == -1) deg = this->size();

  fps inv;
  inv.reserve(deg + 1);
  inv.push_back(mint(0));
  inv.push_back(mint(1));

  auto inplace_integral = [&](fps& F) -> void {
    const int n = (int)F.size();
    auto mod = mint::get_mod();
    while ((int)inv.size() <= n) {
      int i = inv.size();
      inv.push_back((-inv[mod % i]) * (mod / i));
    }
    F.insert(begin(F), mint(0));
    for (int i = 1; i <= n; i++) F[i] *= inv[i];
  };

  auto inplace_diff = [](fps& F) -> void {
    if (F.empty()) return;
    F.erase(begin(F));
    mint coeff = 1, one = 1;
    for (int i = 0; i < (int)F.size(); i++) {
      F[i] *= coeff;
      coeff += one;
    }
  };

  fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
  for (int m = 2; m < deg; m *= 2) {
    auto y = b;
    y.resize(2 * m);
    y.ntt();
    z1 = z2;
    fps z(m);
    for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
    z.intt();
    fill(begin(z), begin(z) + m / 2, mint(0));
    z.ntt();
    for (int i = 0; i < m; ++i) z[i] *= -z1[i];
    z.intt();
    c.insert(end(c), begin(z) + m / 2, end(z));
    z2 = c;
    z2.resize(2 * m);
    z2.ntt();
    fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
    inplace_diff(x);
    x.push_back(mint(0));
    x.ntt();
    for (int i = 0; i < m; ++i) x[i] *= y[i];
    x.intt();
    x -= b.diff();
    x.resize(2 * m);
    for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);
    x.ntt();
    for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
    x.intt();
    x.pop_back();
    inplace_integral(x);
    for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];
    fill(begin(x), begin(x) + m, mint(0));
    x.ntt();
    for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];
    x.intt();
    b.insert(end(b), begin(x) + m, end(x));
  }
  return fps{begin(b), begin(b) + deg};
}

/**
 * @brief NTT mod用FPSライブラリ
 * @docs docs/fps/ntt-friendly-fps.md
 */

template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(r * mod == 1, "invalid, r * mod != 1");
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  constexpr mint inverse() const { return pow(mod - 2); }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }

  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};

template <typename T>
struct Binomial {
  vector<T> fac_, finv_, inv_;
  Binomial(int MAX = 0) : fac_(MAX + 10), finv_(MAX + 10), inv_(MAX + 10) {
    assert(T::get_mod() != 0);
    MAX += 9;
    fac_[0] = finv_[0] = inv_[0] = 1;
    for (int i = 1; i <= MAX; i++) fac_[i] = fac_[i - 1] * i;
    finv_[MAX] = fac_[MAX].inverse();
    for (int i = MAX - 1; i > 0; i--) finv_[i] = finv_[i + 1] * (i + 1);
    for (int i = 1; i <= MAX; i++) inv_[i] = finv_[i] * fac_[i - 1];
  }

  void extend() {
    int n = fac_.size();
    T fac = fac_.back() * n;
    T inv = (-inv_[T::get_mod() % n]) * (T::get_mod() / n);
    T finv = finv_.back() * inv;
    fac_.push_back(fac);
    finv_.push_back(finv);
    inv_.push_back(inv);
  }

  T fac(int i) {
    if(i < 0) return T(0);
    while (i >= (int)fac_.size()) extend();
    return fac_[i];
  }

  T finv(int i) {
    if(i < 0) return T(0);
    while (i >= (int)finv_.size()) extend();
    return finv_[i];
  }

  T inv(int i) {
    if(i < 0) return T(0);
    while (i >= (int)inv_.size()) extend();
    return inv_[i];
  }

  T C(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r) * finv(r);
  }

  T C_naive(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    T ret = T(1);
    r = min(r, n - r);
    for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
    return ret;
  }

  T P(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r);
  }

  T H(int n, int r) {
    if (n < 0 || r < 0) return T(0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

//

// given  : f(0)...f(k) (deg(f) = k), a, n
// return : sum_{i=0...n-1} a^i f(i)
template <typename mint>
mint sum_of_exp(const vector<mint>& f, mint a, long long n,
                Binomial<mint>& C) {
  if (n == 0) return mint(0);
  if (a == mint(0)) return f[0];
  if (a == mint(1)) {
    vector<mint> g(f.size() + 1, mint(0));
    for (int i = 1; i < (int)g.size(); i++) g[i] = g[i - 1] + f[i - 1];
    return lagrange_interpolation(g, n, C);
  }
  int K = f.size() - 1;
  vector<mint> g(f.size());
  mint buf = 1;
  for (int i = 0; i < (int)g.size(); i++) g[i] = f[i] * buf, buf *= a;
  for (int i = 1; i < (int)g.size(); i++) g[i] += g[i - 1];
  mint c = 0, buf2 = 1;
  for (int i = 0; i <= K; i++) c += C.C(K + 1, i) * buf2 * g[K - i], buf2 *= -a;
  c /= (-a + 1).pow(K + 1);
  mint buf3 = 1, ia = a.inverse();
  for (int i = 0; i < (int)g.size(); i++) g[i] = (g[i] - c) * buf3, buf3 *= ia;
  mint tn = lagrange_interpolation(g, n - 1, C);
  return tn * a.pow(n - 1) + c;
}

// given  : f(0)...f(k) (deg(f) = k), a
// return : sum_{i=0...infty} a^i f(i)
template <typename mint>
mint sum_of_exp_limit(const vector<mint>& f, mint a, Binomial<mint>& C) {
  if (a == mint(0)) return f[0];
  int K = f.size() - 1;
  vector<mint> g(f.size());
  mint buf = 1;
  for (int i = 0; i < (int)g.size(); i++) g[i] = f[i] * buf, buf *= a;
  for (int i = 1; i < (int)g.size(); i++) g[i] += g[i - 1];
  mint c = 0, buf2 = 1;
  for (int i = 0; i <= K; i++) c += C.C(K + 1, i) * buf2 * g[K - i], buf2 *= -a;
  c /= (-a + 1).pow(K + 1);
  return c;
}

// given  : p, n
// return : (0^p, 1^p, ... , n^p)
template <typename mint>
vector<mint> exp_enamurate(int p, int n) {
  vector<mint> f(n + 1, mint(0));
  if (!p) {
    f[0] = 1;
    return std::move(f);
  }
  f[1] = 1;
  vector<bool> sieve(n + 1, false);
  vector<int> ps;
  for (int i = 2; i <= n; i++) {
    if (!sieve[i]) {
      f[i] = mint(i).pow(p);
      ps.push_back(i);
    }
    for (int j = 0; j < (int)ps.size() && i * ps[j] <= n; j++) {
      sieve[i * ps[j]] = 1;
      f[i * ps[j]] = f[i] * f[ps[j]];
      if (i % ps[j] == 0) break;
    }
  }
  return std::move(f);
}

// given  : d, r, n
// return : sum_{i=0...n-1} r^i i^d
template <typename mint>
mint sum_of_exp2(int d, mint r, long long n, Binomial<mint>& C) {
  vector<mint> f = exp_enamurate<mint>(d, d);
  return sum_of_exp(f, r, n, C);
}

// given  : d, r
// return : sum_{i=0...infty} r^i i^d
template <typename mint>
mint sum_of_exp_limit2(int d, mint r, Binomial<mint>& C) {
  vector<mint> f = exp_enamurate<mint>(d, d);
  return sum_of_exp_limit(f, r, C);
}

/**
 * @brief $\sum_{i}a^i f(i)$
 * @docs docs/fps/sum-of-exponential-times-poly.md
 */

//
using mint = LazyMontgomeryModInt<998244353>;
using vm = vector<mint>;
using vvm = vector<vm>;
using fps = FormalPowerSeries<mint>;
Binomial<mint> C;

using namespace Nyaan;

void Nyaan::solve() {
  ini(N, K);
  vi l(N);
  in(l);
  int L = accumulate(all(l), 0ll);
  mint iL = mint(L).inverse();
  V<fps> P(L + 1);
  P[0] = fps{1};
  rep(i, N) {
    V<fps> nx(L + 1);
    rep(k, l[i] / K + 1) {
      // x ^ k
      int ds = l[i] - k * K;
      if(ds == 0) break;
      mint coe1 = (iL * ds).pow(k) * C.finv(k);
      mint coe2 = (iL * ds).pow(k - 1) * C.finv(k - 1);
      if (k & 1) coe1 = -coe1, coe2 = -coe2;
      trc(k, ds, coe1, coe2);
      rep(s, L + 1) {
        if (s + ds > L) break;
        if (P[s] == fps{}) continue;
        nx[s + ds] += (P[s] << k) * coe1;
        if(k) {
          nx[s + ds] += (P[s] << (k - 1)) * coe2;
        }
      }
    }
    swap(P, nx);
    trc(P);
  }

  assert(P.back() == fps{1});
  P.pop_back();
  each(f, P) f = -f;

  mint ans = 0;
  rep(t, L) rep(s, sz(P[t])) {
    fps f(s + 1);
    rep(i, s + 1) f[i] = C.fac(i + s) * C.finv(i);

    mint soe = sum_of_exp_limit<mint>(f, iL * t, C);
    trc(t, s, P[t][s], soe);
    ans += P[t][s] * sum_of_exp_limit<mint>(f, iL * t, C);
  }
  out(ans);
}


#include <bits/stdc++.h>

#define itn int
#define all(x) (x).begin(), (x).end()
#define make_unique(x) sort(all((x))); (x).resize(unique(all((x))) - (x).begin())

#define random_shuffle(...) shuffle(__VA_ARGS__, rng)
#define rand() rng()

using namespace std;

inline int nxt() {
	int x;
	scanf("%d", &x);
	return x;
}

struct Field {
	int n, m;
	vector<vector<int>> a;
	vector<vector<int>> ans;

	void scan() {
		n = nxt(), m = nxt();
		a.assign(n, vector<int>(m, 0));
		for (int i = 0; i < n; ++i) {
			for (int j = 0; j < m; ++j) {
				a[i][j] = nxt();
			}
		}
	}

	void add(const vector<pair<int, int>>& cyc) {
		ans.push_back({});
		for (auto p : cyc) {
			ans.back().push_back(a[p.first][p.second]);
		}
		assert(cyc.size() >= 4);
		int lst = a[cyc.back().first][cyc.back().second];
		for (int i = (int)cyc.size() - 2; i >= 0; --i) {
			a[cyc[i + 1].first][cyc[i + 1].second] = a[cyc[i].first][cyc[i].second];
			assert(abs(cyc[i].first - cyc[i + 1].first) + abs(cyc[i].second - cyc[i + 1].second) == 1);
		}
		a[cyc[0].first][cyc[0].second] = lst;
		assert(abs(cyc[0].first - cyc.back().first) + abs(cyc[0].second - cyc.back().second) == 1);
	}

	bool check() {
		int cur = 0;
		for (int i = 0; i < n; ++i) {
			for (int j = 0; j < m; ++j) {
				if (++cur != a[i][j]) {
					return false;
				}
			}
		}
		return true;
	}

	void print() {
		printf("%d\n", (int)ans.size());
		for (const auto& v : ans) {
			printf("%d", (int)v.size());
			for (int x : v) {
				printf(" %d", x);
			}
			printf("\n");
		}
	}

	void printState() {
		for (int i = 0; i < n; ++i) {
			for (int j = 0; j < m; ++j) {
				cerr << a[i][j] << " ";
			}
			cerr << "\n";
		}
		cerr << "\n";
	}
};

int main() {
	mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

	Field field;
	field.scan();
	int n = field.n, m = field.m;

	auto moveRight = [&](int x, int y) {
		if (x == n - 1) {
			field.add({{x, y}, {x, y + 1}, {x - 1, y + 1}, {x - 1, y}});
		} else {
			field.add({{x, y}, {x, y + 1}, {x + 1, y + 1}, {x + 1, y}});
		}
	};

	auto moveLeft = [&](int x, int y) {
		if (x == n - 1) {
			field.add({{x, y}, {x, y - 1}, {x - 1, y - 1}, {x - 1, y}});
		} else {
			field.add({{x, y}, {x, y - 1}, {x + 1, y - 1}, {x + 1, y}});
		}
	};

	auto findNeed = [&](int need, int& x, int& y) {
		x = y = 0;
		while (field.a[x][y] != need) {
			++y;
			if (y == m) {
				y = 0;
				++x;
			}
		}
	};

	auto swapHor = [&](int x, int y) {
		// swaps (x, y) and (x, y + 1)
		field.add({{x - 1, y}, {x - 1, y + 1}, {x, y + 1}, {x, y}});
		field.add({{x - 1, y}, {x, y}, {x + 1, y}, {x + 1, y + 1}, {x, y + 1}, {x - 1, y + 1}});
		field.add({{x, y}, {x, y + 1}, {x + 1, y + 1}, {x + 1, y}});
	};

	auto swapVer = [&](int x, int y) {
		// swaps (x, y) and (x + 1, y)
		field.add({{x, y - 1}, {x + 1, y - 1}, {x + 1, y}, {x, y}});
		field.add({{x, y - 1}, {x, y}, {x, y + 1}, {x + 1, y + 1}, {x + 1, y}, {x + 1, y - 1}});
		field.add({{x, y}, {x + 1, y}, {x + 1, y + 1}, {x, y + 1}});
	};

	auto moveGuyUp = [&](int need, int i, int j) {
		int x, y;
		findNeed(need, x, y);
		if (x == i) {
			while (y > j) {
				field.add({{x, y}, {x, y - 1}, {x + 1, y - 1}, {x + 1, y}});
				--y;
			}
			while (y < j) {
				field.add({{x, y}, {x, y + 1}, {x + 1, y + 1}, {x + 1, y}});
				++y;
			}
		} else {
			while (y < j) {
				moveRight(x, y);
				++y;
			}
			while (y > j) {
				moveLeft(x, y);
				--y;
			}
			while (x > i) {
				field.add({{x, y}, {x - 1, y}, {x - 1, y + 1}, {x, y + 1}});
				--x;
			}
		}
	};

	auto& a = field.a;

	for (int i = 0; i < n - 2; ++i) {
		// make one row
		for (int j = 0; j < m - 2; ++j) {
			int need = i * m + j + 1;
			moveGuyUp(need, i, j);
		}

		int need = i * m + m - 1;
		if (a[i][m - 2] == need && a[i][m - 1] == need + 1) {
			// pass;
		} else if (a[i][m - 2] == need + 1 && a[i][m - 1] == need) {
			swapHor(i, m - 2);
		} else if (a[i][m - 2] == need || a[i][m - 1] == need) {
			if (a[i][m - 2] == need) {
				field.add({{i, m - 2}, {i, m - 1}, {i + 1, m - 1}, {i + 1, m - 2}});
			}
			moveGuyUp(need + 1, i + 1, m - 1);
			field.add({{i + 1, m - 1}, {i, m - 1}, {i, m - 2}, {i + 1, m - 2}});
		} else if (a[i][m - 2] == need + 1 || a[i][m - 1] == need + 1) {
			if (a[i][m - 1] == need + 1) {
				field.add({{i, m - 1}, {i, m - 2}, {i + 1, m - 2}, {i + 1, m - 1}});
			}
			moveGuyUp(need, i + 1, m - 2);
			field.add({{i + 1, m - 2}, {i, m - 2}, {i, m - 1}, {i + 1, m - 1}});
		} else {
			moveGuyUp(need + 1, i, m - 2);
			moveGuyUp(need, i + 1, m - 2);
			field.add({{i + 1, m - 2}, {i, m - 2}, {i, m - 1}, {i + 1, m - 1}});
		}
	}

	for (int j = 0; j < m - 2; ++j) {
		int need = (n - 2) * m + j + 1;
		int x, y;
		findNeed(need, x, y);
		if (x != n - 1) {
			assert(x == n - 2);
			if (y > j) {
				field.add({{x, y}, {x + 1, y}, {x + 1, y - 1}, {x, y - 1}});
			} else {
				field.add({{x, y}, {x + 1, y}, {x + 1, y + 1}, {x, y + 1}});
			}
			++x;
		}

		while (y > j) {
			moveLeft(x, y);
			--y;
		}

		if (field.a[n - 2][j] == need + m) {
			for (int _ = 0; _ < 2; ++_) {
				field.add({{n - 2, j}, {n - 2, j + 1}, {n - 1, j + 1}, {n - 1, j}});
			}
			swapVer(n - 2, j + 1);
			for (int _ = 0; _ < 2; ++_) {
				field.add({{n - 2, j}, {n - 2, j + 1}, {n - 1, j + 1}, {n - 1, j}});
			}
		} else {
			findNeed(need + m, x, y);
			if (x != n - 1) {
				assert(x == n - 2);
				if (y > j + 1) {
					field.add({{x, y}, {x + 1, y}, {x + 1, y - 1}, {x, y - 1}});
				} else {
					field.add({{x, y}, {x + 1, y}, {x + 1, y + 1}, {x, y + 1}});
				}
				++x;
			}
			while (y > j + 1) {
				moveLeft(x, y);
				--y;
			}
			field.add({{n - 1, j + 1}, {n - 1, j}, {n - 2, j}, {n - 2, j + 1}});
		}
	}

	while (a[n - 1][m - 1] != n * m) {
		field.add({{n - 2, m - 2}, {n - 2, m - 1}, {n - 1, m - 1}, {n - 1, m - 2}});
	}
	int x, y;
	findNeed(n * m - 1, x, y);
	if (y == m - 1) {
		swapHor(n - 2, m - 2);
		--y;
	}
	if (x == n - 2) {
		swapVer(n - 2, m - 2);
	}
	if (!field.check()) {
		swapHor(n - 2, m - 2);
	}
	assert(field.check());
	// if (!field.check()) {
	// 	field.printState();
	// 	return 0;
	// }
	field.print();

	return 0;
}


#include <algorithm>
#include <iostream>
#include <sstream>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cctype>
#include <cmath>
#include <list>
#include <cassert>
#include <ctime>
#include <climits>
using namespace std;

#define PB push_back
#define MP make_pair
#define SZ(v) ((int)(v).size())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define FORE(i,a,b) for(int i=(a);i<=(b);++i)
#define REPE(i,n) FORE(i,0,n)
#define FORSZ(i,a,v) FOR(i,a,SZ(v))
#define REPSZ(i,v) REP(i,SZ(v))
typedef long long ll;
typedef unsigned long long ull;
ll gcd(ll a,ll b) { return b==0?a:gcd(b,a%b); }

const int MAXF=2;
const int MAXN=1000;
const int MAXM=MAXN-2;
const int MAXTN=MAXN-2;
const int MAXTM=MAXTN-1;
const int MAXRT=MAXN-1+2*MAXM;
const int MAXRTN=10+MAXTN;
const int MAXRTNSUM=MAXF*MAXRT*MAXRTN+2*MAXTN;

typedef struct RT {
	int root,u,v,vv;
} RT;
typedef struct RF {
	int n;
	int par[MAXRTNSUM];
	int chead[MAXRTNSUM];
	int cnxt[MAXRTNSUM];
	int coff[MAXRTNSUM];
	int ccnt[MAXRTNSUM];
	int cidx[MAXRTNSUM];
	int id[MAXRTNSUM];
	int d[MAXRTNSUM];
	int q[MAXRTNSUM],qhead,qtail;
	int orig[MAXRTNSUM];

	RF() { n=0; }
	int addNode(int p,int o) { assert(n<MAXRTNSUM); int ret=n++; par[ret]=p,chead[ret]=-1,cnxt[ret]=-1,orig[ret]=o; if(p!=-1) cnxt[ret]=chead[p],chead[p]=ret; return ret; }
	void print(int at) { printf("("); for(int to=chead[at];to!=-1;to=cnxt[to]) print(to); printf(")"); }

	int cidcmp(const int &a,const int &b) {
		for(int i=0;i<ccnt[a]||i<ccnt[b];++i) {
			if(i>=ccnt[a]) return -1; if(i>=ccnt[b]) return +1;
			int aa=id[cidx[coff[a]+i]],bb=id[cidx[coff[b]+i]]; if(aa!=bb) return aa<bb?-1:+1;
		}
		return 0;
	}
	struct cidless { RF* rf; cidless(RF* rf):rf(rf) {} bool operator()(const int &a,const int &b) { return rf->cidcmp(a,b)<0; } } ;
	vector<int> calcids(vector<RT> t) {
		int nt=SZ(t); //bool dbg=true;
		qhead=qtail=0; REP(i,nt) { int at=t[i].root; d[at]=0,q[qhead++]=at; }
		while(qtail<qhead) { int at=q[qtail++]; for(int to=chead[at];to!=-1;to=cnxt[to]) d[to]=d[at]+1,q[qhead++]=to; } int nq=qtail;
		int nc=0; REP(i,nq) { int at=q[i]; coff[at]=nc,ccnt[at]=0; for(int to=chead[at];to!=-1;to=cnxt[to]) ++ccnt[at],++nc; }
		int dmx=d[q[nq-1]];
		//if(dbg) printf("nq=%d dmx=%d\n",nq,dmx);
		int c=nq,b=nq,a=nq;
		while(a>0&&d[q[a-1]]==dmx) --a;
		FOR(i,a,b) { int at=q[i]; id[at]=0; }
		for(int cd=dmx-1;cd>=0;--cd) {
			c=b,b=a; while(a>0&&d[q[a-1]]==cd) --a; //if(dbg) printf("\t%d..%d..%d\n",a,b,c);
			FOR(i,b,c) { int at=q[i]; cidx[coff[par[at]]++]=at; }
			FOR(i,a,b) { int at=q[i]; for(int to=chead[at];to!=-1;to=cnxt[to]) --coff[at]; }
			sort(q+a,q+b,cidless(this));
			FOR(i,a,b) { int at=q[i]; id[at]=i==a?0:id[q[i-1]]+(cidcmp(at,q[i-1])==0?0:1); }
			//FOR(i,a,b) { int at=q[i]; printf("%d = [",at); REP(j,ccnt[at]) printf("%d%c",id[cidx[coff[at]+j]],j+1<ccnt[at]?',':']'); if(ccnt[at]==0) printf("]"); printf(" ->  %d\n",id[at]); }
		}
		vector<int> ret(nt,-1); REP(i,nt) ret[i]=id[t[i].root]; return ret;
	}
} RF;
RF rf;

//bool dbg=false;
typedef struct T {
	int n,m,root;
	int ghead[MAXTN],gnxt[2*MAXTM],gto[2*MAXTM];
	int orig[MAXTN];
	int d1[MAXTN],d2[MAXTN],d3[MAXTN];
	int q[MAXTN],qhead,qtail;

	void init(int o) { n=1,m=0; root=0; ghead[0]=-1,orig[0]=o; }
	int addNode(int p,int o) { assert(n<MAXTN); int ret=n++; ghead[ret]=-1,orig[ret]=o; if(p!=-1) { gnxt[m]=ghead[ret],ghead[ret]=m,gto[m]=p,++m; gnxt[m]=ghead[p],ghead[p]=m,gto[m]=ret,++m; }  return ret; }
	vector<int> calcCenters(int rt) {
		REP(i,n) d1[i]=INT_MAX; qhead=qtail=0; d1[rt]=0,q[qhead++]=rt;
		while(qtail<qhead) { int at=q[qtail++]; for(int x=ghead[at];x!=-1;x=gnxt[x]) { int to=gto[x]; if(d1[to]!=INT_MAX) continue; d1[to]=d1[at]+1; q[qhead++]=to; } }
		int u=rt; REP(i,n) if(d1[i]!=INT_MAX&&d1[i]>d1[u]) u=i;
		//if(dbg) { REP(i,n) printf("%d=%d ",orig[i],d1[i]); printf("-> %d\n",orig[u]); }
		REP(i,n) d2[i]=INT_MAX; qhead=qtail=0; d2[u]=0,q[qhead++]=u;
		while(qtail<qhead) { int at=q[qtail++]; for(int x=ghead[at];x!=-1;x=gnxt[x]) { int to=gto[x]; if(d2[to]!=INT_MAX) continue; d2[to]=d2[at]+1; q[qhead++]=to; } }
		int v=u; REP(i,n) if(d2[i]!=INT_MAX&&d2[i]>d2[v]) v=i;
		//if(dbg) { REP(i,n) printf("%d=%d ",orig[i],d2[i]); printf("-> %d\n",orig[v]); }
		REP(i,n) d3[i]=INT_MAX; qhead=qtail=0; d3[v]=0,q[qhead++]=v;
		while(qtail<qhead) { int at=q[qtail++]; for(int x=ghead[at];x!=-1;x=gnxt[x]) { int to=gto[x]; if(d3[to]!=INT_MAX) continue; d3[to]=d3[at]+1; q[qhead++]=to; } }
		int w=v; REP(i,n) if(d3[i]!=INT_MAX&&d3[i]>d3[w]) w=i;
		//if(dbg) { REP(i,n) printf("%d=%d ",orig[i],d3[i]); printf("-> %d\n",orig[w]); }
		vector<int> ret; REP(i,n) if(d2[i]+d3[i]==d2[v]&&d2[v]-1<=2*d2[i]&&2*d2[i]<=d2[v]+1) ret.PB(i); return ret;
	}
	void appendTo(int at,int par,int idx) {
		for(int x=ghead[at];x!=-1;x=gnxt[x]) { int to=gto[x]; if(to==par) continue; int nidx=rf.addNode(idx,orig[to]); appendTo(to,at,nidx); }
	}
} T;
T t;

typedef struct F {
	int n,m;
	vector<vector<int> > adj;

	void input(int _n) { n=_n; adj=vector<vector<int> >(n,vector<int>()); scanf("%d",&m); REP(i,m) { int a,b; scanf("%d%d",&a,&b); --a,--b; adj[a].PB(b); adj[b].PB(a); } }
	void buildTree(int at,vector<bool> &done,int idx) {
		done[at]=true; REPSZ(i,adj[at]) { int to=adj[at][i]; if(done[to]) continue; int nidx=t.addNode(idx,to); buildTree(to,done,nidx); }
	}
	// ( ((u+)) ((uv)()) ((v+)()()) )
	RT createCanonical(int u,int v,int vv,bool swp) {
		//dbg=false; if(!swp&&u==3&&v==4&&vv==2) dbg=true; if(swp&u==4&&v==3&&vv==1) dbg=true;
		RT ret; ret.u=u; ret.v=v; ret.vv=vv; ret.root=rf.addNode(-1,-1);
		int rt=ret.root,a=rf.addNode(rt,-1),b=rf.addNode(rt,-1),c=rf.addNode(rt,-1);
		a=rf.addNode(a,-1); rf.addNode(b,-1),b=rf.addNode(b,-1); rf.addNode(c,-1),rf.addNode(c,-1),c=rf.addNode(c,-1);
		vector<bool> done(n,false); done[u]=true; done[v]=true;
		REPSZ(i,adj[v]) {
			//if(swp&&u==0&&v==3&&vv==2) printf("building %d\n",adj[v][i]);
			t.init(adj[v][i]); buildTree(adj[v][i],done,t.root);
			vector<int> centers=t.calcCenters(t.root);
			//if(swp&&u==0&&v==3&&vv==2) { REPSZ(j,centers) printf("\t%d\n",t->orig[centers[j]]); }
			int par=adj[v][i]==vv?b:swp?a:c,bj=0;
			FORSZ(j,1,centers) {
				int on=rf.n;
				RT a; a.root=rf.addNode(-1,centers[bj]); t.appendTo(centers[bj],-1,a.root);
				RT b; b.root=rf.addNode(-1,centers[j]); t.appendTo(centers[j],-1,b.root);
				vector<RT> c; c.PB(a); c.PB(b); vector<int> id=rf.calcids(c); if(id[1]<id[0]) bj=j;
				rf.n=on;
			}
			{ int ridx=rf.addNode(par,t.orig[centers[bj]]); t.appendTo(centers[bj],-1,ridx); }
		}
		REP(i,n) if(!done[i]) {
			//if(!swp&&u==3&&v==0&&vv==1) printf("building %d\n",i);
			t.init(i); buildTree(i,done,t.root);
			vector<int> centers=t.calcCenters(t.root);
			int par=swp?c:a,bj=0;
			FORSZ(j,1,centers) {
				int on=rf.n;
				RT a; a.root=rf.addNode(-1,centers[bj]); t.appendTo(centers[bj],-1,a.root);
				RT b; b.root=rf.addNode(-1,centers[j]); t.appendTo(centers[j],-1,b.root);
				vector<RT> c; c.PB(a); c.PB(b); vector<int> id=rf.calcids(c); if(id[1]<id[0]) bj=j;
				rf.n=on;
			}
			{ int ridx=rf.addNode(par,t.orig[centers[bj]]); t.appendTo(centers[bj],-1,ridx); }
		}
		return ret;
	}
	vector<RT> createAll(bool swp) {
		int u=-1; REP(i,n) if(SZ(adj[i])==0) { u=i; break; } assert(u!=-1);
		vector<RT> ret; ret.reserve(n-1+2*m);
		REP(v,n) if(v!=u) {
			//if(!swp&&(u!=8||v!=3)) continue;
			//if(swp&&(u!=1||v!=5)) continue;
			ret.PB(createCanonical(u,v,-1,swp));
			REPSZ(i,adj[v]) ret.PB(createCanonical(u,v,adj[v][i],swp));
		}
		return ret;
	}
	void print(RT a,RT b,F &fb) {
		queue<pair<int,int> > q; q.push(MP(a.root,b.root));
		vector<int> ab(n,-1),ba(n,-1); ab[a.u]=b.v,ba[b.v]=a.u; ab[a.v]=b.u,ba[b.u]=a.v;
		while(!q.empty()) {
			int ai=q.front().first,bi=q.front().second; q.pop(); //printf("%d=%d\n",ai,bi); if(ai==0&&bi==0) exit(1);
			if(rf.orig[ai]!=-1&&rf.orig[bi]!=-1) ab[rf.orig[ai]]=rf.orig[bi],ba[rf.orig[bi]]=rf.orig[ai];
			REP(k,rf.ccnt[ai]) q.push(MP(rf.cidx[rf.coff[ai]+k],rf.cidx[rf.coff[bi]+k]));
		}
		//REP(i,n) printf("%d->%d\n",i,ab[i]);
		//REP(i,n) printf("%d<-%d\n",ba[i],i);
		REP(i,n) REPSZ(j,adj[i]) if(i<adj[i][j]) printf("%d %d\n",i+1,adj[i][j]+1);
		int x=ab[a.u]; REPSZ(j,fb.adj[x]) { int y=fb.adj[x][j]; printf("%d %d\n",a.u+1,ba[y]+1); }
		if(a.vv==-1) printf("%d %d\n",a.u+1,a.v+1);
	}
} F;

int n,nf;
F f[2];

void input() {
	scanf("%d%d",&n,&nf);
	REP(i,nf) f[i].input(n);
}

bool solve() {
	vector<RT> a=f[0].createAll(false);
	vector<RT> b=f[1].createAll(true);
	vector<RT> c; REPSZ(i,a) c.PB(a[i]); REPSZ(i,b) c.PB(b[i]);
	vector<int> id=rf.calcids(c);
	//REPSZ(i,c) { printf("%d %2d (%d,%d,%2d): ",i<SZ(a)?0:1,i<SZ(a)?i:i-SZ(a),c[i].u,c[i].v,c[i].vv); rf.print(c[i].root); printf(" = %d\n",id[i]); }
	map<int,int> mp; REPSZ(i,a) if(mp.count(id[i])==0) mp[id[i]]=i;
	REPSZ(j,b) if(mp.count(id[SZ(a)+j])) {
		int i=mp[id[SZ(a)+j]]; //printf("a%d with b%d\n",i,j);
		printf("YES\n");
		f[0].print(a[i],b[j],f[1]);
		rf.n=0;
		return true;
	}
	rf.n=0;
	printf("NO\n"); return false;
}

void run() {
	input();
	solve();
}

void test() {
	while(true) {
		int n=1000;
		vector<int> par(n,-1);
		FOR(i,1,n) par[i]=rand()%i;
		int u=rand()%n,v=rand()%(n-1); if(v>=u) ++v;
		REP(i,2) {
			f[i].n=n;
			f[i].adj=vector<vector<int> >(n);
		}
		FOR(j,1,n) {
			if(j!=u&&par[j]!=u) f[0].adj[j].PB(par[j]),f[0].adj[par[j]].PB(j);
			if(j!=v&&par[j]!=v) f[1].adj[j].PB(par[j]),f[1].adj[par[j]].PB(j);
		}
		if(!solve()) {
			printf("1\n");
			printf("%d %d\n",n,2);
			REP(i,2) {
				int m=0; REP(j,n) REPSZ(k,f[i].adj[j]) if(j<f[i].adj[j][k]) ++m;
				printf("%d\n",m); REP(j,n) REPSZ(k,f[i].adj[j]) if(j<f[i].adj[j][k]) printf("%d %d\n",j+1,f[i].adj[j][k]+1);
			}
			break;
		}
	}
}

int main() {
	int n; scanf("%d",&n); FORE(i,1,n) run();
	//printf("%d\n",MAXRTNSUM); test();
	return 0;
}


#ifndef BZ
#pragma GCC optimize "-O3"
#endif

#include <bits/stdc++.h>

#define FASTIO

#ifdef FASTIO
#define scanf abacaba
#define printf abacaba
#endif

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

using namespace std;
using bb = bitset<C>;

const int C2 = 19;
const int C = 9 * 20 + 1;

vector<bb> vv;
unordered_set<bb> mapa1, mapa2;

bool cmp(const bb &a, const bb &b){
	for (int i = 0; i < 9 * 20; ++i){
		if (a[i] < b[i])
			return 1;
		if (b[i] < a[i])
			return 0;
	}
	return 0;
}

unordered_map<bb, int> mm;

int upd(int x, int j){
	bb cur = (vv[x] << j) | (vv[x] >> j);
	for (int k = 0; k < j; ++k)
		if (vv[x][k])
			cur[j - k] = 1;
	auto it = mm.find(cur);
	if (it == mm.end())
		return -1;
	return it->second;
}
const int MX = 50000;

int go[MX][10];
ll dp[MX][10][20];
int nl;

ll get(ll x, int k) {
	vector<int> dg;
	for (int i = 0; i < C2; ++i)
		dg.push_back(x % 10), x /= 10;
	ll ans = 0;
	ll cur = nl;
	for (int i = C2 - 1; i >= 0; --i){
		for (int j = 0; j < dg[i]; ++j){
			ll tmp = go[cur][j];
			ans += dp[tmp][k][i];
		}
		cur = go[cur][dg[i]];
	}
	return ans;
}

int av[MX][10];

int main() {
	#ifdef FASTIO
		ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	#endif
	bb tmp;
	tmp[0] = 1;
	mapa1.insert(tmp);
	for (int i = 0; i < C2; ++i){
		mapa2.clear();
		for (auto msk: mapa1){
			for (int j = 0; j <= 9; ++j){
				bb cur = (msk << j) | (msk >> j);
				for (int k = 0; k < j; ++k)
					if (msk[k])
						cur[j - k] = 1;
				mapa2.insert(cur);
			}
		}
		mapa1 = mapa2;
	}
	for (auto x: mapa1)
		vv.push_back(x);
	sort(vv.begin(), vv.end(), cmp);
	for (int i = 0; i < vv.size(); ++i)
		mm[vv[i]] = i;
	nl = mm[tmp];
	av[nl][0] = 1;
	for (int i = 0; i < vv.size(); ++i){
		go[i][0] = i;
		for (int j = 1; j <= 9; ++j){
			go[i][j] = upd(i, j);
		}
		for (int j = 0; j <= 9; ++j)
			if (vv[i][j])
				av[i][j] = 1;
	}
	for (int i = vv.size() - 1; i >= 0; --i){
		int x = 0;
		while (!av[i][x]) {
			++x;
		}
		for (int j = x; j <= 9; ++j)
			dp[i][j][0] = 1;
	}
	for (int ad = 1; ad <= C2; ++ad){
		for (int i = 0; i < vv.size(); ++i){
			for (int j = 0; j <= 9; ++j){
				if (go[i][j] == -1)
					continue;
				for (int k = 0; k <= 9; ++k){
					dp[i][k][ad] += dp[go[i][j]][k][ad - 1];
				}
			}
		}
	}
	int n;
	cin >> n;
	for (int i = 0; i < n; ++i){
		ll l, r;
		int k;
		cin >> l >> r >> k;
		cout << get(r + 1, k) - get(l, k) << "\n";
	}
	return 0;
}


#pragma GCC optimize("Ofast", "unroll-loops", "no-stack-protector")

#include <bits/stdc++.h>

using namespace std;

#define all(a) (a).begin(), (a).end()
#define sz(a) (int)(a).size()

using ll = long long;
using ld = long double;
// using ld = __float128;
using pii = pair<int, int>;
using uint = unsigned int;
using ull = unsigned long long;

mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
default_random_engine generator;

void solve();

int main() {
#ifdef LOCAL
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
#endif

    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cout << setprecision(15) << fixed;
    cerr << setprecision(15) << fixed;

    int tests = 1;
    // cin >> tests;

    for (int test = 1; test <= tests; ++test) {
        // cout << "Case #" << test << ": ";
        solve();
    }

#ifdef LOCAL
    cerr << "Time: " << double(clock()) / CLOCKS_PER_SEC << endl;
#endif
}

// -----------------------------------------------------------------

const int MAXN = 3030;

ll pref[MAXN][MAXN];
ll suff[MAXN][MAXN];

void solve() {
    int n, k;
    cin >> n >> k;
    vector<vector<int>> a(n);
    for (int i = 0; i < n; ++i) {
        int m;
        cin >> m;
        a[i].resize(m);
        for (int &x : a[i]) {
            cin >> x;
        }
    }

    for (int i = 0; i <= k; ++i) {
        pref[0][i] = -1;
    }
    pref[0][0] = 0;

    for (int i = 0; i < n; ++i) {
        ll sum = 0;
        for (int x : a[i]) {
            sum += x;
        }
        for(int j = 0; j <= k; ++j) {
            pref[i + 1][j] = pref[i][j];
        }
        for (int j = 0; j + sz(a[i]) <= k; ++j) {
            if (pref[i][j] == -1) {
                continue;
            }
            pref[i + 1][j + sz(a[i])] = max(pref[i + 1][j + sz(a[i])], pref[i][j] + sum);
        }
    }

    for (int i = 0; i <= k; ++i) {
        suff[n][i] = -1;
    }
    suff[n][0] = 0;

    for (int i = n - 1; i >= 0; --i) {
        ll sum = 0;
        for (int x : a[i]) {
            sum += x;
        }
        for(int j = 0; j <= k; ++j) {
            suff[i][j] = suff[i + 1][j];
        }
        for (int j = 0; j + sz(a[i]) <= k; ++j) {
            if (suff[i + 1][j] == -1) {
                continue;
            }
            suff[i][j + sz(a[i])] = max(suff[i][j + sz(a[i])], suff[i + 1][j] + sum);
        }
    }

    vector<vector<pair<ll, int>>> arr(k + 1);
    for (int i = 0; i < n; ++i) {
        ll sum = 0;
        for (int j = 0; j < sz(a[i]); ++j) {
            sum += a[i][j];
            arr[j + 1].push_back({sum, i});
        }
    }

    ll res = pref[n][k];
    for (int i = 1; i <= k; ++i) {
        sort(all(arr[i]), greater());
        arr[i].resize(min(sz(arr[i]), k / i + 1));

        for (auto [s, p] : arr[i]) {
            for (int j = 0; j <= k - i; ++j) {
                if (pref[p][j] == -1 || suff[p + 1][k - i - j] == -1) {
                    continue;
                }
                res = max(res, pref[p][j] + suff[p + 1][k - i - j] + s);
            }
        }
    }

    cout << res << endl;

}


#include <bits/stdc++.h>

using namespace std;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define all(x) (x).begin (),(x).end()
#define sqrt(x) sqrt(abs(x))
#define re return
#define sz(x) ((int)(x.size()))

using ll = long long;
using ii = pair<int, int>;
using ld = long double;
using D = double;
using vi = vector<int>;
using vii = vector<ii>;
using vvi = vector<vi>;
using vs = vector<string>;

template<typename T> T abs (T x) { re x < 0 ? -x : x; }
template<typename T> T sgn (T x) { re x < 0 ? -1 : (x > 0 ? 1 : 0); }
template<typename T> T sqr (T x) { re x * x; }
template<typename T> T gcd (T a, T b) { re a ? gcd (b % a, a) : b; }

int n;
int m;

double p[20];
double res[1 << 20];
double q[20];

int main () {
	scanf ("%d%d", &n, &m);
	for (int i = 0; i < n; i++) scanf ("%lf", &p[i]);
	for (int i = 0; i < n; i++) res[1 << i] = p[i];
	for (int i = 0; i < n; i++) q[i] = 0;
	for (int i = 1; i < (1 << n); i++) {
		vi v, w;
		double sum = 0;
		for (int j = 0; j < n; j++)
			if ((i >> j) & 1)
				v.pb (j);
			else {
				w.pb (j);
				sum += p[j];
			}
		if (sz (v) == m || (sz (v) < m && sum < 1e-5)) {
			for (auto x : v) q[x] += res[i];
		} else
		if (sz (v) < m) {
			for (auto x : w) res[i | (1 << x)] += res[i] * p[x] / sum;
		}
	}
	for (int i = 0; i < n; i++) printf ("%.15f ", q[i]);
	printf ("\n");
	return 0;
}