Question:
You are given two arrays of integers a_1, a_2, …, a_n and b_1, b_2, …, b_m.

You need to insert all elements of b into a in an arbitrary way. As a result you will get an array c_1, c_2, …, c_{n+m} of size n + m.

Note that you are not allowed to change the order of elements in a, while you can insert elements of b at arbitrary positions. They can be inserted at the beginning, between any elements of a, or at the end. Moreover, elements of b can appear in the resulting array in any order.

What is the minimum possible number of inversions in the resulting array c? Recall that an inversion is a pair of indices (i, j) such that i < j and c_i > c_j.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows.

The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 10^6).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).

The third line of each test case contains m integers b_1, b_2, …, b_m (1 ≤ b_i ≤ 10^9).

It is guaranteed that the sum of n for all tests cases in one input doesn't exceed 10^6. The sum of m for all tests cases doesn't exceed 10^6 as well.

Output

For each test case, print one integer — the minimum possible number of inversions in the resulting array c.

Example

Input

3
3 4
1 2 3
4 3 2 1
3 3
3 2 1
1 2 3
5 4
1 3 5 3 1
4 3 6 1

Output

0
4
6

Note

Below is given the solution to get the optimal answer for each of the example test cases (elements of a are underscored).

  * In the first test case, c = [\underline{1}, 1, \underline{2}, 2, \underline{3}, 3, 4].
  * In the second test case, c = [1, 2, \underline{3}, \underline{2}, \underline{1}, 3].
  * In the third test case, c = [\underline{1}, 1, 3, \underline{3}, \underline{5}, \underline{3}, \underline{1}, 4, 6].


Question:
A group of n alpinists has just reached the foot of the mountain. The initial difficulty of climbing this mountain can be described as an integer d.

Each alpinist can be described by two integers s and a, where s is his skill of climbing mountains and a is his neatness.

An alpinist of skill level s is able to climb a mountain of difficulty p only if p ≤ s. As an alpinist climbs a mountain, they affect the path and thus may change mountain difficulty. Specifically, if an alpinist of neatness a climbs a mountain of difficulty p the difficulty of this mountain becomes max(p, a).

Alpinists will climb the mountain one by one. And before the start, they wonder, what is the maximum number of alpinists who will be able to climb the mountain if they choose the right order. As you are the only person in the group who does programming, you are to answer the question.

Note that after the order is chosen, each alpinist who can climb the mountain, must climb the mountain at that time.

Input

The first line contains two integers n and d (1 ≤ n ≤ 500 000; 0 ≤ d ≤ 10^9) — the number of alpinists and the initial difficulty of the mountain.

Each of the next n lines contains two integers s_i and a_i (0 ≤ s_i, a_i ≤ 10^9) that define the skill of climbing and the neatness of the i-th alpinist.

Output

Print one integer equal to the maximum number of alpinists who can climb the mountain if they choose the right order to do so.

Examples

Input

3 2
2 6
3 5
5 7

Output

2

Input

3 3
2 4
6 4
4 6

Output

2

Input

5 0
1 5
4 8
2 7
7 6
3 2

Output

3

Note

In the first example, alpinists 2 and 3 can climb the mountain if they go in this order. There is no other way to achieve the answer of 2.

In the second example, alpinist 1 is not able to climb because of the initial difficulty of the mountain, while alpinists 2 and 3 can go up in any order.

In the third example, the mountain can be climbed by alpinists 5, 3 and 4 in this particular order. There is no other way to achieve optimal answer.


Question:
Students of one unknown college don't have PE courses. That's why q of them decided to visit a gym nearby by themselves. The gym is open for n days and has a ticket system. At the i-th day, the cost of one ticket is equal to a_i. You are free to buy more than one ticket per day.

You can activate a ticket purchased at day i either at day i or any day later. Each activated ticket is valid only for k days. In other words, if you activate ticket at day t, it will be valid only at days t, t + 1, ..., t + k - 1.

You know that the j-th student wants to visit the gym at each day from l_j to r_j inclusive. Each student will use the following strategy of visiting the gym at any day i (l_j ≤ i ≤ r_j):

  1. person comes to a desk selling tickets placed near the entrance and buy several tickets with cost a_i apiece (possibly, zero tickets);
  2. if the person has at least one activated and still valid ticket, they just go in. Otherwise, they activate one of tickets purchased today or earlier and go in.

Note that each student will visit gym only starting l_j, so each student has to buy at least one ticket at day l_j.

Help students to calculate the minimum amount of money they have to spend in order to go to the gym.

Input

The first line contains three integers n, q and k (1 ≤ n, q ≤ 300 000; 1 ≤ k ≤ n) — the number of days, the number of students and the number of days each ticket is still valid.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the cost of one ticket at the corresponding day.

Each of the next q lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n) — the segment of days the corresponding student want to visit the gym.

Output

For each student, print the minimum possible amount of money they have to spend in order to go to the gym at desired days.

Example

Input

7 5 2
2 15 6 3 7 5 6
1 2
3 7
5 5
7 7
3 5

Output

2
12
7
6
9

Note

Let's see how each student have to spend their money:

  * The first student should buy one ticket at day 1.
  * The second student should buy one ticket at day 3 and two tickets at day 4. Note that student can keep purchased tickets for the next days.
  * The third student should buy one ticket at day 5.
  * The fourth student should buy one ticket at day 7.
  * The fifth student should buy one ticket at day 3 and one at day 4.


Question:
Integers from 1 to n (inclusive) were sorted lexicographically (considering integers as strings). As a result, array a_1, a_2, ..., a_n was obtained.

Calculate value of (∑_{i = 1}^n ((i - a_i) mod 998244353)) mod 10^9 + 7.

x mod y here means the remainder after division x by y. This remainder is always non-negative and doesn't exceed y - 1. For example, 5 mod 3 = 2, (-1) mod 6 = 5.

Input

The first line contains the single integer n (1 ≤ n ≤ 10^{12}).

Output

Print one integer — the required sum.

Examples

Input

3

Output

0

Input

12

Output

994733045

Input

21

Output

978932159

Input

1000000000000

Output

289817887

Note

A string a is lexicographically smaller than a string b if and only if one of the following holds:

  * a is a prefix of b, but a ≠ b;
  * in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.

For example, 42 is lexicographically smaller than 6, because they differ in the first digit, and 4 < 6; 42 < 420, because 42 is a prefix of 420.

Let's denote 998244353 as M.

In the first example, array a is equal to [1, 2, 3].

  * (1 - 1) mod M = 0 mod M = 0
  * (2 - 2) mod M = 0 mod M = 0
  * (3 - 3) mod M = 0 mod M = 0

As a result, (0 + 0 + 0) mod 10^9 + 7 = 0

In the second example, array a is equal to [1, 10, 11, 12, 2, 3, 4, 5, 6, 7, 8, 9].

  * (1 - 1) mod M = 0 mod M = 0
  * (2 - 10) mod M = (-8) mod M = 998244345
  * (3 - 11) mod M = (-8) mod M = 998244345
  * (4 - 12) mod M = (-8) mod M = 998244345
  * (5 - 2) mod M = 3 mod M = 3
  * (6 - 3) mod M = 3 mod M = 3
  * (7 - 4) mod M = 3 mod M = 3
  * (8 - 5) mod M = 3 mod M = 3
  * (9 - 6) mod M = 3 mod M = 3
  * (10 - 7) mod M = 3 mod M = 3
  * (11 - 8) mod M = 3 mod M = 3
  * (12 - 9) mod M = 3 mod M = 3

As a result, (0 + 998244345 + 998244345 + 998244345 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3) mod 10^9 + 7 = 2994733059 mod 10^9 + 7 = 994733045


Question:
For two positive integers l and r (l ≤ r) let c(l, r) denote the number of integer pairs (i, j) such that l ≤ i ≤ j ≤ r and \operatorname{gcd}(i, j) ≥ l. Here, \operatorname{gcd}(i, j) is the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers i and j.

YouKn0wWho has two integers n and k where 1 ≤ k ≤ n. Let f(n, k) denote the minimum of ∑_{i=1}^{k}{c(x_i+1,x_{i+1})} over all integer sequences 0=x_1 < x_2 < … < x_{k} < x_{k+1}=n.

Help YouKn0wWho find f(n, k).

Input

The first line contains a single integer t (1 ≤ t ≤ 3 ⋅ 10^5) — the number of test cases.

The first and only line of each test case contains two integers n and k (1 ≤ k ≤ n ≤ 10^5).

Output

For each test case, print a single integer — f(n, k).

Example

Input

4
6 2
4 4
3 1
10 3

Output

8
4
6
11

Note

In the first test case, YouKn0wWho can select the sequence [0, 2, 6]. So f(6, 2) = c(1, 2) + c(3, 6) = 3 + 5 = 8 which is the minimum possible.


Question:
A sequence of integers b_1, b_2, …, b_m is called good if max(b_1, b_2, …, b_m) ⋅ min(b_1, b_2, …, b_m) ≥ b_1 + b_2 + … + b_m.

A sequence of integers a_1, a_2, …, a_n is called perfect if every non-empty subsequence of a is good.

YouKn0wWho has two integers n and M, M is prime. Help him find the number, modulo M, of perfect sequences a_1, a_2, …, a_n such that 1 ≤ a_i ≤ n + 1 for each integer i from 1 to n.

A sequence d is a subsequence of a sequence c if d can be obtained from c by deletion of several (possibly, zero or all) elements.

Input

The first and only line of the input contains two space-separated integers n and M (1 ≤ n ≤ 200; 10^8 ≤ M ≤ 10^9). It is guaranteed that M is prime.

Output

Print a single integer — the number of perfect sequences modulo M.

Examples

Input

2 998244353

Output

4

Input

4 100000007

Output

32

Input

69 999999937

Output

456886663

Note

In the first test case, the perfect sequences are [2, 2], [2, 3], [3, 2] and [3, 3].

In the second test case, some of the perfect sequences are [3, 4, 3, 5], [4, 5, 4, 4], [4, 5, 5, 5] etc. One example of a sequence which is not perfect is [2, 3, 3, 4], because, for example, the subsequence [2, 3, 4] is not an good as 2 ⋅ 4 < 2 + 3 + 4.


Question:
It was October 18, 2017. Shohag, a melancholic soul, made a strong determination that he will pursue Competitive Programming seriously, by heart, because he found it fascinating. Fast forward to 4 years, he is happy that he took this road. He is now creating a contest on Codeforces. He found an astounding problem but has no idea how to solve this. Help him to solve the final problem of the round.

You are given three integers n, k and x. Find the number, modulo 998 244 353, of integer sequences a_1, a_2, …, a_n such that the following conditions are satisfied:

  * 0 ≤ a_i < 2^k for each integer i from 1 to n.
  * There is no non-empty subsequence in a such that the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of the elements of the subsequence is x.

A sequence b is a subsequence of a sequence c if b can be obtained from c by deletion of several (possibly, zero or all) elements.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

The first and only line of each test case contains three space-separated integers n, k, and x (1 ≤ n ≤ 10^9, 0 ≤ k ≤ 10^7, 0 ≤ x < 2^{\operatorname{min}(20, k)}).

It is guaranteed that the sum of k over all test cases does not exceed 5 ⋅ 10^7.

Output

For each test case, print a single integer — the answer to the problem.

Example

Input

6
2 2 0
2 1 1
3 2 3
69 69 69
2017 10 18
5 7 0

Output

6
1
15
699496932
892852568
713939942

Note

In the first test case, the valid sequences are [1, 2], [1, 3], [2, 1], [2, 3], [3, 1] and [3, 2].

In the second test case, the only valid sequence is [0, 0].


Question:
Shohag has an integer sequence a_1, a_2, …, a_n. He can perform the following operation any number of times (possibly, zero):

  * Select any positive integer k (it can be different in different operations).
  * Choose any position in the sequence (possibly the beginning or end of the sequence, or in between any two elements) and insert k into the sequence at this position.
  * This way, the sequence a changes, and the next operation is performed on this changed sequence.

For example, if a=[3,3,4] and he selects k = 2, then after the operation he can obtain one of the sequences [\underline{2},3,3,4], [3,\underline{2},3,4], [3,3,\underline{2},4], or [3,3,4,\underline{2}].

Shohag wants this sequence to satisfy the following condition: for each 1 ≤ i ≤ |a|, a_i ≤ i. Here, |a| denotes the size of a.

Help him to find the minimum number of operations that he has to perform to achieve this goal. We can show that under the constraints of the problem it's always possible to achieve this goal in a finite number of operations.

Input

The first line contains a single integer t (1 ≤ t ≤ 200) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100) — the initial length of the sequence.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the elements of the sequence.

Output

For each test case, print a single integer — the minimum number of operations needed to perform to achieve the goal mentioned in the statement.

Example

Input

4
3
1 3 4
5
1 2 5 7 4
1
1
3
69 6969 696969

Output

1
3
0
696966

Note

In the first test case, we have to perform at least one operation, as a_2=3>2. We can perform the operation [1, 3, 4] → [1, \underline{2}, 3, 4] (the newly inserted element is underlined), now the condition is satisfied.

In the second test case, Shohag can perform the following operations:

[1, 2, 5, 7, 4] → [1, 2, \underline{3}, 5, 7, 4] → [1, 2, 3, \underline{4}, 5, 7, 4] → [1, 2, 3, 4, 5, \underline{3}, 7, 4].

In the third test case, the sequence already satisfies the condition.


Question:
YouKn0wWho has an integer sequence a_1, a_2, … a_n. Now he will split the sequence a into one or more consecutive subarrays so that each element of a belongs to exactly one subarray. Let k be the number of resulting subarrays, and h_1, h_2, …, h_k be the lengths of the longest increasing subsequences of corresponding subarrays.

For example, if we split [2, 5, 3, 1, 4, 3, 2, 2, 5, 1] into [2, 5, 3, 1, 4], [3, 2, 2, 5], [1], then h = [3, 2, 1].

YouKn0wWho wonders if it is possible to split the sequence a in such a way that the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of h_1, h_2, …, h_k is equal to 0. You have to tell whether it is possible.

The longest increasing subsequence (LIS) of a sequence b_1, b_2, …, b_m is the longest sequence of valid indices i_1, i_2, …, i_k such that i_1 < i_2 < … < i_k and b_{i_1} < b_{i_2} < … < b_{i_k}. For example, the LIS of [2, 5, 3, 3, 5] is [2, 3, 5], which has length 3.

An array c is a subarray of an array b if c can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print "YES" (without quotes) if it is possible to split into subarrays in the desired way, print "NO" (without quotes) otherwise. You can print each letter in any register (upper or lower).

Example

Input

4
7
1 3 4 2 2 1 5
3
1 3 4
5
1 3 2 4 2
4
4 3 2 1

Output

YES
NO
YES
YES

Note

In the first test case, YouKn0wWho can split the sequence in the following way: [1, 3, 4], [2, 2], [1, 5]. This way, the LIS lengths are h = [3, 1, 2], and the bitwise XOR of the LIS lengths is 3 ⊕ 1 ⊕ 2 = 0.

In the second test case, it can be shown that it is impossible to split the sequence into subarrays that will satisfy the condition.


Question:
YouKn0wWho has an integer sequence a_1, a_2, …, a_n. He will perform the following operation until the sequence becomes empty: select an index i such that 1 ≤ i ≤ |a| and a_i is not divisible by (i + 1), and erase this element from the sequence. Here |a| is the length of sequence a at the moment of operation. Note that the sequence a changes and the next operation is performed on this changed sequence.

For example, if a=[3,5,4,5], then he can select i = 2, because a_2 = 5 is not divisible by i+1 = 3. After this operation the sequence is [3,4,5].

Help YouKn0wWho determine if it is possible to erase the whole sequence using the aforementioned operation.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print "YES" (without quotes) if it is possible to erase the whole sequence using the aforementioned operation, print "NO" (without quotes) otherwise. You can print each letter in any register (upper or lower).

Example

Input

5
3
1 2 3
1
2
2
7 7
10
384836991 191890310 576823355 782177068 404011431 818008580 954291757 160449218 155374934 840594328
8
6 69 696 69696 696969 6969696 69696969 696969696

Output

YES
NO
YES
YES
NO

Note

In the first test case, YouKn0wWho can perform the following operations (the erased elements are underlined): [1, \underline{2}, 3] → [\underline{1}, 3] → [\underline{3}] → [ ].

In the second test case, it is impossible to erase the sequence as i can only be 1, and when i=1, a_1 = 2 is divisible by i + 1 = 2.


Question:
YouKn0wWho has two even integers x and y. Help him to find an integer n such that 1 ≤ n ≤ 2 ⋅ 10^{18} and n mod x = y mod n. Here, a mod b denotes the remainder of a after division by b. If there are multiple such integers, output any. It can be shown that such an integer always exists under the given constraints.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

The first and only line of each test case contains two integers x and y (2 ≤ x, y ≤ 10^9, both are even).

Output

For each test case, print a single integer n (1 ≤ n ≤ 2 ⋅ 10^{18}) that satisfies the condition mentioned in the statement. If there are multiple such integers, output any. It can be shown that such an integer always exists under the given constraints.

Example

Input

4
4 8
4 2
420 420
69420 42068

Output

4
10
420
9969128

Note

In the first test case, 4 mod 4 = 8 mod 4 = 0.

In the second test case, 10 mod 4 = 2 mod 10 = 2.

In the third test case, 420 mod 420 = 420 mod 420 = 0.


Question:
For an array b of n integers, the extreme value of this array is the minimum number of times (possibly, zero) the following operation has to be performed to make b non-decreasing:

  * Select an index i such that 1 ≤ i ≤ |b|, where |b| is the current length of b.
  * Replace b_i with two elements x and y such that x and y both are positive integers and x + y = b_i.
  * This way, the array b changes and the next operation is performed on this modified array.

For example, if b = [2, 4, 3] and index 2 gets selected, then the possible arrays after this operation are [2, \underline{1}, \underline{3}, 3], [2, \underline{2}, \underline{2}, 3], or [2, \underline{3}, \underline{1}, 3]. And consequently, for this array, this single operation is enough to make it non-decreasing: [2, 4, 3] → [2, \underline{2}, \underline{2}, 3].

It's easy to see that every array of positive integers can be made non-decreasing this way.

YouKn0wWho has an array a of n integers. Help him find the sum of extreme values of all nonempty subarrays of a modulo 998 244 353. If a subarray appears in a multiple times, its extreme value should be counted the number of times it appears.

An array d is a subarray of an array c if d can be obtained from c by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^5).

It is guaranteed that the sum of n over all test cases doesn't exceed 10^5.

Output

For each test case, print a single integer — the sum of extreme values of all subarrays of a modulo 998 244 353.

Example

Input

4
3
5 4 3
4
3 2 1 4
1
69
8
7264 40515 28226 92776 35285 21709 75124 48163

Output

5
9
0
117

Note

Let f(l, r) denote the extreme value of [a_l, a_{l+1}, …, a_r].

In the first test case,

  * f(1, 3) = 3, because YouKn0wWho can perform the following operations on the subarray [5, 4, 3] (the newly inserted elements are underlined):

[5, 4, 3] → [\underline{3}, \underline{2}, 4, 3] → [3, 2, \underline{2}, \underline{2}, 3] → [\underline{1}, \underline{2}, 2, 2, 2, 3];

  * f(1, 2) = 1, because [5, 4] → [\underline{2}, \underline{3}, 4];
  * f(2, 3) = 1, because [4, 3] → [\underline{1}, \underline{3}, 3];
  * f(1, 1) = f(2, 2) = f(3, 3) = 0, because they are already non-decreasing.

So the total sum of extreme values of all subarrays of a = 3 + 1 + 1 + 0 + 0 + 0 = 5.


Question:
You are given a string s of length n consisting of characters a and/or b.

Let \operatorname{AB}(s) be the number of occurrences of string ab in s as a substring. Analogically, \operatorname{BA}(s) is the number of occurrences of ba in s as a substring.

In one step, you can choose any index i and replace s_i with character a or b.

What is the minimum number of steps you need to make to achieve \operatorname{AB}(s) = \operatorname{BA}(s)?

Reminder:

The number of occurrences of string d in s as substring is the number of indices i (1 ≤ i ≤ |s| - |d| + 1) such that substring s_i s_{i + 1} ... s_{i + |d| - 1} is equal to d. For example, \operatorname{AB}(aabbbabaa) = 2 since there are two indices i: i = 2 where aabbbabaa and i = 6 where aabbbabaa.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 1000). Description of the test cases follows.

The first and only line of each test case contains a single string s (1 ≤ |s| ≤ 100, where |s| is the length of the string s), consisting only of characters a and/or b.

Output

For each test case, print the resulting string s with \operatorname{AB}(s) = \operatorname{BA}(s) you'll get making the minimum number of steps.

If there are multiple answers, print any of them.

Example

Input

4
b
aabbbabaa
abbb
abbaab

Output

b
aabbbabaa
bbbb
abbaaa

Note

In the first test case, both \operatorname{AB}(s) = 0 and \operatorname{BA}(s) = 0 (there are no occurrences of ab (ba) in b), so can leave s untouched.

In the second test case, \operatorname{AB}(s) = 2 and \operatorname{BA}(s) = 2, so you can leave s untouched.

In the third test case, \operatorname{AB}(s) = 1 and \operatorname{BA}(s) = 0. For example, we can change s_1 to b and make both values zero.

In the fourth test case, \operatorname{AB}(s) = 2 and \operatorname{BA}(s) = 1. For example, we can change s_6 to a and make both values equal to 1.


Question:
Berland State University has received a new update for the operating system. Initially it is installed only on the 1-st computer.

Update files should be copied to all n computers. The computers are not connected to the internet, so the only way to transfer update files from one computer to another is to copy them using a patch cable (a cable connecting two computers directly). Only one patch cable can be connected to a computer at a time. Thus, from any computer where the update files are installed, they can be copied to some other computer in exactly one hour.

Your task is to find the minimum number of hours required to copy the update files to all n computers if there are only k patch cables in Berland State University.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

Each test case consists of a single line that contains two integers n and k (1 ≤ k ≤ n ≤ 10^{18}) — the number of computers and the number of patch cables.

Output

For each test case print one integer — the minimum number of hours required to copy the update files to all n computers.

Example

Input

4
8 3
6 6
7 1
1 1

Output

4
3
6
0

Note

Let's consider the test cases of the example:

  * n=8, k=3:
    1. during the first hour, we copy the update files from the computer 1 to the computer 2;
    2. during the second hour, we copy the update files from the computer 1 to the computer 3, and from the computer 2 to the computer 4;
    3. during the third hour, we copy the update files from the computer 1 to the computer 5, from the computer 2 to the computer 6, and from the computer 3 to the computer 7;
    4. during the fourth hour, we copy the update files from the computer 2 to the computer 8.
  * n=6, k=6:
    1. during the first hour, we copy the update files from the computer 1 to the computer 2;
    2. during the second hour, we copy the update files from the computer 1 to the computer 3, and from the computer 2 to the computer 4;
    3. during the third hour, we copy the update files from the computer 1 to the computer 5, and from the computer 2 to the computer 6.
  * n=7, k=1:
    1. during the first hour, we copy the update files from the computer 1 to the computer 2;
    2. during the second hour, we copy the update files from the computer 1 to the computer 3;
    3. during the third hour, we copy the update files from the computer 1 to the computer 4;
    4. during the fourth hour, we copy the update files from the computer 4 to the computer 5;
    5. during the fifth hour, we copy the update files from the computer 4 to the computer 6;
    6. during the sixth hour, we copy the update files from the computer 3 to the computer 7.


Question:
In Berland, n different types of banknotes are used. Banknotes of the i-th type have denomination 10^{a_i} burles (burles are the currency used in Berland); the denomination of banknotes of the first type is exactly 1.

Let's denote f(s) as the minimum number of banknotes required to represent exactly s burles. For example, if the denominations of banknotes used in Berland are 1, 10 and 100, then f(59) = 14: 9 banknotes with denomination of 1 burle and 5 banknotes with denomination of 10 burles can be used to represent exactly 9 ⋅ 1 + 5 ⋅ 10 = 59 burles, and there's no way to do it with fewer banknotes.

For a given integer k, find the minimum positive number of burles s that cannot be represented with k or fewer banknotes (that is, f(s) > k).

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — number of test cases.

The first line of each test case contains two integers n and k (1 ≤ n ≤ 10; 1 ≤ k ≤ 10^9).

The next line contains n integers a_1, a_2, ..., a_n (0 = a_1 < a_2 < ... < a_n ≤ 9).

Output

For each test case, print one integer — the minimum positive number of burles s that cannot be represented with k or fewer banknotes.

Example

Input

4
3 13
0 1 2
2 777
0 4
3 255
0 1 3
10 1000000000
0 1 2 3 4 5 6 7 8 9

Output

59
778
148999
999999920999999999


Question:
You are given a matrix, consisting of n rows and m columns. The j-th cell of the i-th row contains an integer a_{ij}.

First, you have to color each row of the matrix either red or blue in such a way that at least one row is colored red and at least one row is colored blue.

Then, you have to choose an integer k (1 ≤ k < m) and cut the colored matrix in such a way that the first k columns become a separate matrix (the left matrix) and the last m-k columns become a separate matrix (the right matrix).

The coloring and the cut are called perfect if two properties hold:

  * every red cell in the left matrix contains an integer greater than every blue cell in the left matrix;
  * every blue cell in the right matrix contains an integer greater than every red cell in the right matrix.

Find any perfect coloring and cut, or report that there are none.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

Then the descriptions of t testcases follow.

The first line of each testcase contains two integers n and m (2 ≤ n, m ≤ 5 ⋅ 10^5; n ⋅ m ≤ 10^6) — the number of rows and the number of columns in the matrix, respectively.

The i-th of the next n lines contains m integers a_{i1}, a_{i2}, ..., a_{im} (1 ≤ a_{ij} ≤ 10^6).

The sum of n ⋅ m over all testcases doesn't exceed 10^6.

Output

For each testcase print an answer. If there are no perfect colorings and cuts in the matrix, then print "NO".

Otherwise, first, print "YES". Then a string, consisting of n characters: the i-th character should be 'R' if the i-th row is colored red and 'B' if it's colored blue. The string should contain at least one 'R' and at least one 'B'. Finally, print an integer k (1 ≤ k < m) — the number of columns from the left that are cut.

Example

Input

3
5 5
1 5 8 8 7
5 2 1 4 3
1 6 9 7 5
9 3 3 3 2
1 7 9 9 8
3 3
8 9 8
1 5 3
7 5 7
2 6
3 3 3 2 2 2
1 1 1 4 4 4

Output

YES
BRBRB 1
NO
YES
RB 3

Note

The coloring and the cut for the first testcase:

<image>


Question:
There are n heroes fighting in the arena. Initially, the i-th hero has a_i health points.

The fight in the arena takes place in several rounds. At the beginning of each round, each alive hero deals 1 damage to all other heroes. Hits of all heroes occur simultaneously. Heroes whose health is less than 1 at the end of the round are considered killed.

If exactly 1 hero remains alive after a certain round, then he is declared the winner. Otherwise, there is no winner.

Your task is to calculate the number of ways to choose the initial health points for each hero a_i, where 1 ≤ a_i ≤ x, so that there is no winner of the fight. The number of ways can be very large, so print it modulo 998244353. Two ways are considered different if at least one hero has a different amount of health. For example, [1, 2, 1] and [2, 1, 1] are different.

Input

The only line contains two integers n and x (2 ≤ n ≤ 500; 1 ≤ x ≤ 500).

Output

Print one integer — the number of ways to choose the initial health points for each hero a_i, where 1 ≤ a_i ≤ x, so that there is no winner of the fight, taken modulo 998244353.

Examples

Input

2 5

Output

5

Input

3 3

Output

15

Input

5 4

Output

1024

Input

13 37

Output

976890680


Question:
You are given a tree consisting of n vertices. Recall that a tree is an undirected connected acyclic graph. The given tree is rooted at the vertex 1.

You have to process q queries. In each query, you are given a vertex of the tree v and an integer k.

To process a query, you may delete any vertices from the tree in any order, except for the root and the vertex v. When a vertex is deleted, its children become the children of its parent. You have to process a query in such a way that maximizes the value of c(v) - m ⋅ k (where c(v) is the resulting number of children of the vertex v, and m is the number of vertices you have deleted). Print the maximum possible value you can obtain.

The queries are independent: the changes you make to the tree while processing a query don't affect the tree in other queries.

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.

Then n-1 lines follow, the i-th of them contains two integers x_i and y_i (1 ≤ x_i, y_i ≤ n; x_i ≠ y_i) — the endpoints of the i-th edge. These edges form a tree.

The next line contains one integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of queries.

Then q lines follow, the j-th of them contains two integers v_j and k_j (1 ≤ v_j ≤ n; 0 ≤ k_j ≤ 2 ⋅ 10^5) — the parameters of the j-th query.

Output

For each query, print one integer — the maximum value of c(v) - m ⋅ k you can achieve.

Example

Input

8
6 7
3 2
8 3
5 7
7 4
7 1
7 3
6
1 0
1 2
1 3
7 1
5 0
7 200000

Output

5
2
1
4
0
4

Note

The tree in the first example is shown in the following picture:

<image>

Answers to the queries are obtained as follows:

  1. v=1,k=0: you can delete vertices 7 and 3, so the vertex 1 has 5 children (vertices 2, 4, 5, 6, and 8), and the score is 5 - 2 ⋅ 0 = 5;
  2. v=1,k=2: you can delete the vertex 7, so the vertex 1 has 4 children (vertices 3, 4, 5, and 6), and the score is 4 - 1 ⋅ 2 = 2.
  3. v=1,k=3: you shouldn't delete any vertices, so the vertex 1 has only one child (vertex 7), and the score is 1 - 0 ⋅ 3 = 1;
  4. v=7,k=1: you can delete the vertex 3, so the vertex 7 has 5 children (vertices 2, 4, 5, 6, and 8), and the score is 5 - 1 ⋅ 1 = 4;
  5. v=5,k=0: no matter what you do, the vertex 5 will have no children, so the score is 0;
  6. v=7,k=200000: you shouldn't delete any vertices, so the vertex 7 has 4 children (vertices 3, 4, 5, and 6), and the score is 4 - 0 ⋅ 200000 = 4.


Question:
You are given a keyboard that consists of 26 keys. The keys are arranged sequentially in one row in a certain order. Each key corresponds to a unique lowercase Latin letter.

You have to type the word s on this keyboard. It also consists only of lowercase Latin letters.

To type a word, you need to type all its letters consecutively one by one. To type each letter you must position your hand exactly over the corresponding key and press it.

Moving the hand between the keys takes time which is equal to the absolute value of the difference between positions of these keys (the keys are numbered from left to right). No time is spent on pressing the keys and on placing your hand over the first letter of the word.

For example, consider a keyboard where the letters from 'a' to 'z' are arranged in consecutive alphabetical order. The letters 'h', 'e', 'l' and 'o' then are on the positions 8, 5, 12 and 15, respectively. Therefore, it will take |5 - 8| + |12 - 5| + |12 - 12| + |15 - 12| = 13 units of time to type the word "hello".

Determine how long it will take to print the word s.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The next 2t lines contain descriptions of the test cases.

The first line of a description contains a keyboard — a string of length 26, which consists only of lowercase Latin letters. Each of the letters from 'a' to 'z' appears exactly once on the keyboard.

The second line of the description contains the word s. The word has a length from 1 to 50 letters inclusive and consists of lowercase Latin letters.

Output

Print t lines, each line containing the answer to the corresponding test case. The answer to the test case is the minimal time it takes to type the word s on the given keyboard.

Example

Input

5
abcdefghijklmnopqrstuvwxyz
hello
abcdefghijklmnopqrstuvwxyz
i
abcdefghijklmnopqrstuvwxyz
codeforces
qwertyuiopasdfghjklzxcvbnm
qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
qwertyuiopasdfghjklzxcvbnm
abacaba

Output

13
0
68
0
74


Question:
The grasshopper is located on the numeric axis at the point with coordinate x_0.

Having nothing else to do he starts jumping between integer points on the axis. Making a jump from a point with coordinate x with a distance d to the left moves the grasshopper to a point with a coordinate x - d, while jumping to the right moves him to a point with a coordinate x + d.

The grasshopper is very fond of positive integers, so for each integer i starting with 1 the following holds: exactly i minutes after the start he makes a jump with a distance of exactly i. So, in the first minutes he jumps by 1, then by 2, and so on.

The direction of a jump is determined as follows: if the point where the grasshopper was before the jump has an even coordinate, the grasshopper jumps to the left, otherwise he jumps to the right.

For example, if after 18 consecutive jumps he arrives at the point with a coordinate 7, he will jump by a distance of 19 to the right, since 7 is an odd number, and will end up at a point 7 + 19 = 26. Since 26 is an even number, the next jump the grasshopper will make to the left by a distance of 20, and it will move him to the point 26 - 20 = 6.

Find exactly which point the grasshopper will be at after exactly n jumps.

Input

The first line of input contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases.

Each of the following t lines contains two integers x_0 (-10^{14} ≤ x_0 ≤ 10^{14}) and n (0 ≤ n ≤ 10^{14}) — the coordinate of the grasshopper's initial position and the number of jumps.

Output

Print exactly t lines. On the i-th line print one integer — the answer to the i-th test case — the coordinate of the point the grasshopper will be at after making n jumps from the point x_0.

Example

Input

9
0 1
0 2
10 10
10 99
177 13
10000000000 987654321
-433494437 87178291199
1 0
-1 1

Output

-1
1
11
110
190
9012345679
-87611785637
1
0

Note

The first two test cases in the example correspond to the first two jumps from the point x_0 = 0.

Since 0 is an even number, the first jump of length 1 is made to the left, and the grasshopper ends up at the point 0 - 1 = -1.

Then, since -1 is an odd number, a jump of length 2 is made to the right, bringing the grasshopper to the point with coordinate -1 + 2 = 1.


Question:
Yelisey has an array a of n integers.

If a has length strictly greater than 1, then Yelisei can apply an operation called minimum extraction to it:

  1. First, Yelisei finds the minimal number m in the array. If there are several identical minima, Yelisey can choose any of them.
  2. Then the selected minimal element is removed from the array. After that, m is subtracted from each remaining element.

Thus, after each operation, the length of the array is reduced by 1.

For example, if a = [1, 6, -4, -2, -4], then the minimum element in it is a_3 = -4, which means that after this operation the array will be equal to a=[1 {- (-4)}, 6 {- (-4)}, -2 {- (-4)}, -4 {- (-4)}] = [5, 10, 2, 0].

Since Yelisey likes big numbers, he wants the numbers in the array a to be as big as possible.

Formally speaking, he wants to make the minimum of the numbers in array a to be maximal possible (i.e. he want to maximize a minimum). To do this, Yelisey can apply the minimum extraction operation to the array as many times as he wants (possibly, zero). Note that the operation cannot be applied to an array of length 1.

Help him find what maximal value can the minimal element of the array have after applying several (possibly, zero) minimum extraction operations to the array.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The next 2t lines contain descriptions of the test cases.

In the description of each test case, the first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the original length of the array a. The second line of the description lists n space-separated integers a_i (-10^9 ≤ a_i ≤ 10^9) — elements of the array a.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

Print t lines, each of them containing the answer to the corresponding test case. The answer to the test case is a single integer — the maximal possible minimum in a, which can be obtained by several applications of the described operation to it.

Example

Input

8
1
10
2
0 0
3
-1 2 0
4
2 10 1 7
2
2 3
5
3 2 -4 -2 0
2
-1 1
1
-2

Output

10
0
2
5
2
2
2
-2

Note

In the first example test case, the original length of the array n = 1. Therefore minimum extraction cannot be applied to it. Thus, the array remains unchanged and the answer is a_1 = 10.

In the second set of input data, the array will always consist only of zeros.

In the third set, the array will be changing as follows: [\color{blue}{-1}, 2, 0] → [3, \color{blue}{1}] → [\color{blue}{2}]. The minimum elements are highlighted with \color{blue}{blue}. The maximal one is 2.

In the fourth set, the array will be modified as [2, 10, \color{blue}{1}, 7] → [\color{blue}{1}, 9, 6] → [8, \color{blue}{5}] → [\color{blue}{3}]. Similarly, the maximum of the minimum elements is 5.


Question:
You are given an array of integers a of length n. The elements of the array can be either different or the same.

Each element of the array is colored either blue or red. There are no unpainted elements in the array. One of the two operations described below can be applied to an array in a single step:

  * either you can select any blue element and decrease its value by 1;
  * or you can select any red element and increase its value by 1.

Situations in which there are no elements of some color at all are also possible. For example, if the whole array is colored blue or red, one of the operations becomes unavailable.

Determine whether it is possible to make 0 or more steps such that the resulting array is a permutation of numbers from 1 to n?

In other words, check whether there exists a sequence of steps (possibly empty) such that after applying it, the array a contains in some order all numbers from 1 to n (inclusive), each exactly once.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of input data sets in the test.

The description of each set of input data consists of three lines. The first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the original array a. The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the array elements themselves.

The third line has length n and consists exclusively of the letters 'B' and/or 'R': ith character is 'B' if a_i is colored blue, and is 'R' if colored red.

It is guaranteed that the sum of n over all input sets does not exceed 2 ⋅ 10^5.

Output

Print t lines, each of which contains the answer to the corresponding test case of the input. Print YES as an answer if the corresponding array can be transformed into a permutation, and NO otherwise.

You can print the answer in any case (for example, the strings yEs, yes, Yes, and YES will be recognized as a positive answer).

Example

Input

8
4
1 2 5 2
BRBR
2
1 1
BB
5
3 1 4 2 5
RBRRB
5
3 1 3 1 3
RBRRB
5
5 1 5 1 5
RBRRB
4
2 2 2 2
BRBR
2
1 -2
BR
4
-2 -1 4 0
RRRR

Output

YES
NO
YES
YES
NO
YES
YES
YES

Note

In the first test case of the example, the following sequence of moves can be performed:

  * choose i=3, element a_3=5 is blue, so we decrease it, we get a=[1,2,4,2];
  * choose i=2, element a_2=2 is red, so we increase it, we get a=[1,3,4,2];
  * choose i=3, element a_3=4 is blue, so we decrease it, we get a=[1,3,3,2];
  * choose i=2, element a_2=2 is red, so we increase it, we get a=[1,4,3,2].

We got that a is a permutation. Hence the answer is YES.


Question:
The robot is located on a checkered rectangular board of size n × m (n rows, m columns). The rows in the board are numbered from 1 to n from top to bottom, and the columns — from 1 to m from left to right.

The robot is able to move from the current cell to one of the four cells adjacent by side.

The sequence of commands s executed by the robot is given. Each command is denoted by one of the symbols 'L', 'R', 'D' or 'U', and triggers the movement to left, right, down or up, respectively.

The robot can start its movement in any cell. The robot executes the commands starting from the first one, strictly in the order in which they are listed in s. If the robot moves beyond the edge of the board, it falls and breaks. A command that causes the robot to break is not considered successfully executed.

The robot's task is to execute as many commands as possible without falling off the board. For example, on board 3 × 3, if the robot starts a sequence of actions s="RRDLUU" ("right", "right", "down", "left", "up", "up") from the central cell, the robot will perform one command, then the next command will force him to cross the edge. If the robot starts moving from the cell (2, 1) (second row, first column) then all commands will be executed successfully and the robot will stop at the cell (1, 2) (first row, second column).

<image> The robot starts from cell (2, 1) (second row, first column). It moves right, right, down, left, up, and up. In this case it ends in the cell (1, 2) (first row, second column).

Determine the cell from which the robot should start its movement in order to execute as many commands as possible.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The next 2t lines contain descriptions of the test cases.

In the description of each test case, the first line contains two integers n and m (1 ≤ n, m ≤ 10^6) — the height and width of the field that the robot is located on. The second line of the description is a string s consisting solely of characters 'L', 'R', 'D' and 'U' — the sequence of commands the robot executes. The string has a length from 1 to 10^6 commands.

It is guaranteed that the total length of s over all test cases does not exceed 10^6.

Output

Print t lines, each of which contains the answer to the corresponding test case. The answer to the test case are two integers r (1 ≤ r ≤ n) and c (1 ≤ c ≤ m), separated by a space — the coordinates of the cell (row number and column number) from which the robot should start moving to perform as many commands as possible.

If there are several such cells, you may output any of them.

Example

Input

4
1 1
L
1 2
L
3 3
RRDLUU
4 3
LUURRDDLLLUU

Output

1 1
1 2
2 1
3 2

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3\nLUUURRDLLLDU\n", "4\n1 1\nL\n4 2\nL\n5 3\nRRDLUU\n4 4\nUULLLDRRDUUL\n", "4\n1 2\nL\n4 2\nL\n3 3\nUULRRD\n6 1\nUULLLDRRDUUL\n", "4\n1 2\nL\n7 2\nL\n4 3\nRRDLUU\n3 4\nDUULRRDLLLUU\n", "4\n1 1\nL\n3 2\nL\n3 2\nUULRRD\n6 2\nUULULDRRDULL\n", "4\n1 1\nL\n1 2\nL\n3 3\nRRDLUU\n8 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n2 2\nL\n3 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n3 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n3 3\nRRDLUU\n6 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n2 2\nL\n5 3\nRRDLUU\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n2 2\nL\n6 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n4 3\nRRDLUU\n8 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n4 2\nL\n3 3\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n5 3\nRRDLUU\n6 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n3 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n7 2\nL\n3 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n3 3\nRRDLUU\n8 3\nLUURRDDLLLVU\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n5 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n7 2\nL\n3 3\nRRDLUU\n3 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n2 2\nL\n6 3\nRRDLUU\n4 4\nLUURRDDLLLUU\n", "4\n1 2\nL\n4 2\nL\n3 3\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n10 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n7 2\nL\n2 3\nRRDLUU\n6 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n13 2\nL\n2 3\nRRDLUU\n6 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n3 3\nRRDLUU\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n2 2\nL\n3 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n4 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n3 3\nRRDUUL\n5 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n1 2\nL\n3 3\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n7 2\nL\n3 3\nRRDLUU\n3 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n9 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n22 2\nL\n2 3\nRRDLUU\n6 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n2 2\nL\n3 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n4 3\nRRDLUU\n4 3\nLLUDRRDLLUUU\n", "4\n1 2\nL\n2 2\nL\n6 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n3 3\nRRDUUL\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n3 3\nRRDLUU\n6 2\nLUUDRRDLLLUU\n", "4\n1 1\nL\n2 2\nL\n8 3\nRRDLUU\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n4 2\nL\n5 3\nRRDLUU\n6 4\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n2 3\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n3 2\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n6 3\nRRDLUU\n8 3\nLUURRDDLLLVU\n", "4\n1 1\nL\n1 1\nL\n1 3\nRRDKUU\n8 3\nLUURRDDLLLUU\n", "4\n1 2\nL\n7 2\nL\n2 2\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 3\nUULDRR\n10 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n3 2\nL\n3 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n4 3\nUULDRR\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n1 3\nRRDUUL\n5 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n1 2\nL\n3 3\nRRDLUU\n5 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n3 2\nL\n3 3\nRRDLUU\n3 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n2 2\nL\n11 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n3 3\nRDRLUU\n6 2\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n2 3\nRRDLUU\n5 3\nLUUDRRDLLLVU\n", "4\n1 1\nL\n1 1\nL\n5 3\nRRDLUU\n8 3\nLUURRDDLLLVU\n", "4\n1 1\nL\n7 2\nL\n3 3\nUULDRR\n10 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 2\nL\n3 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n1 2\nL\n4 3\nRRDLUU\n5 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n3 2\nL\n3 3\nRRDLUU\n3 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 2\nL\n3 3\nUULDRR\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n2 2\nL\n3 3\nRRDLUU\n4 3\nLUUDRRDLLLUT\n", "4\n1 1\nL\n4 2\nL\n3 3\nDRRLUU\n6 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n2 2\nL\n5 3\nRRDLUU\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n4 2\nL\n6 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n3 3\nRDRLUU\n8 3\nLUURRDDLLLVU\n", "4\n1 1\nL\n1 1\nL\n1 3\nRRDLUU\n7 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n1 2\nL\n6 3\nRRDLUU\n4 4\nLUURRDDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n2 2\nL\n4 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n6 3\nRRDUUL\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n4 3\nRRULDU\n4 3\nLLUDRRDLLUUU\n", "4\n1 2\nL\n2 2\nL\n6 3\nRRDLUU\n4 3\nUULLLDURDURL\n", "4\n1 1\nL\n4 2\nL\n10 3\nRRDLUU\n6 4\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n3 2\nLUUDRLDLRLUU\n", "4\n2 2\nL\n7 2\nL\n2 2\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n12 2\nL\n3 3\nUULDRR\n10 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n3 2\nL\n3 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n1 1\nL\n7 3\nRRDLUU\n8 4\nUULLLDDRRUUL\n", "4\n1 1\nL\n7 2\nL\n2 3\nRRDLUU\n6 3\nLUUDRRDLLLVU\n", "4\n1 1\nL\n1 1\nL\n4 3\nRRDLUU\n8 3\nLUURRDDLLLVU\n", "4\n1 1\nL\n2 2\nL\n3 3\nUULDRR\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n2 2\nL\n3 3\nRRDLUU\n8 3\nLUUDRRDLLLUT\n", "4\n1 1\nL\n4 2\nL\n3 3\nDRRLUU\n6 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n2 2\nL\n5 3\nRRDLUU\n8 3\nLUURRDDLLLUU\n", "4\n1 2\nL\n1 1\nL\n3 3\nRRDUUL\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n4 2\nL\n4 3\nRRULDU\n6 3\nLLUDRRDLLUUU\n", "4\n1 1\nL\n12 2\nL\n3 3\nUULDRR\n11 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n3 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n1 1\nL\n7 3\nRRDLUU\n8 2\nUULLLDDRRUUL\n", "4\n1 1\nL\n2 2\nL\n3 3\nUULDRR\n3 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n4 2\nL\n4 3\nDRRLUU\n6 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n1 1\nL\n12 3\nRRDLUU\n8 2\nUULLLDDRRUUL\n", "4\n1 1\nL\n1 2\nL\n2 3\nRRDLUU\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n5 2\nL\n3 3\nRRDLUU\n6 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n3 2\nL\n5 3\nRRDLUU\n4 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n4 2\nL\n5 3\nRRDLUU\n10 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n4 3\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n6 2\nL\n3 3\nRRDLUU\n3 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n7 2\nL\n3 3\nRRDLUU\n4 3\nLUULRRDLDLUU\n", "4\n1 2\nL\n7 2\nL\n3 3\nUULDRR\n3 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n2 2\nL\n11 3\nRRDLUU\n4 4\nLUURRDDLLLUU\n", "4\n1 2\nL\n6 2\nL\n3 3\nRRDLUU\n3 3\nLUUDRUDLLLUR\n", "4\n1 1\nL\n2 2\nL\n2 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n1 2\nL\n3 3\nRRDLUU\n8 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n1 2\nL\n1 3\nRRDLUU\n8 3\nLUURRDDLLLUU\n", "4\n1 2\nL\n7 2\nL\n1 3\nRRDLUU\n3 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n4 3\nRRDLUU\n5 3\nLLUDRRDLLUUU\n", "4\n2 2\nL\n2 2\nL\n6 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n3 3\nRRDUUL\n3 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n10 2\nL\n2 3\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n6 3\nRRDLUU\n9 3\nLUURRDDLLLVU\n", "4\n1 1\nL\n3 2\nL\n3 3\nRRDLUU\n8 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n2 3\nRRDUUL\n5 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n1 2\nL\n3 3\nUULDRR\n5 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n6 2\nL\n3 3\nRRDLUU\n3 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n7 2\nL\n4 3\nRRDLUU\n9 1\nUULLLDRRDUUL\n", "4\n1 1\nL\n3 2\nL\n3 3\nRDRLUU\n6 2\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 3\nUULDRR\n10 3\nLUULRRDDLLUU\n", "4\n1 1\nL\n1 2\nL\n3 3\nUULDRR\n4 2\nLUURRDDLLLUU\n", "4\n1 1\nL\n1 2\nL\n6 3\nRRDLUU\n4 3\nLUURRDDLLLUU\n", "4\n1 2\nL\n7 2\nL\n2 3\nRRDLUU\n4 4\nLUUDRRLLLDUU\n", "4\n1 1\nL\n2 2\nL\n6 3\nRRDLUU\n4 3\nUULLLDURDURL\n", "4\n1 2\nL\n1 1\nL\n1 3\nRRDLUU\n8 3\nLUURRDDLLLUU\n", "4\n2 2\nL\n7 2\nL\n2 2\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n12 2\nL\n5 3\nUULDRR\n10 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n3 2\nL\n3 3\nRRDLUU\n8 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n7 2\nL\n2 3\nDRRLUU\n6 3\nLUUDRRDLLLVU\n", "4\n1 1\nL\n1 1\nL\n4 3\nRRDLUU\n5 3\nLUURRDDLLLVU\n", "4\n1 1\nL\n4 2\nL\n3 3\nDRRLUU\n6 1\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n4 3\nRRULDU\n12 3\nLLUDRRDLLUUU\n", "4\n1 1\nL\n6 2\nL\n3 3\nUULDRR\n3 3\nLUUDRRDLLLUU\n", "4\n2 2\nL\n7 2\nL\n3 3\nUULDRR\n5 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n2 2\nL\n11 3\nRRDLUU\n4 4\nLUURRDDLLLUU\n", "4\n1 2\nL\n7 2\nL\n1 3\nRRDLUU\n3 3\nUULLLDRRDTUL\n", "4\n1 1\nL\n4 2\nL\n4 3\nRRDLUU\n5 3\nUUULLDRRDULL\n", "4\n1 1\nL\n10 2\nL\n2 3\nRRDLUU\n8 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n3 2\nUULDRR\n10 3\nLUULRRDDLLUU\n", "4\n1 1\nL\n4 2\nL\n4 3\nRRULDU\n23 3\nLLUDRRDLLUUU\n", "4\n2 2\nL\n7 2\nL\n3 3\nUULDRR\n6 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n7 2\nL\n1 3\nRRDLUU\n3 3\nUULLLDRRDTUL\n", "4\n1 1\nL\n13 2\nL\n2 3\nRRDLUU\n8 3\nLUUDRRDLLLUU\n", "4\n2 2\nL\n7 2\nL\n3 3\nUULDRR\n6 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n1 2\nL\n3 3\nRRDLUU\n7 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n6 2\nL\n3 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n2 2\nL\n9 3\nRRDLUU\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n3 3\nRRDLUU\n15 3\nLUURRDDLLLUU\n", "4\n1 1\nL\n4 2\nL\n5 3\nRRDLUU\n6 2\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n3 3\nRRDLUU\n8 3\nLRUURDDLLLVU\n", "4\n1 1\nL\n3 2\nL\n6 3\nRRDLUU\n4 4\nLUURRDDLLLUU\n", "4\n1 2\nL\n4 2\nL\n3 3\nRRDLUU\n3 3\nLUUDRUDLLLUR\n", "4\n1 2\nL\n7 2\nL\n4 3\nRRDLUU\n6 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n2 2\nL\n3 3\nRRDLUU\n5 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n1 2\nL\n3 3\nUULDRR\n5 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n2 2\nL\n3 3\nRRDLUU\n5 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n4 2\nL\n3 3\nRRDUUL\n4 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n4 2\nL\n5 3\nRRDLUU\n4 4\nLUUDRRDLLLUU\n", "4\n1 1\nL\n11 2\nL\n2 3\nRRDLUU\n5 3\nLUUDRRDLLLUU\n", "4\n1 1\nL\n1 1\nL\n1 3\nRRDKUU\n8 3\nLUURRDDLLLUV\n", "4\n1 2\nL\n7 2\nL\n2 2\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n2 2\nL\n3 3\nUULDRR\n10 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n3 2\nL\n5 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n", "4\n1 2\nL\n4 2\nL\n4 3\nUULDRR\n4 3\nLUUDRRDLLLUU\n", "4\n1 2\nL\n1 2\nL\n3 3\nRRDLUU\n3 3\nUULLLDRRDUUL\n", "4\n1 1\nL\n7 2\nL\n3 3\nRRDLUU\n12 1\nUULLLDRRDUUL\n", "4\n1 1\nL\n4 2\nL\n3 3\nUULRDR\n6 2\nLUUDRRDLLLUU\n", "4\n1 2\nL\n1 2\nL\n3 3\nRRDLUU\n4 3\nUULLLDRRDUUL\n"], "outputs": ["1 1\n1 2\n2 1\n3 2\n", "1 1\n1 2\n2 1\n3 2\n", "1 1\n1 1\n2 1\n3 2\n", "1 1\n1 2\n2 1\n3 3\n", "1 2\n1 2\n2 1\n3 2\n", "1 1\n1 1\n1 1\n3 2\n", "1 2\n1 2\n1 1\n3 2\n", "1 2\n1 2\n2 1\n3 3\n", "1 1\n1 2\n3 2\n3 2\n", "1 1\n1 1\n2 1\n3 3\n", "1 1\n1 2\n1 1\n3 2\n", "1 1\n1 2\n3 2\n3 3\n", "1 2\n1 2\n3 2\n3 3\n", "1 1\n1 1\n2 1\n3 4\n", "1 1\n1 2\n2 1\n3 1\n", "1 1\n1 2\n1 1\n3 1\n", "1 1\n1 2\n2 1\n4 3\n", "1 2\n1 2\n1 1\n3 3\n", "1 2\n1 1\n2 1\n3 2\n", "1 2\n1 1\n1 1\n3 2\n", "1 2\n1 2\n2 1\n3 1\n", "1 1\n1 1\n1 1\n3 3\n", "1 1\n1 1\n1 1\n3 4\n", "1 1\n1 2\n1 1\n3 3\n", "1 2\n1 2\n3 2\n3 2\n", "1 1\n1 1\n2 1\n4 3\n", "1 2\n1 2\n2 1\n4 3\n", "1 1\n1 2\n2 1\n2 2\n", "1 1\n1 2\n3 1\n3 2\n", "1 1\n1 1\n1 1\n4 3\n", "1 1\n1 2\n3 2\n3 1\n", "1 1\n1 2\n2 2\n3 2\n", "1 2\n1 2\n1 1\n3 1\n", "1 1\n1 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"1 1\n1 2\n1 1\n3 2\n", "1 1\n1 2\n2 1\n3 2\n", "1 1\n1 1\n2 1\n3 2\n", "1 1\n1 1\n1 1\n3 2\n", "1 2\n1 2\n1 1\n3 2\n", "1 1\n1 2\n3 2\n3 3\n", "1 1\n1 2\n2 1\n3 3\n", "1 1\n1 2\n3 2\n3 2\n", "1 1\n1 2\n1 1\n3 2\n", "1 2\n1 2\n2 1\n3 3\n", "1 2\n1 2\n2 1\n3 3\n", "1 2\n1 2\n2 1\n3 3\n", "1 1\n1 2\n2 1\n3 2\n", "1 1\n1 2\n1 1\n3 2\n", "1 1\n1 1\n2 1\n3 2\n", "1 1\n1 2\n3 2\n3 2\n", "1 1\n1 2\n2 1\n3 3\n", "1 2\n1 2\n2 1\n3 3\n", "1 2\n1 2\n2 1\n3 2\n", "1 1\n1 2\n3 2\n3 2\n", "1 1\n1 2\n2 1\n3 2\n", "1 1\n1 2\n2 1\n3 2\n", "1 2\n1 2\n2 1\n3 2\n", "1 1\n1 2\n2 1\n3 2\n", "1 1\n1 1\n2 1\n3 2\n", "1 1\n1 1\n1 1\n3 2\n", "1 1\n1 2\n2 1\n3 3\n", "1 1\n1 2\n2 1\n3 3\n", "1 1\n1 2\n2 1\n3 2\n", "1 1\n1 2\n2 1\n3 2\n", "1 1\n1 2\n2 1\n3 3\n", "1 2\n1 2\n2 1\n3 3\n", "1 1\n1 2\n2 1\n3 3\n", "1 1\n1 2\n2 1\n3 2\n", "1 2\n1 2\n1 1\n3 2\n", "1 1\n1 2\n3 2\n3 3\n", "1 2\n1 2\n2 1\n3 3\n", "1 1\n1 1\n2 1\n3 4\n", "1 1\n1 2\n1 1\n3 2\n", "1 1\n1 1\n2 1\n3 2\n", "1 1\n1 2\n3 2\n3 2\n", "1 1\n1 2\n2 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2\n", "1 2\n1 2\n2 1\n3 3\n"]}