'''simple docstring'''





SCREAMING_SNAKE_CASE_:     Optional[int]  =2_56
# Modulus to hash a string
SCREAMING_SNAKE_CASE_:     Tuple  =1_00_00_03





def 	lowerCAmelCase_				(					snake_case_       : str					,    snake_case_       : str			)    ->      Tuple:


     '''simple docstring'''




     UpperCAmelCase_           =   len(__lowerCamelCase			)
     UpperCAmelCase_           =   len(__lowerCamelCase			)
     if p_len > t_len:
          return False

     UpperCAmelCase_           =   0
     UpperCAmelCase_           =   0
     UpperCAmelCase_           =   1

     # Calculating the hash of pattern and substring of text
     for i in range(__lowerCamelCase			):
          UpperCAmelCase_           =   (ord(pattern[i]			) + p_hash * alphabet_size) % modulus
          UpperCAmelCase_           =   (ord(text[i]			) + text_hash * alphabet_size) % modulus
          if i == p_len - 1:
               continue
          UpperCAmelCase_           =   (modulus_power * alphabet_size) % modulus

     for i in range(0					,    t_len - p_len + 1			):
          if text_hash == p_hash and text[i : i + p_len] == pattern:
               return True
          if i == t_len - p_len:
               continue
          # Calculate the https://en.wikipedia.org/wiki/Rolling_hash
          UpperCAmelCase_           =   (
              (text_hash - ord(text[i]			) * modulus_power) * alphabet_size
              + ord(text[i + p_len]			)
          ) % modulus
     return False





def 	lowerCAmelCase_				(					)    ->      int:


     '''simple docstring'''




     UpperCAmelCase_           =   "abc1abc12"
     UpperCAmelCase_           =   "alskfjaldsabc1abc1abc12k23adsfabcabc"
     UpperCAmelCase_           =   "alskfjaldsk23adsfabcabc"
     assert rabin_karp(__lowerCamelCase					,    __lowerCamelCase			) and not rabin_karp(__lowerCamelCase					,    __lowerCamelCase			)

     # Test 2)
     UpperCAmelCase_           =   "ABABX"
     UpperCAmelCase_           =   "ABABZABABYABABX"
     assert rabin_karp(__lowerCamelCase					,    __lowerCamelCase			)

     # Test 3)
     UpperCAmelCase_           =   "AAAB"
     UpperCAmelCase_           =   "ABAAAAAB"
     assert rabin_karp(__lowerCamelCase					,    __lowerCamelCase			)

     # Test 4)
     UpperCAmelCase_           =   "abcdabcy"
     UpperCAmelCase_           =   "abcxabcdabxabcdabcdabcy"
     assert rabin_karp(__lowerCamelCase					,    __lowerCamelCase			)

     # Test 5)
     UpperCAmelCase_           =   "Lü"
     UpperCAmelCase_           =   "Lüsai"
     assert rabin_karp(__lowerCamelCase					,    __lowerCamelCase			)
     UpperCAmelCase_           =   "Lue"
     assert not rabin_karp(__lowerCamelCase					,    __lowerCamelCase			)
     print("Success."			)


if __name__ == "__main__":
    test_rabin_karp()











'''simple docstring'''


import math
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int ):
   lowercase_			:Dict    			= []
   lowercase_			:List[Any]    			= 2
   lowercase_			:Optional[Any]    			= int(math.sqrt(__lowerCamelCase ) )  # Size of every segment
   lowercase_			:Optional[Any]    			= [True] * (end + 1)
   lowercase_			:Dict    			= []

   while start <= end:
      if temp[start] is True:
         in_prime.append(__lowerCamelCase )
         for i in range(start * start	,end + 1	,__lowerCamelCase ):
            lowercase_			:List[str]    			= False
      start += 1
   prime += in_prime

   lowercase_			:Dict    			= end + 1
   lowercase_			:Dict    			= min(2 * end	,__lowerCamelCase )

   while low <= n:
      lowercase_			:Any    			= [True] * (high - low + 1)
      for each in in_prime:
         lowercase_			:List[Any]    			= math.floor(low / each ) * each
         if t < low:
            t += each

         for j in range(__lowerCamelCase	,high + 1	,__lowerCamelCase ):
            lowercase_			:str    			= False

      for j in range(len(__lowerCamelCase ) ):
         if temp[j] is True:
            prime.append(j + low )

      lowercase_			:Dict    			= high + 1
      lowercase_			:Dict    			= min(high + end	,__lowerCamelCase )

   return prime


print(sieve(10**6))


