
SCREAMING_SNAKE_CASE							:Any							 =				256
# Modulus to hash a string
SCREAMING_SNAKE_CASE							:Union[str, Any]							 =				100_0003


def 						UpperCAmelCase			(	a_		,   a_						)		->	bool:







				"""simple docstring"""



				__A   			= len(a_						)
				__A   			= len(a_						)
				if p_len > t_len:
								return False

				__A   			= 0
				__A   			= 0
				__A   			= 1

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


def 						UpperCAmelCase			(	)		->	None:







				"""simple docstring"""



				__A   			= "abc1abc12"
				__A   			= "alskfjaldsabc1abc1abc12k23adsfabcabc"
				__A   			= "alskfjaldsk23adsfabcabc"
				assert rabin_karp(a_		,   a_						) and not rabin_karp(a_		,   a_						)

				# Test 2)
				__A   			= "ABABX"
				__A   			= "ABABZABABYABABX"
				assert rabin_karp(a_		,   a_						)

				# Test 3)
				__A   			= "AAAB"
				__A   			= "ABAAAAAB"
				assert rabin_karp(a_		,   a_						)

				# Test 4)
				__A   			= "abcdabcy"
				__A   			= "abcxabcdabxabcdabcdabcy"
				assert rabin_karp(a_		,   a_						)

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


if __name__ == "__main__":
					test_rabin_karp()

"""simple docstring"""
import math







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->bool:

  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5		,     int(math.sqrt(_SCREAMING_SNAKE_CASE   ) + 1   )		,     6   ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True







def 						__a   (	_SCREAMING_SNAKE_CASE = 0.1   )	->int:
  a__:     str										=	3
  a__:     Optional[Any]										=	3

  while primes / (2 * j - 1) >= ratio:
    for i in range(j * j + j + 1		,     (j + 2) * (j + 2)		,     j + 1   ):
      primes += is_prime(_SCREAMING_SNAKE_CASE   )
    j += 2
  return j


if __name__ == "__main__":
 import doctest

 doctest.testmod()


