


def 							__lowercase       (			__lowerCAmelCase							:    int ,   __lowerCAmelCase							:    int       ):
							if a < 0 or b < 0:
														raise ValueError('the value of both inputs must be positive'       )

							a__					=					str(bin(__lowerCAmelCase       )       )[2:]  # remove the leading "0b"
							a__					=					str(bin(__lowerCAmelCase       )       )[2:]  # remove the leading "0b"

							a__					=					max(len(__lowerCAmelCase       ) ,   len(__lowerCAmelCase       )       )

							return "0b" + "".join(
							    str(int(char_a == '1' and char_b == '1'       )       )
							    for char_a, char_b in zip(a_binary.zfill(__lowerCAmelCase       ) ,   b_binary.zfill(__lowerCAmelCase       )       )       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()








def 							__lowercase       (			__lowerCAmelCase							:    int       ):

							if num <= 0:
														raise ValueError('Input must be a positive integer'       )

							a__					=					[True] * (num + 1)

							a__					=					2
							while p * p <= num:
														if primes[p]:
																					for i in range(p * p ,   num + 1 ,   __lowerCAmelCase       ):
																												a__					=					False
														p += 1

							return [prime for prime in range(2 ,   num + 1       ) if primes[prime]]


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						snake_case							:	Optional[Any]					      =				int(input('''Enter a positive integer: ''').strip())
						print(prime_sieve_eratosthenes(user_num))




