





def      A__       (    SCREAMING_SNAKE_CASE_   :      int				,	SCREAMING_SNAKE_CASE_   :      int						)  ->  str:






   """simple docstring"""







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

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

   _UpperCAmelCase           =   max(len(SCREAMING_SNAKE_CASE_						)				,	len(SCREAMING_SNAKE_CASE_						)						)

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()






from math import sqrt
def      A__       (    SCREAMING_SNAKE_CASE_   :      int						)  ->  bool:






   """simple docstring"""







   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(sqrt(SCREAMING_SNAKE_CASE_						) + 1						)				,	6						):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True
def      A__       (    SCREAMING_SNAKE_CASE_   :      int = 1_00_01						)  ->  int:






   """simple docstring"""







   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   1
   while count != nth and number < 3:
      number += 1
      if is_prime(SCREAMING_SNAKE_CASE_						):
         count += 1
   while count != nth:
      number += 2
      if is_prime(SCREAMING_SNAKE_CASE_						):
         count += 1
   return number


if __name__ == "__main__":
   print(f'''{solution() = }''')