





from math import isqrt, loga
def      A__       (    SCREAMING_SNAKE_CASE_   :      int						)  ->  list[int]:






   """simple docstring"""







   _UpperCAmelCase           =   [True] * max_number
   for i in range(2				,	isqrt(max_number - 1						) + 1						):
      if is_prime[i]:
         for j in range(i**2				,	SCREAMING_SNAKE_CASE_				,	SCREAMING_SNAKE_CASE_						):
            _UpperCAmelCase           =   False

   return [i for i in range(2				,	SCREAMING_SNAKE_CASE_						) if is_prime[i]]
def      A__       (    SCREAMING_SNAKE_CASE_   :      int = 80_08_00				,	SCREAMING_SNAKE_CASE_   :      int = 80_08_00						)  ->  int:






   """simple docstring"""







   _UpperCAmelCase           =   degree * loga(SCREAMING_SNAKE_CASE_						)
   _UpperCAmelCase           =   int(SCREAMING_SNAKE_CASE_						)
   _UpperCAmelCase           =   calculate_prime_numbers(SCREAMING_SNAKE_CASE_						)

   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   len(SCREAMING_SNAKE_CASE_						) - 1
   while left < right:
      while (
          prime_numbers[right] * loga(prime_numbers[left]						)
          + prime_numbers[left] * loga(prime_numbers[right]						)
          > upper_bound
      ):
         right -= 1
      hybrid_integers_count += right - left
      left += 1

   return hybrid_integers_count


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






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()