

"""simple docstring"""
def 					a__						(						lowerCAmelCase = 1			,	lowerCAmelCase = 10_00    )	-> int:
      UpperCAmelCase__			:							Optional[int]							=    1
      UpperCAmelCase__			:							Union[str, Any]							=    0

      for divide_by_number in range(lowerCAmelCase			,	digit + 1    ):
            UpperCAmelCase__			:							list[int]							=    []
            UpperCAmelCase__			:							Dict							=    numerator
            for _ in range(1			,	digit + 1    ):
                  if now_divide in has_been_divided:
                        if longest_list_length < len(lowerCAmelCase    ):
                              UpperCAmelCase__			:							List[str]							=    len(lowerCAmelCase    )
                              UpperCAmelCase__			:							List[str]							=    divide_by_number
                  else:
                        has_been_divided.append(lowerCAmelCase    )
                        UpperCAmelCase__			:							str							=    now_divide * 10 % divide_by_number

      return the_digit


# Tests
if __name__ == "__main__":
    import doctest

    doctest.testmod()




"""simple docstring"""
def 					a__						(						lowerCAmelCase			,	lowerCAmelCase    )	-> str:
      if a < 0 or b < 0:
            raise ValueError("""the value of both inputs must be positive"""    )

      UpperCAmelCase__			:							Dict							=    str(bin(lowerCAmelCase    )    )[2:]  # remove the leading "0b"
      UpperCAmelCase__			:							Any							=    str(bin(lowerCAmelCase    )    )[2:]  # remove the leading "0b"

      UpperCAmelCase__			:							Optional[Any]							=    max(len(lowerCAmelCase    )			,	len(lowerCAmelCase    )    )

      return "0b" + "".join(
          str(int(char_a != char_b    )    )
          for char_a, char_b in zip(a_binary.zfill(lowerCAmelCase    )			,	b_binary.zfill(lowerCAmelCase    )    )    )


if __name__ == "__main__":
    import doctest

    doctest.testmod()

