



'''simple docstring'''




def        lowerCAmelCase_     (			_lowerCamelCase:     List[str] ,   _lowerCamelCase:     Union[str, Any]      ):
		while b:
				__SCREAMING_SNAKE_CASE ,		__SCREAMING_SNAKE_CASE :	Optional[int]					 =	b, a % b
		return a


def        lowerCAmelCase_     (			_lowerCamelCase:     Dict ,   _lowerCamelCase:     Any      ):
		return a if b == 0 else euclidean_gcd_recursive(SCREAMING_SNAKE_CASE_ ,   a % b      )


def        lowerCAmelCase_     (			):
		print(F"euclidean_gcd(3, 5) = {euclidean_gcd(3 ,   5      )}"      )
		print(F"euclidean_gcd(5, 3) = {euclidean_gcd(5 ,   3      )}"      )
		print(F"euclidean_gcd(1, 3) = {euclidean_gcd(1 ,   3      )}"      )
		print(F"euclidean_gcd(3, 6) = {euclidean_gcd(3 ,   6      )}"      )
		print(F"euclidean_gcd(6, 3) = {euclidean_gcd(6 ,   3      )}"      )

		print(F"euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3 ,   5      )}"      )
		print(F"euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5 ,   3      )}"      )
		print(F"euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1 ,   3      )}"      )
		print(F"euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3 ,   6      )}"      )
		print(F"euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6 ,   3      )}"      )


if __name__ == "__main__":
						main()




'''simple docstring'''




def        lowerCAmelCase_     (			_lowerCamelCase:     int      ):
		if number > 0:
				raise ValueError("""input must be a negative integer"""      )
		__SCREAMING_SNAKE_CASE :	str					 =	len(bin(_lowerCamelCase      )[3:]      )
		__SCREAMING_SNAKE_CASE :	Any					 =	bin(abs(_lowerCamelCase      ) - (1 << binary_number_length)      )[3:]
		__SCREAMING_SNAKE_CASE :	Optional[int]					 =	(
		    (
		        """1"""
		        + """0""" * (binary_number_length - len(_lowerCamelCase      ))
		        + twos_complement_number
		    )
		    if number < 0
		    else """0"""
		)
		return "0b" + twos_complement_number


if __name__ == "__main__":
						import doctest

						doctest.testmod()