






def      lowercase__      (     __snake_case    :							int     ,       __snake_case    :							int  ):


					'''simple docstring'''


					while b:
										UpperCAmelCase_       ,  UpperCAmelCase_    :      List[Any]            =						b, a % b
					return a




def      lowercase__      (     __snake_case    :							int     ,       __snake_case    :							int  ):


					'''simple docstring'''


					return a if b == 0 else euclidean_gcd_recursive(__snake_case     ,       a % b  )




def      lowercase__      (     ):


					'''simple docstring'''


					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_						(UpperCamelCase__		:		int     ,       UpperCamelCase__		:		int							):
    if a < 0 or b < 0:
        raise ValueError('''the value of both inputs must be positive'''							)
    _UpperCAmelCase							:  List[str]											=    str(bin(UpperCamelCase__							)							)[2:]  # remove the leading "0b"
    _UpperCAmelCase							:  str											=    str(bin(UpperCamelCase__							)							)[2:]
    _UpperCAmelCase							:  List[str]											=    max(len(UpperCamelCase__							)     ,       len(UpperCamelCase__							)							)
    return "0b" + "".join(
        str(int('''1''' in (char_a, char_b)							)							)
        for char_a, char_b in zip(a_binary.zfill(UpperCamelCase__							)     ,       b_binary.zfill(UpperCamelCase__							)							)							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()


