





"""simple docstring"""





def 			UpperCAmelCase__							(  SCREAMING_SNAKE_CASE     :						int							,						SCREAMING_SNAKE_CASE     :						int			):







      '''simple docstring'''




      if a < 0 or b < 0:
            raise ValueError("""the value of both inputs must be positive"""			)
      lowerCAmelCase  						=       str(bin(SCREAMING_SNAKE_CASE			)			)[2:]  # remove the leading "0b"
      lowerCAmelCase  						=       str(bin(SCREAMING_SNAKE_CASE			)			)[2:]
      lowerCAmelCase  						=       max(len(SCREAMING_SNAKE_CASE			)							,						len(SCREAMING_SNAKE_CASE			)			)
      return "0b" + "".join(
          str(int("""1""" in (char_a, char_b)			)			)
          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()








class      A__							:






				def __init__(						self					:      Dict    ,     a					:      list[int]   ):






							'''simple docstring'''







							lowerCAmelCase__      :      Union[str, Any]         =		len(a   )
							lowerCAmelCase__      :      Optional[Any]         =		[0] * len_array

							if len_array > 0:
										lowerCAmelCase__      :      List[Any]         =		array[0]

							for i in range(1    ,     a   ):
										lowerCAmelCase__      :      Optional[int]         =		self.prefix_sum[i - 1] + array[i]






				def 							_lowerCamelCase		(						self					:      int    ,     a					:      int    ,     a					:      int   ):






							'''simple docstring'''







							if start == 0:
										return self.prefix_sum[end]

							return self.prefix_sum[end] - self.prefix_sum[start - 1]






				def 							_lowerCamelCase		(						self					:      Optional[Any]    ,     a					:      int   ):






							'''simple docstring'''







							lowerCAmelCase__      :      Any         =		{0}
							for sum_item in self.prefix_sum:
										if sum_item - target_sum in sums:
													return True

										sums.add(a   )

							return False


if __name__ == "__main__":
					import doctest

					doctest.testmod()