






"""simple docstring"""


def        UpperCAmelCase      (					a__     ,      a__ ):





						'''simple docstring'''






						lowerCAmelCase   :str						=			''
						for word_or_phrase in separated:
												if not isinstance(UpperCAmelCase__     ,      UpperCAmelCase__ ):
																		raise Exception('join() accepts only strings to be joined' )
												joined += word_or_phrase + separator
						return joined.strip(UpperCAmelCase__ )


if __name__ == "__main__":
		from doctest import testmod

		testmod()


'''simple docstring'''







from math import pow
def    UpperCAmelCase__     (   UpperCAmelCase__,							UpperCAmelCase__,							UpperCAmelCase__,							UpperCAmelCase__,							UpperCAmelCase__,							)      ->      tuple[int, int]:
       if current_sum == needed_sum:
              # If the sum of the powers is equal to needed_sum, then we have a solution.
              solutions_count += 1
              return current_sum, solutions_count

       A_						       =   int(pow(UpperCAmelCase__,							UpperCAmelCase__					)					)
       if current_sum + i_to_n <= needed_sum:
              # If the sum of the powers is less than needed_sum, then continue adding powers.
              current_sum += i_to_n
              A_       ,      A_						       =   backtrack(
                  UpperCAmelCase__,							UpperCAmelCase__,							current_number + 1,							UpperCAmelCase__,							UpperCAmelCase__					)
              current_sum -= i_to_n
       if i_to_n < needed_sum:
              # If the power of i is less than needed_sum, then try with the next power.
              A_       ,      A_						       =   backtrack(
                  UpperCAmelCase__,							UpperCAmelCase__,							current_number + 1,							UpperCAmelCase__,							UpperCAmelCase__					)
       return current_sum, solutions_count
def    UpperCAmelCase__     (   UpperCAmelCase__,							UpperCAmelCase__					)      ->      int:
       if not (1 <= needed_sum <= 10_00 and 2 <= power <= 10):
              raise ValueError(
                  """Invalid input\n"""
                  """needed_sum must be between 1 and 1000, power between 2 and 10."""					)

       return backtrack(UpperCAmelCase__,							UpperCAmelCase__,							1,							0,							0					)[1]  # Return the solutions_count


if __name__ == "__main__":
      import doctest

      doctest.testmod()
