



"""simple docstring"""




from math import pow


def      lowercase__   (	_UpperCAmelCase		,					_UpperCAmelCase		,					_UpperCAmelCase		,					_UpperCAmelCase		,					_UpperCAmelCase		,					)   ->	tuple[int, int]:






      '''simple docstring'''


      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

      lowercase     :					List[str] 		=      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
            lowercase		,			lowercase     :					List[str] 		=      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.
            lowercase		,			lowercase     :					Optional[Any] 		=      backtrack(
                UpperCamelCase_		,					UpperCamelCase_		,					current_number + 1		,					UpperCamelCase_		,					UpperCamelCase_ )
      return current_sum, solutions_count


def      lowercase__   (	_UpperCAmelCase		,					_UpperCAmelCase )   ->	int:






      '''simple docstring'''


      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()


def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_		)		->		str:
					'''simple docstring'''


					if not isinstance(UpperCamelCase_	,	UpperCamelCase_		):
										raise ValueError('iterations must be defined as integers'		)
					if not isinstance(UpperCamelCase_	,	UpperCamelCase_		) or not number >= 1:
										raise ValueError(
										    'starting number must be\n                         and integer and be more than 0'		)
					if not iterations >= 1:
										raise ValueError('Iterations must be done more than 0 times to play FizzBuzz'		)

					SCREAMING_SNAKE_CASE__													= ''
					while number <= iterations:
										if number % 3 == 0:
															out += "Fizz"
										if number % 5 == 0:
															out += "Buzz"
										if 0 not in (number % 3, number % 5):
															out += str(UpperCamelCase_		)

										# print(out)
										number += 1
										out += " "
					return out


if __name__ == "__main__":
				import doctest

				doctest.testmod()





