





import os


# All paths are set with the intent you should run this script from the root of the repo with the command
# python utils/check_doctest_list.py
__A     =    "."


if __name__ == "__main__":
   __A     =    os.path.join(REPO_PATH, "utils/documentation_tests.txt")
   __A     =    []
   __A     =    []
   with open(doctest_file_path) as fp:
      for line in fp:
         __A     =    line.strip()
         __A     =    os.path.join(REPO_PATH, line)
         if not (os.path.isfile(path) or os.path.isdir(path)):
            non_existent_paths.append(line)
         all_paths.append(path)
   if len(non_existent_paths) > 0:
      __A     =    "\n".join(non_existent_paths)
      raise ValueError(f'`utils/documentation_tests.txt` contains non-existent paths:\n{non_existent_paths}')
   if all_paths != sorted(all_paths):
      raise ValueError("Files in `utils/documentation_tests.txt` are not in alphabetical order.")








from math import pow





def 					lowerCAmelCase_			(	__a     ,   __a     ,   __a     ,   __a     ,   __a     ,   )					->		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

  lowerCamelCase__:				Optional[Any]        =int(pow(__a     ,   __a		)		)
  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
    lowerCamelCase__  , lowerCamelCase__:				int        =backtrack(
        __a     ,   __a     ,   current_number + 1     ,   __a     ,   __a		)
    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.
    lowerCamelCase__  , lowerCamelCase__:				Dict        =backtrack(
        __a     ,   __a     ,   current_number + 1     ,   __a     ,   __a		)
  return current_sum, solutions_count





def 					lowerCAmelCase_			(	__a     ,   __a		)					->		int:







  """simple docstring"""





  if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
    raise ValueError(
        "Invalid input\n"
        "needed_sum must be between 1 and 1000, power between 2 and 10."		)

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()

