
"""simple docstring"""



import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp
def 					_UpperCAmelCase      ( )     ->					Optional[Any]:
  _snake_case					     =       ArgumentParser(
      description=(
          '''PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes'''
      )		)

  # Optional arguments for the launch helper
  parser.add_argument('''--num_cores''' ,					type=__lowerCamelCase ,					default=1 ,					help='''Number of TPU cores to use (1 or 8).'''		)

  # positional
  parser.add_argument(
      '''training_script''' ,					type=__lowerCamelCase ,					help=(
          '''The full path to the single TPU training '''
          '''program/script to be launched in parallel, '''
          '''followed by all the arguments for the '''
          '''training script'''
      ) ,					)

  # rest from the training program
  parser.add_argument('''training_script_args''' ,					nargs=__lowerCamelCase		)

  return parser.parse_args()
def 					_UpperCAmelCase      ( )     ->					List[Any]:
  _snake_case					     =       parse_args()

  # Import training_script as a module.
  _snake_case					     =       Path(args.training_script		)
  sys.path.append(str(script_fpath.parent.resolve()		)		)
  _snake_case					     =       script_fpath.stem
  _snake_case					     =       importlib.import_module(__lowerCamelCase		)

  # Patch sys.argv
  _snake_case					     =       [args.training_script] + args.training_script_args + ['''--tpu_num_cores''', str(args.num_cores		)]

  xmp.spawn(mod._mp_fn ,					args=() ,					nprocs=args.num_cores		)


if __name__ == "__main__":
 main()





"""simple docstring"""



from math import pow
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					)     ->					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

  _snake_case					     =       int(pow(__lowerCamelCase ,					__lowerCamelCase		)		)
  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
    _snake_case     ,					_snake_case					     =       backtrack(
        __lowerCamelCase ,					__lowerCamelCase ,					current_number + 1 ,					__lowerCamelCase ,					__lowerCamelCase		)
    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.
    _snake_case     ,					_snake_case					     =       backtrack(
        __lowerCamelCase ,					__lowerCamelCase ,					current_number + 1 ,					__lowerCamelCase ,					__lowerCamelCase		)
  return current_sum, solutions_count
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int ,					__lowerCamelCase   :       int		)     ->					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(__lowerCamelCase ,					__lowerCamelCase ,					1 ,					0 ,					0		)[1]  # Return the solutions_count


if __name__ == "__main__":
 import doctest

 doctest.testmod()



