


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCAmelCase			=							{
    "configuration_time_series_transformer": [
        "TIME_SERIES_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "TimeSeriesTransformerConfig",
    ],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __lowerCAmelCase			=							[
     "TIME_SERIES_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
     "TimeSeriesTransformerForPrediction",
     "TimeSeriesTransformerModel",
     "TimeSeriesTransformerPreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_time_series_transformer import (
     TIME_SERIES_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
     TimeSeriesTransformerConfig,
 )

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_time_series_transformer import (
      TIME_SERIES_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      TimeSeriesTransformerForPrediction,
      TimeSeriesTransformerModel,
      TimeSeriesTransformerPreTrainedModel,
  )

else:
 import sys

 __lowerCAmelCase			=							_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



from math import pow




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							)  ->    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

       lowercase__:       int        =       int(pow(snake_case      ,							snake_case					)					)
       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__:       Any        =       backtrack(
                  snake_case      ,							snake_case      ,							current_number + 1      ,							snake_case      ,							snake_case					)
              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[int]        =       backtrack(
                  snake_case      ,							snake_case      ,							current_number + 1      ,							snake_case      ,							snake_case					)
       return current_sum, solutions_count




def        snake_case_					(  snake_case      ,							snake_case					)  ->    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(snake_case      ,							snake_case      ,							1      ,							0      ,							0					)[1]  # Return the solutions_count


if __name__ == "__main__":
 import doctest

 doctest.testmod()


