
'''simple docstring'''



from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_torch_available


_lowercase          =						{
    """configuration_gpt_neo""": ["""GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPTNeoConfig""", """GPTNeoOnnxConfig"""],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_lowercase          =						[
						    """GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """GPTNeoForCausalLM""",
						    """GPTNeoForQuestionAnswering""",
						    """GPTNeoForSequenceClassification""",
						    """GPTNeoForTokenClassification""",
						    """GPTNeoModel""",
						    """GPTNeoPreTrainedModel""",
						    """load_tf_weights_in_gpt_neo""",
						]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_lowercase          =						[
						    """FlaxGPTNeoForCausalLM""",
						    """FlaxGPTNeoModel""",
						    """FlaxGPTNeoPreTrainedModel""",
						]


if TYPE_CHECKING:
						from .configuration_gpt_neo import GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoConfig, GPTNeoOnnxConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_gpt_neo import (
												    GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST,
												    GPTNeoForCausalLM,
												    GPTNeoForQuestionAnswering,
												    GPTNeoForSequenceClassification,
												    GPTNeoForTokenClassification,
												    GPTNeoModel,
												    GPTNeoPreTrainedModel,
												    load_tf_weights_in_gpt_neo,
												)

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flax_gpt_neo import FlaxGPTNeoForCausalLM, FlaxGPTNeoModel, FlaxGPTNeoPreTrainedModel


else:
						import sys

						_lowercase          =						_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



'''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()
