



'''simple docstring'''




from typing import TYPE_CHECKING

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


lowerCamelCase							:Optional[Any]				    =					{
    '''configuration_gpt_neo''': ['''GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''GPTNeoConfig''', '''GPTNeoOnnxConfig'''],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase							:Optional[Any]				    =					[
						    '''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:
						lowerCamelCase							:int				    =					[
						    '''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

						lowerCamelCase							:str				    =					_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




'''simple docstring'''




from math import pow



def 	a			( lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__						,      ):
			'''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

			A_	:						Optional[int]	=     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
						A_,    A_	:						int	=     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.
						A_,    A_	:						int	=     backtrack(
						    lowerCamelCase__						,      lowerCamelCase__						,      current_number + 1						,      lowerCamelCase__						,      lowerCamelCase__    )
			return current_sum, solutions_count



def 	a			( lowerCamelCase__						,      lowerCamelCase__    ):
			'''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(lowerCamelCase__						,      lowerCamelCase__						,      1						,      0						,      0    )[1]  # Return the solutions_count


if __name__ == "__main__":
						import doctest

						doctest.testmod()