






from math import pow





def 	lowerCAmelCase_		(lowercase__						:       int     ,					lowercase__						:       int     ,					lowercase__						:       int     ,					lowercase__						:       int     ,					lowercase__						:       int     ,					)		->    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__      			=						int(pow(lowercase__     ,					lowercase__       )       )
				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__      			=						backtrack(
								    lowercase__     ,					lowercase__     ,					current_number + 1     ,					lowercase__     ,					lowercase__       )
								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__      			=						backtrack(
								    lowercase__     ,					lowercase__     ,					current_number + 1     ,					lowercase__     ,					lowercase__       )
				return current_sum, solutions_count





def 	lowerCAmelCase_		(lowercase__						:       int     ,					lowercase__						:       int       )		->    int:


				'''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(lowercase__     ,					lowercase__     ,					1     ,					0     ,					0       )[1]  # Return the solutions_count


if __name__ == "__main__":
			import doctest

			doctest.testmod()













from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_UpperCAmelCase			:		int   				=    {
    "configuration_git": ["GIT_PRETRAINED_CONFIG_ARCHIVE_MAP", "GitConfig", "GitVisionConfig"],
    "processing_git": ["GitProcessor"],
}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_UpperCAmelCase			:		Dict   				=    [
			    "GIT_PRETRAINED_MODEL_ARCHIVE_LIST",
			    "GitForCausalLM",
			    "GitModel",
			    "GitPreTrainedModel",
			    "GitVisionModel",
			]

if TYPE_CHECKING:
			from .configuration_git import GIT_PRETRAINED_CONFIG_ARCHIVE_MAP, GitConfig, GitVisionConfig
			from .processing_git import GitProcessor

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_git import (
						    GIT_PRETRAINED_MODEL_ARCHIVE_LIST,
						    GitForCausalLM,
						    GitModel,
						    GitPreTrainedModel,
						    GitVisionModel,
						)

else:
			import sys

			_UpperCAmelCase			:		Optional[int]   				=    _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





