
from math import pow



def   __lowerCAmelCase    (				UpperCAmelCase__					:   int      ,					UpperCAmelCase__					:   int      ,					UpperCAmelCase__					:   int      ,					UpperCAmelCase__					:   int      ,					UpperCAmelCase__					:   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

							lowerCamelCase_					=       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
														lowerCamelCase_	, lowerCamelCase_					=       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.
														lowerCamelCase_	, lowerCamelCase_					=       backtrack(
														    UpperCAmelCase__      ,					UpperCAmelCase__      ,					current_number + 1      ,					UpperCAmelCase__      ,					UpperCAmelCase__							)
							return current_sum, solutions_count



def   __lowerCAmelCase    (				UpperCAmelCase__					:   int      ,					UpperCAmelCase__					:   int							)	->     int:
							if not (1 <= needed_sum <= 1_0_0_0 and 2 <= power <= 1_0):
														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()







import os
import sys

lowercase   =	os.path.join(os.path.dirname(__file__), '''src''')
sys.path.append(SRC_DIR)


from transformers import (
    AutoConfig,
    AutoModel,
    AutoModelForCausalLM,
    AutoModelForMaskedLM,
    AutoModelForQuestionAnswering,
    AutoModelForSequenceClassification,
    AutoTokenizer,
    add_start_docstrings,
)


lowercase   =	[
    '''torch''',
    '''numpy''',
    '''tokenizers''',
    '''filelock''',
    '''requests''',
    '''tqdm''',
    '''regex''',
    '''sentencepiece''',
    '''sacremoses''',
    '''importlib_metadata''',
    '''huggingface_hub''',
]



@add_start_docstrings(AutoConfig.__doc__							)
def   __lowerCAmelCase    (				*UpperCAmelCase__					:   List[Any]      ,					**UpperCAmelCase__					:   List[str]							)	->     List[str]:
							return AutoConfig.from_pretrained(*UpperCAmelCase__      ,					**UpperCAmelCase__							)



@add_start_docstrings(AutoTokenizer.__doc__							)
def   __lowerCAmelCase    (				*UpperCAmelCase__					:   List[str]      ,					**UpperCAmelCase__					:   List[Any]							)	->     Any:
							return AutoTokenizer.from_pretrained(*UpperCAmelCase__      ,					**UpperCAmelCase__							)



@add_start_docstrings(AutoModel.__doc__							)
def   __lowerCAmelCase    (				*UpperCAmelCase__					:   Union[str, Any]      ,					**UpperCAmelCase__					:   Dict							)	->     Union[str, Any]:
							return AutoModel.from_pretrained(*UpperCAmelCase__      ,					**UpperCAmelCase__							)



@add_start_docstrings(AutoModelForCausalLM.__doc__							)
def   __lowerCAmelCase    (				*UpperCAmelCase__					:   List[str]      ,					**UpperCAmelCase__					:   List[Any]							)	->     Optional[Any]:
							return AutoModelForCausalLM.from_pretrained(*UpperCAmelCase__      ,					**UpperCAmelCase__							)



@add_start_docstrings(AutoModelForMaskedLM.__doc__							)
def   __lowerCAmelCase    (				*UpperCAmelCase__					:   Union[str, Any]      ,					**UpperCAmelCase__					:   Dict							)	->     int:
							return AutoModelForMaskedLM.from_pretrained(*UpperCAmelCase__      ,					**UpperCAmelCase__							)



@add_start_docstrings(AutoModelForSequenceClassification.__doc__							)
def   __lowerCAmelCase    (				*UpperCAmelCase__					:   List[Any]      ,					**UpperCAmelCase__					:   Dict							)	->     Dict:
							return AutoModelForSequenceClassification.from_pretrained(*UpperCAmelCase__      ,					**UpperCAmelCase__							)



@add_start_docstrings(AutoModelForQuestionAnswering.__doc__							)
def   __lowerCAmelCase    (				*UpperCAmelCase__					:   Any      ,					**UpperCAmelCase__					:   List[str]							)	->     Union[str, Any]:
							return AutoModelForQuestionAnswering.from_pretrained(*UpperCAmelCase__      ,					**UpperCAmelCase__							)





