


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

    snake_case					:   List[str]         =					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
        snake_case					:   Optional[int]         =					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.
        snake_case					:   Optional[Any]         =					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 <= 1000 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()









"""simple docstring"""



import os
import unittest

from transformers import LayoutLMTokenizer, LayoutLMTokenizerFast
from transformers.models.layoutlm.tokenization_layoutlm import VOCAB_FILES_NAMES
from transformers.testing_utils import require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin







@require_tokenizers
class _lowerCAmelCase       (   snake_case_					,							unittest.TestCase			):
   __UpperCAmelCase				: List[Any]													=						LayoutLMTokenizer
   __UpperCAmelCase				: List[Any]													=						LayoutLMTokenizerFast
   __UpperCAmelCase				: List[Any]													=						True
   __UpperCAmelCase				: Dict													=						True







   def 				lowerCamelCase	(			self		)			->	str:

       '''simple docstring'''




       super().setUp()

       snake_case					:   Dict         =					[
           "[UNK]",
           "[CLS]",
           "[SEP]",
           "want",
           "##want",
           "##ed",
           "wa",
           "un",
           "runn",
           "##ing",
           ",",
           "low",
           "lowest",
       ]
       snake_case					:   List[str]         =					os.path.join(self.tmpdirname		,			VOCAB_FILES_NAMES["vocab_file"]		)
       with open(self.vocab_file		,			"w"		,			encoding="utf-8"		) as vocab_writer:
           vocab_writer.write("".join([x + "\n" for x in vocab_tokens]		)		)







   def 				lowerCamelCase	(			self		,			**UpperCamelCase__		)			->	Dict:

       '''simple docstring'''




       return LayoutLMTokenizer.from_pretrained(self.tmpdirname		,			**UpperCamelCase__		)







   def 				lowerCamelCase	(			self		,			UpperCamelCase__		)			->	Tuple:

       '''simple docstring'''




       snake_case					:   str         =					"UNwant\u00E9d,running"
       snake_case					:   Optional[int]         =					"unwanted, running"
       return input_text, output_text







   def 				lowerCamelCase	(			self		)			->	Any:

       '''simple docstring'''




       snake_case					:   List[str]         =					self.tokenizer_class(self.vocab_file		)

       snake_case					:   Optional[Any]         =					tokenizer.tokenize("UNwant\u00E9d,running"		)
       self.assertListEqual(UpperCamelCase__		,			["un", "##want", "##ed", ",", "runn", "##ing"]		)
       self.assertListEqual(tokenizer.convert_tokens_to_ids(UpperCamelCase__		)		,			[7, 4, 5, 10, 8, 9]		)







   def 				lowerCamelCase	(			self		)			->	Dict:

       '''simple docstring'''




       pass





