


from math import pow




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							)  ->    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

       lowercase__:       int        =       int(pow(snake_case      ,							snake_case					)					)
       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
              lowercase__      ,						lowercase__:       Any        =       backtrack(
                  snake_case      ,							snake_case      ,							current_number + 1      ,							snake_case      ,							snake_case					)
              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.
              lowercase__      ,						lowercase__:       Optional[int]        =       backtrack(
                  snake_case      ,							snake_case      ,							current_number + 1      ,							snake_case      ,							snake_case					)
       return current_sum, solutions_count




def        snake_case_					(  snake_case      ,							snake_case					)  ->    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(snake_case      ,							snake_case      ,							1      ,							0      ,							0					)[1]  # Return the solutions_count


if __name__ == "__main__":
 import doctest

 doctest.testmod()






import os
from typing import Dict, List, Union

import tensorflow as tf
from keras_nlp.tokenizers import BytePairTokenizer
from tensorflow_text import pad_model_inputs

from .tokenization_gpta import GPTaTokenizer





class   __a      (   tf.keras.layers.Layer				):
 def __init__(       self    ,			lowerCAmelCase__    ,			lowerCAmelCase__    ,			lowerCAmelCase__ = None    ,			lowerCAmelCase__ = None			) ->    int:




        '''simple docstring'''
        super().__init__()
        lowercase__:       Union[str, Any]        =       pad_token_id
        lowercase__:       List[str]        =       max_length
        lowercase__:       int        =       vocab
        lowercase__:       List[Any]        =       merges
        lowercase__:       str        =       BytePairTokenizer(lowerCAmelCase__    ,			lowerCAmelCase__    ,			sequence_length=lowerCAmelCase__			)
 @classmethod
 def 		SCREAMING_SNAKE_CASE__       (       cls    ,			lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			) ->    Any:




        '''simple docstring'''
        lowercase__:       Tuple        =       [' '.join(lowerCAmelCase__			) for m in tokenizer.bpe_ranks.keys()]
        lowercase__:       List[Any]        =       tokenizer.get_vocab()
        return cls(lowerCAmelCase__    ,			lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			)
 @classmethod
 def 		SCREAMING_SNAKE_CASE__       (       cls    ,			lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			) ->    List[Any]:




        '''simple docstring'''
        lowercase__:       int        =       GPTaTokenizer.from_pretrained(lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			)
        return cls.from_tokenizer(lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			)
 @classmethod
 def 		SCREAMING_SNAKE_CASE__       (       cls    ,			lowerCAmelCase__			) ->    Dict:




        '''simple docstring'''
        return cls(**lowerCAmelCase__			)
 def 		SCREAMING_SNAKE_CASE__       (       self			) ->    List[Any]:




        '''simple docstring'''
        return {
            "vocab": self.vocab,
            "merges": self.merges,
            "max_length": self.max_length,
            "pad_token_id": self.pad_token_id,
        }
 def 		SCREAMING_SNAKE_CASE__       (       self    ,			lowerCAmelCase__    ,			lowerCAmelCase__ = None			) ->    Optional[Any]:




        '''simple docstring'''
        lowercase__:       Optional[Any]        =       self.tf_tokenizer(lowerCAmelCase__			)
        lowercase__:       List[Any]        =       tf.ones_like(lowerCAmelCase__			)

        if self.pad_token_id is not None:
               # pad the tokens up to max length
               lowercase__:       int        =       max_length if max_length is not None else self.max_length

               if max_length is not None:
                      lowercase__      ,						lowercase__:       List[Any]        =       pad_model_inputs(
                          lowerCAmelCase__    ,			max_seq_length=lowerCAmelCase__    ,			pad_value=self.pad_token_id			)

        return {"attention_mask": attention_mask, "input_ids": input_ids}


