


from math import pow

def 			_a  (				SCREAMING_SNAKE_CASE	:				List[str]    , SCREAMING_SNAKE_CASE	:				List[Any]    , SCREAMING_SNAKE_CASE	:				Union[str, Any]    , SCREAMING_SNAKE_CASE	:				Tuple    , SCREAMING_SNAKE_CASE	:				List[str]    , ):







 """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

 UpperCamelCase__					:    str          =   int(pow(SCREAMING_SNAKE_CASE    , SCREAMING_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
  UpperCamelCase__       ,				UpperCamelCase__					:    int          =   backtrack(
      SCREAMING_SNAKE_CASE    , SCREAMING_SNAKE_CASE    , current_number + 1    , SCREAMING_SNAKE_CASE    , SCREAMING_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.
  UpperCamelCase__       ,				UpperCamelCase__					:    List[str]          =   backtrack(
      SCREAMING_SNAKE_CASE    , SCREAMING_SNAKE_CASE    , current_number + 1    , SCREAMING_SNAKE_CASE    , SCREAMING_SNAKE_CASE     )
 return current_sum, solutions_count

def 			_a  (				SCREAMING_SNAKE_CASE	:				Dict    , SCREAMING_SNAKE_CASE	:				Dict     ):







 """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(SCREAMING_SNAKE_CASE    , SCREAMING_SNAKE_CASE    , 1    , 0    , 0     )[1]  # Return the solutions_count


if __name__ == "__main__":
       import doctest

       doctest.testmod()






from collections import OrderedDict
from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


__UpperCamelCase       :       Any						       =				logging.get_logger(__name__)

__UpperCamelCase       :       Any						       =				{
    "andreasmadsen/efficient_mlm_m0.40": (
        "https://huggingface.co/andreasmadsen/efficient_mlm_m0.40/resolve/main/config.json"
    ),
}

class       __magic_name__	(     __lowerCAmelCase):
     A:		List[Any]			=      "roberta-prelayernorm"


     def __init__(      self							:     Tuple							,	lowerCamelCase__							:     List[Any]=50265							,	lowerCamelCase__							:     Optional[Any]=768							,	lowerCamelCase__							:     str=12							,	lowerCamelCase__							:     Union[str, Any]=12							,	lowerCamelCase__							:     Dict=3072							,	lowerCamelCase__							:     int="gelu"							,	lowerCamelCase__							:     Tuple=0.1							,	lowerCamelCase__							:     Tuple=0.1							,	lowerCamelCase__							:     List[str]=512							,	lowerCamelCase__							:     int=2							,	lowerCamelCase__							:     Tuple=0.02							,	lowerCamelCase__							:     List[Any]=1E-1_2							,	lowerCamelCase__							:     str=1							,	lowerCamelCase__							:     int=0							,	lowerCamelCase__							:     int=2							,	lowerCamelCase__							:     Union[str, Any]="absolute"							,	lowerCamelCase__							:     Optional[Any]=True							,	lowerCamelCase__							:     Dict=None							,	**lowerCamelCase__							:     Any							,	)  ->      Optional[int]:





      '''simple docstring'''






      super().__init__(pad_token_id=lowerCamelCase__							,	bos_token_id=lowerCamelCase__							,	eos_token_id=lowerCamelCase__							,	**lowerCamelCase__			)

      UpperCamelCase__					:    Optional[int]          =   vocab_size
      UpperCamelCase__					:    Union[str, Any]          =   hidden_size
      UpperCamelCase__					:    List[str]          =   num_hidden_layers
      UpperCamelCase__					:    Optional[int]          =   num_attention_heads
      UpperCamelCase__					:    List[str]          =   hidden_act
      UpperCamelCase__					:    Optional[int]          =   intermediate_size
      UpperCamelCase__					:    Optional[int]          =   hidden_dropout_prob
      UpperCamelCase__					:    List[str]          =   attention_probs_dropout_prob
      UpperCamelCase__					:    Optional[int]          =   max_position_embeddings
      UpperCamelCase__					:    Optional[Any]          =   type_vocab_size
      UpperCamelCase__					:    Union[str, Any]          =   initializer_range
      UpperCamelCase__					:    Dict          =   layer_norm_eps
      UpperCamelCase__					:    Union[str, Any]          =   position_embedding_type
      UpperCamelCase__					:    Optional[int]          =   use_cache
      UpperCamelCase__					:    int          =   classifier_dropout



class       __magic_name__	(     __lowerCAmelCase):


     @property
     def      UpperCAmelCase__	(      self							:     int			)  ->      Mapping[str, Mapping[int, str]]:





      '''simple docstring'''






      if self.task == "multiple-choice":
       UpperCamelCase__					:    Dict          =   {0: '''batch''', 1: '''choice''', 2: '''sequence'''}
      else:
       UpperCamelCase__					:    Any          =   {0: '''batch''', 1: '''sequence'''}
      return OrderedDict(
          [
              ('''input_ids''', dynamic_axis),
              ('''attention_mask''', dynamic_axis),
          ]			)


