






"""simple docstring"""


from ...configuration_utils import PretrainedConfig
from ...utils import logging


__SCREAMING_SNAKE_CASE   =   logging.get_logger(__name__)

__SCREAMING_SNAKE_CASE   =   {
    'alibaba-damo/mgp-str-base': 'https://huggingface.co/alibaba-damo/mgp-str-base/resolve/main/config.json',
}




class 						__UpperCamelCase     (     _snake_case						):
					lowercase_    :				Union[str, Any]      =  """mgp-str"""
					def __init__(							self							:	Dict     , UpperCAmelCase							:	str=[32, 128]     , UpperCAmelCase							:	List[str]=4     , UpperCAmelCase							:	Union[str, Any]=3     , UpperCAmelCase							:	Dict=27     , UpperCAmelCase							:	Tuple=38     , UpperCAmelCase							:	List[Any]=5_0257     , UpperCAmelCase							:	List[str]=3_0522     , UpperCAmelCase							:	Optional[Any]=768     , UpperCAmelCase							:	Dict=12     , UpperCAmelCase							:	Union[str, Any]=12     , UpperCAmelCase							:	Tuple=4.0     , UpperCAmelCase							:	List[str]=True     , UpperCAmelCase							:	int=False     , UpperCAmelCase							:	Optional[Any]=1e-5     , UpperCAmelCase							:	Union[str, Any]=0.0     , UpperCAmelCase							:	List[Any]=0.0     , UpperCAmelCase							:	Dict=0.0     , UpperCAmelCase							:	int=False     , UpperCAmelCase							:	Optional[int]=0.0_2     , **UpperCAmelCase							:	Any     , )	->       List[str]:
											super().__init__(**UpperCamelCase__   )

											lowerCAmelCase   :str						=			image_size
											lowerCAmelCase   :Optional[Any]						=			patch_size
											lowerCAmelCase   :Union[str, Any]						=			num_channels
											lowerCAmelCase   :List[str]						=			max_token_length
											lowerCAmelCase   :Tuple						=			num_character_labels
											lowerCAmelCase   :List[str]						=			num_bpe_labels
											lowerCAmelCase   :Tuple						=			num_wordpiece_labels
											lowerCAmelCase   :Dict						=			hidden_size
											lowerCAmelCase   :Optional[Any]						=			num_hidden_layers
											lowerCAmelCase   :Optional[Any]						=			num_attention_heads
											lowerCAmelCase   :Optional[int]						=			mlp_ratio
											lowerCAmelCase   :str						=			distilled
											lowerCAmelCase   :List[Any]						=			layer_norm_eps
											lowerCAmelCase   :Dict						=			drop_rate
											lowerCAmelCase   :Union[str, Any]						=			qkv_bias
											lowerCAmelCase   :Optional[int]						=			attn_drop_rate
											lowerCAmelCase   :Any						=			drop_path_rate
											lowerCAmelCase   :str						=			output_aa_attentions
											lowerCAmelCase   :Optional[Any]						=			initializer_range


'''simple docstring'''







from math import pow
def    UpperCAmelCase__     (   UpperCAmelCase__,							UpperCAmelCase__,							UpperCAmelCase__,							UpperCAmelCase__,							UpperCAmelCase__,							)      ->      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

       A_						       =   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
              A_       ,      A_						       =   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.
              A_       ,      A_						       =   backtrack(
                  UpperCAmelCase__,							UpperCAmelCase__,							current_number + 1,							UpperCAmelCase__,							UpperCAmelCase__					)
       return current_sum, solutions_count
def    UpperCAmelCase__     (   UpperCAmelCase__,							UpperCAmelCase__					)      ->      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(UpperCAmelCase__,							UpperCAmelCase__,							1,							0,							0					)[1]  # Return the solutions_count


if __name__ == "__main__":
      import doctest

      doctest.testmod()
