



from math import pow






def      lowerCAmelCase__		(   lowerCamelCase_		:		int	,lowerCamelCase_		:		int	,lowerCamelCase_		:		int	,lowerCamelCase_		:		int	,lowerCamelCase_		:		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

				lowerCAmelCase__					:    Tuple												=					int(pow(lowerCamelCase_	,lowerCamelCase_))
				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__					:    int												=					backtrack(
								    lowerCamelCase_	,lowerCamelCase_	,current_number + 1	,lowerCamelCase_	,lowerCamelCase_)
								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__					:    Any												=					backtrack(
								    lowerCamelCase_	,lowerCamelCase_	,current_number + 1	,lowerCamelCase_	,lowerCamelCase_)
				return current_sum, solutions_count






def      lowerCAmelCase__		(   lowerCamelCase_		:		int	,lowerCamelCase_		:		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(lowerCamelCase_	,lowerCamelCase_	,1	,0	,0)[1]  # Return the solutions_count


if __name__ == "__main__":
							import doctest

							doctest.testmod()






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


__snake_case    :		Any  =logging.get_logger(__name__)

__snake_case    :		Tuple  ={
    'sayakpaul/vit-msn-base': 'https://huggingface.co/sayakpaul/vit-msn-base/resolve/main/config.json',
    # See all ViT MSN models at https://huggingface.co/models?filter=vit_msn
}



class 	lowerCamelCase__      (							lowerCamelCase__):




		'''simple docstring'''



		snake_case_     ="""vit_msn"""



		def __init__(self		,__lowerCamelCase=7_68		,__lowerCamelCase=12		,__lowerCamelCase=12		,__lowerCamelCase=30_72		,__lowerCamelCase="gelu"		,__lowerCamelCase=0.0		,__lowerCamelCase=0.0		,__lowerCamelCase=0.02		,__lowerCamelCase=1e-06		,__lowerCamelCase=2_24		,__lowerCamelCase=16		,__lowerCamelCase=3		,__lowerCamelCase=True		,**__lowerCamelCase		,)					->      Any:

						"""simple docstring"""






						super().__init__(**__lowerCamelCase			)

						lowerCAmelCase__					:    List[Any]												=					hidden_size
						lowerCAmelCase__					:    str												=					num_hidden_layers
						lowerCAmelCase__					:    List[str]												=					num_attention_heads
						lowerCAmelCase__					:    Optional[int]												=					intermediate_size
						lowerCAmelCase__					:    List[Any]												=					hidden_act
						lowerCAmelCase__					:    Tuple												=					hidden_dropout_prob
						lowerCAmelCase__					:    List[Any]												=					attention_probs_dropout_prob
						lowerCAmelCase__					:    int												=					initializer_range
						lowerCAmelCase__					:    Union[str, Any]												=					layer_norm_eps
						lowerCAmelCase__					:    List[str]												=					image_size
						lowerCAmelCase__					:    str												=					patch_size
						lowerCAmelCase__					:    Optional[int]												=					num_channels
						lowerCAmelCase__					:    int												=					qkv_bias

