



"""simple docstring"""

from math import pow





def       __magic_name__    (   _lowerCamelCase				: int  ,       _lowerCamelCase				: int  ,       _lowerCamelCase				: int  ,       _lowerCamelCase				: int  ,       _lowerCamelCase				: 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		:		Optional[int]									=       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
														__a							,     __a		:		Optional[Any]									=       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.
														__a							,     __a		:		Any									=       backtrack(
														    _lowerCamelCase  ,       _lowerCamelCase  ,       current_number + 1  ,       _lowerCamelCase  ,       _lowerCamelCase					)
							return current_sum, solutions_count





def       __magic_name__    (   _lowerCamelCase				: int  ,       _lowerCamelCase				: int					):
							if not (1 <= needed_sum <= 1_0_0_0 and 2 <= power <= 1_0):
														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()






"""simple docstring"""

from dataclasses import dataclass
from enum import Enum
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import BaseOutput, is_torch_available, is_transformers_available




@dataclass
class SCREAMING_SNAKE_CASE__					(		__snake_case      ):
						_lowerCAmelCase							=					42
						_lowerCAmelCase							=					42


if is_transformers_available() and is_torch_available():
	from .pipeline_semantic_stable_diffusion import SemanticStableDiffusionPipeline

