





"""simple docstring"""





from math import pow


def       a__					(					_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	):




		"""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   =	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   =	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   =	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  ,	_SCREAMING_SNAKE_CASE    ):




		"""simple docstring"""


		if not (1 <= needed_sum <= 1_000 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()













"""simple docstring"""





from typing import List

from .keymap import KEYMAP, get_character


def       a__					(					_SCREAMING_SNAKE_CASE    ):




		"""simple docstring"""


		def decorator(_SCREAMING_SNAKE_CASE    ):
				UpperCamelCase   =	getattr(_SCREAMING_SNAKE_CASE  ,	"handle_key"  ,	[]    )
				handle += [key]
				setattr(_SCREAMING_SNAKE_CASE  ,	"handle_key"  ,	_SCREAMING_SNAKE_CASE    )
				return func

		return decorator


def       a__					(					*_SCREAMING_SNAKE_CASE    ):




		"""simple docstring"""


		def decorator(_SCREAMING_SNAKE_CASE    ):
				UpperCamelCase   =	getattr(_SCREAMING_SNAKE_CASE  ,	"handle_key"  ,	[]    )
				handle += keys
				setattr(_SCREAMING_SNAKE_CASE  ,	"handle_key"  ,	_SCREAMING_SNAKE_CASE    )
				return func

		return decorator





class        _lowerCamelCase      (       _lowercase ):


						def __new__(cls   ,							__a   ,							__a   ,							__a		) ->   Any:
								UpperCamelCase   =	super().__new__(cls   ,							__a   ,							__a   ,							__a		)
								if not hasattr(__a   ,							"key_handler"		):
										setattr(__a   ,							"key_handler"   ,							{}		)
								setattr(__a   ,							"handle_input"   ,							KeyHandler.handle_input		)

								for value in attrs.values():
										UpperCamelCase   =	getattr(__a   ,							"handle_key"   ,							[]		)
										for key in handled_keys:
												UpperCamelCase   =	value
								return new_cls




						@staticmethod
						def     snake_case_   (cls		) ->   Optional[Any]:
								UpperCamelCase   =	get_character()
								if char != KEYMAP["undefined"]:
										UpperCamelCase   =	ord(__a		)
								UpperCamelCase   =	cls.key_handler.get(__a		)
								if handler:
										UpperCamelCase   =	char
										return handler(cls		)
								else:
										return None



def       a__					(					cls    ):




		"""simple docstring"""


		return KeyHandler(cls.__name__  ,	cls.__bases__  ,	cls.__dict__.copy()    )






