



from math import pow
def  UpperCamelCase						(       _A			:				int			,							_A			:				int			,							_A			:				int			,							_A			:				int			,							_A			:				int			,							)->       tuple[int, 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

						A__							=       int(pow(_A			,							_A    )    )
						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(
												    _A			,							_A			,							current_number + 1			,							_A			,							_A    )
												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(
												    _A			,							_A			,							current_number + 1			,							_A			,							_A    )
						return current_sum, solutions_count
def  UpperCamelCase						(       _A			:				int			,							_A			:				int    )->       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(_A			,							_A			,							1			,							0			,							0    )[1]  # Return the solutions_count


if __name__ == "__main__":
		import doctest

		doctest.testmod()










import multiprocessing
import os
from typing import BinaryIO, Optional, Union

import fsspec

from .. import Dataset, Features, NamedSplit, config
from ..formatting import query_table
from ..packaged_modules.json.json import Json
from ..utils import logging
from ..utils.typing import NestedDataStructureLike, PathLike
from .abc import AbstractDatasetReader






class      UpperCamelCase    (						_UpperCAmelCase     ):



	def __init__(       self			,	UpperCAmelCase__			,	UpperCAmelCase__ = None			,	UpperCAmelCase__ = None			,	UpperCAmelCase__ = None			,	UpperCAmelCase__ = False			,	UpperCAmelCase__ = False			,	UpperCAmelCase__ = None			,	UpperCAmelCase__ = None			,	**UpperCAmelCase__			,	):
							super().__init__(
							    UpperCAmelCase__			,	split=UpperCAmelCase__			,	features=UpperCAmelCase__			,	cache_dir=UpperCAmelCase__			,	keep_in_memory=UpperCAmelCase__			,	streaming=UpperCAmelCase__			,	num_proc=UpperCAmelCase__			,	**UpperCAmelCase__			,	)
							A__							=       field
							A__							=       path_or_paths if isinstance(UpperCAmelCase__			,	UpperCAmelCase__		) else {self.split: path_or_paths}
							A__							=       Json(
							    cache_dir=UpperCAmelCase__			,	data_files=UpperCAmelCase__			,	features=UpperCAmelCase__			,	field=UpperCAmelCase__			,	**UpperCAmelCase__			,	)



	def 			__A							(       self		):
							# Build iterable dataset
							if self.streaming:
													A__							=       self.builder.as_streaming_dataset(split=self.split		)
							# Build regular (map-style) dataset
							else:
													A__							=       None
													A__							=       None
													A__							=       None
													A__							=       None

													self.builder.download_and_prepare(
													    download_config=UpperCAmelCase__			,	download_mode=UpperCAmelCase__			,	verification_mode=UpperCAmelCase__			,	base_path=UpperCAmelCase__			,	num_proc=self.num_proc			,	)
													A__							=       self.builder.as_dataset(
													    split=self.split			,	verification_mode=UpperCAmelCase__			,	in_memory=self.keep_in_memory		)
							return dataset






class      UpperCamelCase    :



	def __init__(       self			,	UpperCAmelCase__			,	UpperCAmelCase__			,	UpperCAmelCase__ = None			,	UpperCAmelCase__ = None			,	**UpperCAmelCase__			,	):
							if num_proc is not None and num_proc <= 0:
													raise ValueError(F"""num_proc {num_proc} must be an integer > 0."""		)

							A__							=       dataset
							A__							=       path_or_buf
							A__							=       batch_size if batch_size else config.DEFAULT_MAX_BATCH_SIZE
							A__							=       num_proc
							A__							=       "utf-8"
							A__							=       to_json_kwargs



	def 			__A							(       self		):
							A__							=       self.to_json_kwargs.pop("path_or_buf"			,	UpperCAmelCase__		)
							A__							=       self.to_json_kwargs.pop("orient"			,	"records"		)
							A__							=       self.to_json_kwargs.pop("lines"			,	True if orient == "records" else False		)
							A__							=       self.to_json_kwargs.pop("index"			,	False if orient in ["split", "table"] else True		)
							A__							=       self.to_json_kwargs.pop("compression"			,	UpperCAmelCase__		)

							if compression not in [None, "infer", "gzip", "bz2", "xz"]:
													raise NotImplementedError(F"""`datasets` currently does not support {compression} compression"""		)

							if isinstance(self.path_or_buf			,	(str, bytes, os.PathLike)		):
													with fsspec.open(self.path_or_buf			,	"wb"			,	compression=UpperCAmelCase__		) as buffer:
																			A__							=       self._write(file_obj=UpperCAmelCase__			,	orient=UpperCAmelCase__			,	lines=UpperCAmelCase__			,	index=UpperCAmelCase__			,	**self.to_json_kwargs		)
							else:
													if compression:
																			raise NotImplementedError(
																			    F"""The compression parameter is not supported when writing to a buffer, but compression={compression}"""
																			    " was passed. Please provide a local path instead."		)
													A__							=       self._write(
													    file_obj=self.path_or_buf			,	orient=UpperCAmelCase__			,	lines=UpperCAmelCase__			,	index=UpperCAmelCase__			,	**self.to_json_kwargs		)
							return written



	def 			__A							(       self			,	UpperCAmelCase__		):
							A__						,       A__						,       A__						,       A__						,       A__							=       args

							A__							=       query_table(
							    table=self.dataset.data			,	key=slice(UpperCAmelCase__			,	offset + self.batch_size		)			,	indices=self.dataset._indices			,	)
							A__							=       batch.to_pandas().to_json(
							    path_or_buf=UpperCAmelCase__			,	orient=UpperCAmelCase__			,	lines=UpperCAmelCase__			,	index=UpperCAmelCase__			,	**UpperCAmelCase__		)
							if not json_str.endswith("\n"		):
													json_str += "\n"
							return json_str.encode(self.encoding		)



	def 			__A							(       self			,	UpperCAmelCase__			,	UpperCAmelCase__			,	UpperCAmelCase__			,	UpperCAmelCase__			,	**UpperCAmelCase__			,	):
							A__							=       0

							if self.num_proc is None or self.num_proc == 1:
													for offset in logging.tqdm(
													    range(0			,	len(self.dataset		)			,	self.batch_size		)			,	unit="ba"			,	disable=not logging.is_progress_bar_enabled()			,	desc="Creating json from Arrow format"			,	):
																			A__							=       self._batch_json((offset, orient, lines, index, to_json_kwargs)		)
																			written += file_obj.write(UpperCAmelCase__		)
							else:
													A__						,       A__							=       len(self.dataset		), self.batch_size
													with multiprocessing.Pool(self.num_proc		) as pool:
																			for json_str in logging.tqdm(
																			    pool.imap(
																			        self._batch_json			,	[(offset, orient, lines, index, to_json_kwargs) for offset in range(0			,	UpperCAmelCase__			,	UpperCAmelCase__		)]			,	)			,	total=(num_rows // batch_size) + 1 if num_rows % batch_size else num_rows // batch_size			,	unit="ba"			,	disable=not logging.is_progress_bar_enabled()			,	desc="Creating json from Arrow format"			,	):
																									written += file_obj.write(UpperCAmelCase__		)

							return written





