



from functools import lru_cache





@lru_cache
def     __lowerCamelCase							(   __magic_name__						:	int    ):





							if not isinstance(UpperCAmelCase_  ,			UpperCAmelCase_    ):
														raise TypeError("k must be an integer."    )
							if k < 0:
														raise ValueError("k integer must be greater or equal to zero."    )
							if k == 0:
														return 0
							elif k == 1:
														return 1
							else:
														return fibonacci(k - 1    ) + fibonacci(k - 2    )





def     __lowerCamelCase							(   __magic_name__						:	list  ,			__magic_name__						:	int    ):
							a__:							int									=len(UpperCAmelCase_    )
							# Find m such that F_m >= n where F_i is the i_th fibonacci number.
							a__:							str									=0
							while True:
														if fibonacci(UpperCAmelCase_    ) >= len_list:
																					a__:							Any									=i
																					break
														i += 1
							a__:							List[str]									=0
							while fibb_k > 0:
														a__:							Tuple									=min(
														    offset + fibonacci(fibb_k - 1    )  ,			len_list - 1    )  # Prevent out of range
														a__:							Dict									=arr[index_k]
														if item_k_1 == val:
																					return index_k
														elif val < item_k_1:
																					fibb_k -= 1
														elif val > item_k_1:
																					offset += fibonacci(fibb_k - 1    )
																					fibb_k -= 2
							else:
														return -1


if __name__ == "__main__":
		import doctest

		doctest.testmod()






"""simple docstring"""







from typing import TypeVar

from .arrow_dataset import Dataset, _split_by_node_map_style_dataset
from .iterable_dataset import IterableDataset, _split_by_node_iterable_dataset


_a	:	List[Any]=					TypeVar("DatasetType", Dataset, IterableDataset)
def     __UpperCAmelCase							(       UpperCAmelCase_       :							DatasetType     ,				UpperCAmelCase_       :							int     ,				UpperCAmelCase_       :							int    )				->     DatasetType:

	'''simple docstring'''





	if isinstance(UpperCAmelCase_     ,				UpperCAmelCase_    ):
		return _split_by_node_map_style_dataset(UpperCAmelCase_     ,				rank=UpperCAmelCase_     ,				world_size=UpperCAmelCase_    )
	else:
		return _split_by_node_iterable_dataset(UpperCAmelCase_     ,				rank=UpperCAmelCase_     ,				world_size=UpperCAmelCase_    )





