



'''simple docstring'''



from functools import lru_cache


@lru_cache
def 							__UpperCAmelCase				(				UpperCamelCase__				:int			)		->						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 							__UpperCAmelCase				(				UpperCamelCase__				:list   ,				UpperCamelCase__				:int			)		->						int:
				snake_case__      :   List[Any]      =    len(UpperCamelCase__			)
				# Find m such that F_m >= n where F_i is the i_th fibonacci number.
				snake_case__      :   Any      =    0
				while True:
								if fibonacci(UpperCamelCase__			) >= len_list:
												snake_case__      :   Union[str, Any]      =    i
												break
								i += 1
				snake_case__      :   Dict      =    0
				while fibb_k > 0:
								snake_case__      :   Optional[Any]      =    min(
								    offset + fibonacci(fibb_k - 1			)   ,				len_list - 1			)  # Prevent out of range
								snake_case__      :   str      =    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'''



import pytest

from datasets.utils.version import Version


@pytest.mark.parametrize(
    '''other, expected_equality'''   ,				[
        (Version('''1.0.0'''			), True),
        ('''1.0.0''', True),
        (Version('''2.0.0'''			), False),
        ('''2.0.0''', False),
        ('''1''', False),
        ('''a''', False),
        (1, False),
        (None, False),
    ]   ,				)
def 							__UpperCAmelCase				(				UpperCamelCase__				:Optional[int]   ,				UpperCamelCase__				:int			)		->						List[str]:
				snake_case__      :   Optional[int]      =    Version('''1.0.0'''			)
				assert (version == other) is expected_equality
				assert (version != other) is not expected_equality
				assert (hash(UpperCamelCase__			) == hash(UpperCamelCase__			)) is expected_equality




