



from functools import lru_cache

@lru_cache
def      A_ (		__a       :			int						):

				"""simple docstring"""
				if not isinstance(__a	,						__a						):
								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      A_ (		__a       :			list	,						__a       :			int						):

				"""simple docstring"""
				a__			 =						len(__a						)
				# Find m such that F_m >= n where F_i is the i_th fibonacci number.
				a__			 =						0
				while True:
								if fibonacci(__a						) >= len_list:
												a__			 =						i
												break
								i += 1
				a__			 =						0
				while fibb_k > 0:
								a__			 =						min(
								    offset + fibonacci(fibb_k - 1						)	,						len_list - 1						)  # Prevent out of range
								a__			 =						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()






def      A_ (		__a       :			float						):

				"""simple docstring"""
				return int(__a						) if x - int(__a						) >= 0 else int(__a						) - 1


if __name__ == "__main__":
	import doctest

	doctest.testmod()

