




"""simple docstring"""

from __future__ import annotations




def       snake_case__	(       lowerCAmelCase   :		Union[str, Any]		):



					if len(__A		) == 0:
										raise ValueError("""find_max() arg is an empty sequence"""		)
					__snake_case          =	nums[0]
					for x in nums:
										if x > max_num:
															__snake_case          =	x
					return max_num


if __name__ == "__main__":
		import doctest

		doctest.testmod(verbose=True)








"""simple docstring"""

from functools import lru_cache




@lru_cache
def       snake_case__	(       lowerCAmelCase   :		int		):
					if not isinstance(lowerCAmelCase				,					lowerCAmelCase		):
										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       snake_case__	(       lowerCAmelCase   :		list				,					lowerCAmelCase   :		int		):
					__snake_case          =	len(lowerCAmelCase		)
					# Find m such that F_m >= n where F_i is the i_th fibonacci number.
					__snake_case          =	0
					while True:
										if fibonacci(lowerCAmelCase		) >= len_list:
															__snake_case          =	i
															break
										i += 1
					__snake_case          =	0
					while fibb_k > 0:
										__snake_case          =	min(
										    offset + fibonacci(fibb_k - 1		)				,					len_list - 1		)  # Prevent out of range
										__snake_case          =	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()


