





"""simple docstring"""
def    A__							(     UpperCamelCase   ,    UpperCamelCase			):
							if not root or root not in binary_tree_mirror_dictionary:
														return
							A,      A						=    binary_tree_mirror_dictionary[root][:2]
							A						=    [right_child, left_child]
							binary_tree_mirror_dict(UpperCamelCase   ,    UpperCamelCase			)
							binary_tree_mirror_dict(UpperCamelCase   ,    UpperCamelCase			)






def    A__							(     UpperCamelCase   ,    UpperCamelCase = 1			):
							if not binary_tree:
														raise ValueError("binary tree cannot be empty"			)
							if root not in binary_tree:
														A						=    F"root {root} is not present in the binary_tree"
														raise ValueError(UpperCamelCase			)
							A						=    dict(UpperCamelCase			)
							binary_tree_mirror_dict(UpperCamelCase   ,    UpperCamelCase			)
							return binary_tree_mirror_dictionary


if __name__ == "__main__":
		_snake_case	:						str					=					{1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
		print(F"""Binary tree: {binary_tree}""")
		_snake_case	:						List[str]					=					binary_tree_mirror(binary_tree, 5)
		print(F"""Binary tree mirror: {binary_tree_mirror_dictionary}""")









"""simple docstring"""
from functools import lru_cache






@lru_cache
def    A__							(     UpperCamelCase			):
							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    A__							(     UpperCamelCase   ,    UpperCamelCase			):
							A						=    len(UpperCamelCase			)
							# Find m such that F_m >= n where F_i is the i_th fibonacci number.
							A						=    0
							while True:
														if fibonacci(UpperCamelCase			) >= 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()


