from functools import lru_cache




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





from __future__ import annotations




class 					_snake_case						:
					def __init__(  self:				List[Any]	,  __lowerCamelCase:				int = 0     )    ->				None:
												__UpperCAmelCase						:			Dict         =   value
												__UpperCAmelCase						:			Node | None         =   None
												__UpperCAmelCase						:			Node | None         =   None




def   _UpperCamelCase   (			snake_case__,    snake_case__							)						->   Node | None:
							if treea is None:
														return treea
							if treea is None:
														return treea

							__UpperCAmelCase						:			Tuple         =   treea.value + treea.value
							__UpperCAmelCase						:			Optional[Any]         =   merge_two_binary_trees(treea.left,    treea.left							)
							__UpperCAmelCase						:			List[str]         =   merge_two_binary_trees(treea.right,    treea.right							)
							return treea




def   _UpperCamelCase   (			snake_case__							)						->   None:
							if root:
														print(root.value							)
														print_preorder(root.left							)
														print_preorder(root.right							)


if __name__ == "__main__":
	_snake_case			=						Node(1)
	_snake_case			=						Node(2)
	_snake_case			=						Node(3)
	_snake_case			=						Node(4)

	_snake_case			=						Node(2)
	_snake_case			=						Node(4)
	_snake_case			=						Node(6)
	_snake_case			=						Node(9)
	_snake_case			=						Node(5)

	print('''Tree1 is: ''')
	print_preorder(treea)
	print('''Tree2 is: ''')
	print_preorder(treea)
	_snake_case			=						merge_two_binary_trees(treea, treea)
	print('''Merged Tree is: ''')
	print_preorder(merged_tree)




