We are given the root node of a maximum tree: a tree where every node has a value greater than any other value in its subtree.

Just as in the previous problem, the given tree was constructed from an list A (root = Construct(A)) recursively with the following Construct(A) routine:

• If A is empty, return null.
• Otherwise, let A[i] be the largest element of A.  Create a root node with value A[i].
• The left child of root will be Construct([A, A, ..., A[i-1]])
• The right child of root will be Construct([A[i+1], A[i+2], ..., A[A.length - 1]])
• Return root.

Note that we were not given A directly, only a root node root = Construct(A).

Suppose B is a copy of A with the value val appended to it.  It is guaranteed that B has unique values.

Return Construct(B).

Example 1:

Input: root = [4,1,3,null,null,2], val = 5
Output: [5,4,null,1,3,null,null,2]
Explanation: A = [1,4,2,3], B = [1,4,2,3,5]


Example 2:

Input: root = [5,2,4,null,1], val = 3
Output: [5,2,4,null,1,null,3]
Explanation: A = [2,1,5,4], B = [2,1,5,4,3]


Example 3:

Input: root = [5,2,3,null,1], val = 4
Output: [5,2,4,null,1,3]
Explanation: A = [2,1,5,3], B = [2,1,5,3,4]


Note:

1. 1 <= B.length <= 100

## Solution: Recursion

Since val is the last element of the array, we compare root->val with val, if root->val > val then val can be inserted into the right subtree recursively, otherwise, root will be the left subtree of val.

Time complexity: O(n)
Space complexity: O(n)

## C++

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