A maximum tree is a tree where every node has a value greater than any other value in its subtree.

You are given the `root` of a maximum binary tree and an integer `val`.

Just as in the previous problem, the given tree was constructed from a 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 the value `a[i]`.
- The left child of `root` will be `Construct([a[0], a[1], ..., 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]

Constraints:

- The number of nodes in the tree is in the range `[1, 100]`.
- `1 <= Node.val <= 100`
- All the values of the tree are unique.
- `1 <= val <= 100`