Please solve the programming task below using a self-contained code snippet in a markdown code block.

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).
 
Please complete the following python code precisely:
```python
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def insertIntoMaxTree(self, root: Optional[TreeNode], val: int) -> Optional[TreeNode]:
```