'''
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[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]
'''
# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
        
    def insertIntoMaxTree(self, root, val):
        """
        :type root: TreeNode
        :type val: int
        :rtype: TreeNode
        """
        new_node = TreeNode(val)
        if not root:
            return new_node
        
        if root.val < val:
            new_node.left = root
            return new_node
        
        nrwwt = root
        start, prev = root.right, root
    
        while start:
            if(start.val > val):
                prev = start
                start = start.right
            else:
                break
            

        prev.right = new_node
        if not start:
            new_node.right = start
        else:
            new_node.left = start
        
        return root
        
