"""
Given the root of a Binary Search Tree (BST), convert it to a Greater Tree such that every key of the original BST is changed to the original key plus the sum of all keys greater than the original key in BST.

As a reminder, a binary search tree is a tree that satisfies these constraints:

The left subtree of a node contains only nodes with keys less than the node's key.
The right subtree of a node contains only nodes with keys greater than the node's key.
Both the left and right subtrees must also be binary search trees.


Example 1:


Input: root = [4,1,6,0,2,5,7,null,null,null,3,null,null,null,8]
Output: [30,36,21,36,35,26,15,null,null,null,33,null,null,null,8]
Example 2:

Input: root = [0,null,1]
Output: [1,null,1]


Constraints:

The number of nodes in the tree is in the range [0, 10^4].
-10^4 <= Node.val <= 10^4
All the values in the tree are unique.
root is guaranteed to be a valid binary search tree.
"""
from typing import Optional


class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right


class ConvertBSTtoGreaterTree:
    sum = 0

    def convertBST(self, root: Optional[TreeNode]) -> Optional[TreeNode]:
        if not root:
            return root
        self.convertBST(root.right)
        self.sum += root.val
        root.val = self.sum
        self.convertBST(root.left)
        return root
