# 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:
    # Perform reverse in-order traversal of the given BST.
    # This will give us numbers in descending order as we
    # touch each node.
    #
    # Right subtree -> Current node -> Left subtree
    #
    def convertBST(self, root: Optional[TreeNode]) -> Optional[TreeNode]:
        self.walk(root, 0)
        
        return root
    
    # `total` will be the state used to keep the sum of
    # all numbers greater than `node.val`
    def walk(self, node, total):
        if node is not None:
            # Since all nums to the right will be greater
            # than current, we need to get the total of
            # the right subtree
            right_total = self.walk(node.right, total)
            
            # Need to store the new total based on the right
            # subtree's total we obtained
            next_total = node.val + right_total
            
            # Update current node's total to its value plus
            # total of all numbers greater than it (i.e right
            # subtree)
            node.val = next_total
            
            # If there's a left subtree, it could mean that the
            # there might be a new total that we need to return one
            # level down the call stack
            next_total = self.walk(node.left, next_total)
            
            return next_total
        
        # If node isn't present, we can't just return 0.
        #
        # 0 would be valid for the very first rightmost subtree.
        # But as soon as we touch left subtrees, `total` could
        # be different from initial 0 we pass
        return total