# 1038. Binary Search Tree to Greater Sum Tree

Given the root of a binary **search** tree with distinct values, modify it so that every `node` has a new value equal to the sum of the values of the original tree that are greater than or equal to `node.val`.

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:**

![](https://assets.leetcode.com/uploads/2019/05/02/tree.png)

```
Input: [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]
```

**Note:**

1. The number of nodes in the tree is between `1` and `100`.
2. Each node will have value between `0` and `100`.
3. The given tree is a binary search tree.

```cpp
// Reverse In-Order Traversal
void helper(TreeNode*& node, int& preSum) {
    if (!node) return;
    helper(node->right, preSum);
    node->val += preSum;
    preSum = node->val;
    helper(node->left, preSum);
    return;
}
TreeNode* bstToGst(TreeNode* root) { // time: O(n); space: O(h)
    int preSum = 0;
    helper(root, preSum);
    return root;
}
```
