BST to Greater Sum Tree

The tests write a tree as a level-order list (row by row, left to right) with None for a missing child: [3, 9, 20, None, None, 15, 7] is a root 3 with children 9 and 20, where 20 has children 15 and 7. All trees in this topic that are called BSTs have different values.

Change the tree so that every node's value becomes the original value plus the sum of all original values greater than it. Return the root.

For [4, 1, 6, 0, 2, 5, 7, None, None, None, 3, None, None, None, 8] the answer is [30, 36, 21, 36, 35, 26, 15, None, None, None, 33, None, None, None, 8].

Examples

Example 1

Input:

convert_bst(root)  # root = [4, 1, 6, 0, 2, 5, 7, None, None, None, 3, None, None, None, 8]

Output:

[30, 36, 21, 36, 35, 26, 15, None, None, None, 33, None, None, None, 8]

Example 2

Input:

convert_bst(root)  # root = [0, None, 1]

Output:

[1, None, 1]

Constraints

• 0 <= number of nodes <= 100000
• The tree is a BST, not deeper than 800 levels.
• 0 <= val <= 10**4