Cutting Binary Search Tree

Given a binary search tree root, an integer lo, and another an integer hi, remove all nodes that are not between [lo, hi] inclusive.

Constraints

• n ≤ 100,000 where n is the number of nodes in root

https://binarysearch.com/problems/Cutting-Binary-Search-Tree

Examples

Example 1

Input

• root =

• lo = 3
• hi = 4

Output

• answer =

Example 2

Input

• root =

• lo = 7
• hi = 10

Output

• answer =

Solution