Search in a BST

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.

Return the subtree whose root has the value val (the node with all its descendants), or an empty tree if there is no such node.

For [4, 2, 7, 1, 3] and val = 2 the answer is [2, 1, 3].

Examples

Example 1

Input:

search_bst(root, 2)  # root = [4, 2, 7, 1, 3]

Output:

[2, 1, 3]

Example 2

Input:

search_bst(root, 5)  # root = [4, 2, 7, 1, 3]

Output:

[]

Constraints

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