K-th Largest Perfect Subtree Size in Binary Tree

You are given the root of a binary tree and an integer k.

Return an integer denoting the size of the k^th largest perfect binary subtree, or -1 if it doesn't exist.

A perfect binary tree is a tree where all leaves are on the same level, and every parent has two children.

Example 1

            5
          /   \
         3     6
        / \   / \
       5   2 5   7
      / \   / \
     1   8 6   8

Inputroot = [5,3,6,5,2,5,7,1,8,null,null,6,8], k = 2

Output3

The perfect binary subtree sizes in non-increasing order are [3, 3, 1, 1, 1, 1, 1, 1], so the 2^nd largest size is 3.

Example 2

Inputroot = [1,2,3,4,5,6,7], k = 1

Output7

The perfect binary subtree sizes in non-increasing order are [7, 3, 3, 1, 1, 1, 1], so the largest size is 7.

Constraints