<h2><a href="https://leetcode.com/problems/kth-largest-sum-in-a-binary-tree/">2583. Kth Largest Sum in a Binary Tree</a></h2><h3>Medium</h3><hr><div><p>You are given the <code>root</code> of a binary tree and a positive integer <code>k</code>.</p>

<p>The <strong>level sum</strong> in the tree is the sum of the values of the nodes that are on the <strong>same</strong> level.</p>

<p>Return<em> the </em><code>k^th</code><em> <strong>largest</strong> level sum in the tree (not necessarily distinct)</em>. If there are fewer than <code>k</code> levels in the tree, return <code>-1</code>.</p>

<p><strong>Note</strong> that two nodes are on the same level if they have the same distance from the root.</p>

<p>&nbsp;</p>

<p><strong class="example">Example 1:</strong></p>

<img alt="" src="https://assets.leetcode.com/uploads/2022/12/14/binaryytreeedrawio-2.png" style="width: 301px; height: 284px;">

<pre><strong>Input:</strong> root = [5,8,9,2,1,3,7,4,6], k = 2

<strong>Output:</strong> 13

<strong>Explanation:</strong> The level sums are the following:

- Level 1: 5.

- Level 2: 8 + 9 = 17.

- Level 3: 2 + 1 + 3 + 7 = 13.

- Level 4: 4 + 6 = 10.

The 2^nd largest level sum is 13.

</pre>

<p><strong class="example">Example 2:</strong></p>

<img alt="" src="https://assets.leetcode.com/uploads/2022/12/14/treedrawio-3.png" style="width: 181px; height: 181px;">

<pre><strong>Input:</strong> root = [1,2,null,3], k = 1

<strong>Output:</strong> 3

<strong>Explanation:</strong> The largest level sum is 3.

</pre>

<p>&nbsp;</p>

<p><strong>Constraints:</strong></p>

<ul>

<li>The number of nodes in the tree is <code>n</code>.</li>

<li><code>2 &lt;= n &lt;= 10⁵</code></li>

<li><code>1 &lt;= Node.val &lt;= 10⁶</code></li>

<li><code>1 &lt;= k &lt;= n</code></li>

</ul>

</div>