Sum of Node Values at Given Depths

You are given a binary tree represented as a list of nodes. Each node is described by a triplet of integers: (value, left, right). The value represents the node's value, and left and right are the indices of its left and right children respectively (with 0 indicating the absence of a child). The nodes are provided in level order, where the first node is the root (at depth \(0\)).

Your task is to compute the sum of the node values at a given depth \(d\) (using 0-indexing for depth). You will be provided with multiple test cases. For each test case, you need to output the sum for that test case on a separate line.

Note: The tree is constructed using the given list. The children indices refer to the 1-indexed positions in the list.

inputFormat

The input is read from standard input and has the following format:

• The first line contains an integer \(T\), the number of test cases.
• Each test case begins with a line containing two integers \(d\) and \(n\):
  • \(d\): the target depth (0-indexed).
  • \(n\): the number of nodes in the tree.
• This is followed by \(n\) lines, each containing three integers: value left right. Here, left and right are indices (1-indexed) of the left and right children respectively, with a value of 0 indicating that the child does not exist.

outputFormat

For each test case, output a single integer representing the sum of the node values at depth \(d\) on a separate line. The output is written to standard output.

## sample

5
2 5
1 2 3
2 4 5
3 0 0
4 0 0
5 0 0
1 3
6 2 3
2 0 0
3 0 0
3 3
6 2 3
2 0 0
3 0 0
0 1
10 0 0
1 5
5 2 3
3 4 0
8 0 5
1 0 0
7 0 0

9
5
0
10
11

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