Root-to-Leaf Path Sum in Binary Tree

You are given a binary tree represented as an array of nodes. Each node is described by a tuple \( (\text{value},\; \text{left_index},\; \text{right_index}) \), where \(-1\) denotes a missing child. The tree is zero-indexed and its root is at index 0.

Your task is to determine whether there exists a root-to-leaf path along which the sum of the node values equals a given target sum \(S\), i.e., \[ S = \sum_{i=1}^{k} v_i \] where \(v_i\) are the node values along the path. If such a path exists, print Yes; otherwise, print No.

Note: A leaf is a node with no children.

inputFormat

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

1. The first line contains two integers, targetSum and n, where targetSum is the sum to be checked and n is the number of nodes in the tree.
2. The next n lines each contain three integers: value, left_index, and right_index. A value of -1 for an index indicates that the corresponding child does not exist. The tree is built with node 0 as the root.

outputFormat

The output should be printed to stdout and consists of a single line: Yes if there exists a root-to-leaf path with a sum equal to targetSum, and No otherwise.

10 0

No