Path Sum in Binary Tree

You are given a binary tree and a target integer \(S\). Determine if there exists a path from the root to any leaf such that the sum of the node values along the path equals \(S\).

The binary tree is provided in level-order traversal form. A value of -1 in the input represents a missing (null) node. For example, the level-order list [1, 2, 3, -1, -1, 4, 5] represents the tree:

1
/ \ 2 3
/ \ 4 5

Your task is to implement an algorithm that returns "YES" if such a path exists, or "NO" otherwise. Use appropriate techniques such as depth-first search (DFS) or breadth-first search (BFS) to solve the problem efficiently.

inputFormat

The input is given via stdin in the following format:

• The first line contains two integers: n (the number of nodes in the tree) and S (the target sum).
• The second line contains n integers separated by spaces, representing the values of the nodes in level-order traversal. A value of -1 denotes a null node.

outputFormat

Output a single line to stdout which is either "YES" if there exists a root-to-leaf path with a sum equal to \(S\), or "NO" otherwise.

## sample

5 6
1 2 3 4 5

YES

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