Exact Weight Path in an Undirected Graph

You are given an undirected graph with (N) nodes and (M) edges. Each edge connects two nodes (u) and (v) with a positive integer weight (w). Additionally, you are given two special nodes: a start node (S) and a target node (T), as well as an integer (K). Your task is to determine whether there exists a path from (S) to (T) such that the sum of the weights of the edges along the path is exactly (K). If such a path exists, output "YES"; otherwise, output "NO".

Note: A path may pass through the same node or edge multiple times, and each traversal contributes to the total weight.

inputFormat

The input is read from stdin with the following format:

• The first line contains three integers \(N\), \(M\), and \(K\) \( (1 \leq N \leq 10^5,\ 1 \leq M \leq 10^5,\ 1 \leq K \leq 10^9)\).
• Each of the following \(M\) lines contains three integers \(u\), \(v\), and \(w\), representing an undirected edge between nodes \(u\) and \(v\) with weight \(w\).
• The last line contains two integers \(S\) and \(T\), indicating the start and target nodes, respectively.

outputFormat

Output a single line to stdout containing "YES" if a path from (S) to (T) with total weight exactly (K) exists, or "NO" otherwise.## sample

4 4 7
1 2 3
1 3 4
2 4 4
3 4 3
1 4

YES