Connecting Villages Within Budget

You are given N villages and M possible roads connecting them. Each road connects two villages with a given length. You are also provided a budget B. Your task is to determine whether it is possible to connect all the villages (i.e. form a spanning tree) using some of the given roads such that the total length (cost) does not exceed the budget.

In other words, let \(T\) be a set of roads that connects all the villages. Then the condition to satisfy is:

[ \sum_{e \in T} \text{length}(e) \leq B ]

If such a set \(T\) exists, print YES; otherwise, print NO.

You are expected to use a Minimum Spanning Tree (MST) algorithm (such as Kruskal's or Prim's algorithm) with a Disjoint Set Union (Union-Find) to solve this problem.

inputFormat

The input is read from stdin and is formatted as follows:

• The first line contains three integers N, M, and B where N is the number of villages, M is the number of roads, and B is the budget.
• The following M lines each contain three space‑separated integers u, v, and l, representing a road connecting village u and village v with a length (cost) l.

Villages are numbered from 1 to N.

outputFormat

The output is written to stdout and should be a single line containing either YES if it is possible to connect all villages within the budget, or NO otherwise.

## sample

5 7 15
1 2 3
1 3 4
2 3 1
2 4 2
3 4 5
3 5 6
4 5 1

YES