Check if a Graph is a Tree

You are given an undirected graph with n vertices (numbered from 0 to n-1) and m edges. Your task is to determine whether the graph forms a tree.

A graph is a tree if and only if:

• It has exactly n-1 edges.
• It is connected, i.e. there is a path between any two vertices.

Recall that the mathematical condition for being a tree is:

$$ m=n-1 \quad \text{and} \quad \forall v \in \{0, 1, \dots, n-1\}, \text{ vertex } v \text{ is reachable from vertex } 0.$$

You should read the input from standard input and output the result to standard output. If the graph is a tree, print YES; otherwise, print NO.

inputFormat

The first line contains two integers n and m — the number of vertices and the number of edges, respectively.

The following m lines each contain two integers u and v indicating that there is an undirected edge connecting vertex u and vertex v.

It is guaranteed that 0 ≤ u, v < n.

outputFormat

Output a single line containing YES if the given graph is a tree, otherwise output NO.

## sample

5 4
0 1
0 2
0 3
1 4

YES