Tree Verification

You are given an undirected graph with N nodes and M edges. Your task is to determine whether the graph forms a tree. Recall that a tree is a connected acyclic graph that always satisfies \( M = N - 1 \). In other words, for the graph to be a tree, it must:

• Have exactly \( N - 1 \) edges.
• Be connected (there is a path between every pair of nodes).

If both conditions are met, output YES; otherwise, output NO.

inputFormat

The input is read from standard input (stdin):

N M
u1 v1
u2 v2
... 
 vM

Here, N is the number of nodes, M is the number of edges, and each of the next M lines contains two integers u and v representing an undirected edge between nodes u and v.

outputFormat

The output should be printed to standard output (stdout) and is a single line containing either YES if the graph is a tree, or NO otherwise.

5 4
1 2
2 3
4 3
5 3

YES