Is the Graph a Tree?

You are given an undirected graph with n nodes and m edges. A graph is a tree if and only if it satisfies two conditions:

• The number of edges is exactly \( m = n - 1 \).
• The graph is connected, i.e. there is a path between any two vertices.

Your task is to determine whether a given graph is a tree. If both conditions are satisfied, output YES; otherwise, output NO.

Input format: The first line contains two integers n and m. The next m lines each contain two integers representing an undirected edge between the two given nodes.

Output format: Output a single line containing YES if the graph is a tree, otherwise NO.

inputFormat

The input is given from standard input (stdin) and is structured as follows:

n m
u1 v1
...
um vm

where n is the number of nodes, m is the number of edges, and each subsequent line contains two integers u and v representing an edge between nodes u and v.

outputFormat

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

## sample

4 3
1 2
2 3
3 4

YES

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