You are given an unweighted, undirected graph. Write a program to check if it's a tree topology.

Input

The first line of the input file contains two integers N and M – number of nodes and number of edges in the graph (0 < N ≤ 10000, 0 ≤ M ≤ 20000). Next M lines contain M edges of that graph – Each line contains a pair (u, v) means there is an edge between node u and node v (1 ≤ u, v ≤ N).

Output

Print YES if the given graph is a tree, otherwise print NO.

Example

Input:
3 2
1 2
2 3

Output:
YES