Cycles in the graph

Input

The first line contains two integers $n$ and $k$ (1 \leq n \leq 10^5, 0 \leq k \leq 10^5), representing the number of vertices and edges in the graph. Then follow $k$ lines, each containing two distinct integers $a$ and $b$ (1 \leq a, b \leq n), indicating that there is an edge between vertices $a$ and $b$. Each unordered pair $(a,b)$ appears at most once.

Output

If the graph contains no cycles, print a single word No. Otherwise, print Yes on the first line, and on the next line, print the smallest number of any vertex belonging to at least one cycle.

Examples