Articulation Points

The undirected graph is given. Find all its articulation points.

Input

The first line contains two positive integers $n$ and $m(n\le 2\cdot 10^4,m\le 2\cdot 10^5)$ — the number of vertices and edges respectively.

Each of the next $m$ lines contains the description of an edge. The edge number $i$ is given with two positive integers $b_i,e_i(1\le b_i,e_i\le n)$ — the numbers of the vertices it connects.

Output

Print in the first line the number $b$ of articulation points in a given graph. In the next $b$ lines print the numbers of the vertices that are articulation points in increasing order.

Examples