Given an undirected graph with $n$ vertices and $m$ edges, find all the articulation points of the graph.

Input

The first line contains two positive integers $n$ and $m$.

The following $m$ lines each contain two positive integers $x$ and $y$, representing an edge between $x$ and $y$.

Output

The first line outputs the number of articulation points.

The second line outputs the vertex indices in ascending order, separated by spaces.

Examples

Input 1

6 7
1 2
1 3
1 4
2 5
3 5
4 5
5 6

Output 1

1 
5

Subtasks

For all data, $1 \leq n \leq 2 \times 10^4$, $1 \leq x, y \leq n$, $1 \leq m \leq 10^5$.