Articulation Points

Find articulation points of a given undirected graph G(V, E).

A vertex in an undirected graph is an articulation point (or cut vertex) iff removing it disconnects the graph.

Constraints

• 1 ≤ |V| ≤ 100,000
• 0 ≤ |E| ≤ 100,000
• The graph is connected
• There are no parallel edges
• There are no self-loops

Input

|V| |E| s0 t0 s1 t1 : s|E|-1 t|E|-1

, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target verticess of i-th edge (undirected).

Output

A list of articulation points of the graph G ordered by name.

Examples

Input

4 4 0 1 0 2 1 2 2 3

Output

2

Input

5 4 0 1 1 2 2 3 3 4

Output

1 2 3

inputFormat

Input

|V| |E| s0 t0 s1 t1 : s|E|-1 t|E|-1

, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target verticess of i-th edge (undirected).

outputFormat

Output

A list of articulation points of the graph G ordered by name.

Examples

Input

4 4 0 1 0 2 1 2 2 3

Output

2

Input

5 4 0 1 1 2 2 3 3 4

Output

1 2 3

样例

5 4
0 1
1 2
2 3
3 4

1
2
3

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