p02366 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
```python
import sys
sys.setrecursionlimit(10**7)

v, e = list(map(int, input().split()))

G = [[] for _ in range(v)]
for _ in range(e):
    s, t = map(int, input().split())
    G[s].append(t)
    G[t].append(s)


def solve():
    
    used = [False for _ in range(v)]
    ord = [0 for _ in range(v)]
    low = [float("inf") for _ in range(v)]
    is_articulation = [False for _ in range(v)]
    
    def dfs(v, prev, k):
        if used[v]:
            return
        used[v] = True
        k = k+1
        ord[v] = k
        low[v] = ord[v]
        cnt = 0
        for u in G[v]:
            if not used[u]:
                cnt += 1
                dfs(u, v, k)
                low[v] = min(low[v], low[u])
                if prev >= 0 and ord[v] <= low[u]:
                    is_articulation[v] = True
            elif u != prev:
                low[v] = min(low[v], ord[u])
        if prev == -1 and cnt >= 2:
            is_articulation[v] = True
        
        return k
    
    dfs(0, -1, 0)
    
    for i in range(v):
        if is_articulation[i]:
            print(i)

solve()

        
    
    







        
    
    







```