Problem: Find bridges of an undirected graph G(V, E).

A bridge (also known as a cut-edge) is an edge whose deletion increase the number of connected components.

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

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

Output

A list of bridges of the graph ordered by name. For each bridge, names of its end-ponints, source and target (source < target), should be printed separated by a space. The sources should be printed ascending order, then the target should also be printed ascending order for the same source.

Examples

Input

4 4
0 1
0 2
1 2
2 3


Output

2 3


Input

5 4
0 1
1 2
2 3
3 4


Output

0 1
1 2
2 3
3 4

Solution (in CPP):

Solution:
//ライブラリにするほどか？
//橋
#include<bits/stdc++.h>
using namespace std;
#define MAX_N 100001
vector<int> G[MAX_N];
vector<pair<int,int> > ans;
int cnt[MAX_N],dep[MAX_N];

void dfs(int pos,int pre){
    for(int i = 0; i < G[pos].size(); i++){
        int nx = G[pos][i];
        if (nx == pre || dep[nx] > dep[pos]) continue;
        
        if (dep[nx] != -1 && dep[nx] < dep[pos]){
            cnt[nx]--;
            cnt[pos]++;
        } else {
            dep[nx] = dep[pos] + 1;
            dfs(nx,pos);
            if (cnt[nx] == 0){
                ans.push_back({min(pos,nx),max(pos,nx)});
            }
            cnt[pos] += cnt[nx];
        }
    }
}


int main(){
    int n,m; cin >> n >> m;
    for(int i = 0; i < m; i++){
        int a,b; cin >> a >> b;
        G[a].push_back(b);
        G[b].push_back(a);
    }
    memset(dep,-1,sizeof(dep));
    dep[0] = 0;
    dfs(0,-1);
    sort(ans.begin(),ans.end());
    for(int i = 0; i < ans.size(); i++){
        cout << ans[i].first << " " << ans[i].second << endl;
    }
    //return 0;
}