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:
#include <bits/stdc++.h>

#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define FOR(i,n,m) for(int i=(int)(n); i<=(int)(m); i++)
#define RFOR(i,n,m) for(int i=(int)(n); i>=(int)(m); i--)
#define ITR(x,c) for(__typeof(c.begin()) x=c.begin();x!=c.end();x++)
#define RITR(x,c) for(__typeof(c.rbegin()) x=c.rbegin();x!=c.rend();x++)
#define setp(n) fixed << setprecision(n)

template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }

#define ll long long
#define vll vector<ll>
#define vi vector<int>
#define pll pair<ll,ll>
#define pi pair<int,int>

#define all(a) (a.begin()),(a.end())
#define rall(a) (a.rbegin()),(a.rend())
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define ins insert

using namespace std;

void dfs(int v, int p, vector<vi> &G, vi &ord, vi &low, int &idx)
{
    ord[v] = low[v] = idx++;
    for(auto u:G[v]){
        if (u==p) continue;
        if (ord[u]!=-1){
            chmin(low[v],ord[u]);
            continue;
        }
        dfs(u,v,G,ord,low,idx);
        chmin(low[v],low[u]);
    }
}

//-------------------------------------------------

int main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N,M; cin>>N>>M;
    vector<vi> G(N);
    rep(i,M){
        int a,b; cin>>a>>b;
        G[a].pb(b);
        G[b].pb(a);
    }
    vi ord(N,-1),low(N);
    int idx=0;
    dfs(0,-1,G,ord,low,idx);
    vector<pi> ans;
    rep(v,N){
        for(auto u:G[v]){
            if (ord[v]<low[u]){
                int a = min(v,u);
                int b = max(v,u);
                ans.pb({a,b});
            }
        }
    }
    sort(all(ans));
    for(auto e:ans){
        cout<<e.fi<<" "<<e.se<<"\n";
    }
    return 0;
}