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 <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <complex>
#include <string>
#include <sstream>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <functional>
#include <iostream>
#include <map>
#include <set>
using namespace std;
typedef pair<int,int> P;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;
#define pu push
#define pb push_back
#define mp make_pair
#define eps 1e-9
#define INF 2000000000
#define sz(x) ((int)(x).size())
#define fi first
#define sec second
#define SORT(x) sort((x).begin(),(x).end())
#define all(x) (x).begin(),(x).end()
int V,E;
vector<int> g[100100];
int dep[100100],low[100100],ord[100100];
int cnt = 0;
void dfs(int v,int p,int d){
	dep[v] = d;
	ord[v] = cnt++;
	low[v] = ord[v];
	for(int i=0;i<g[v].size();i++){
		if(g[v][i]==p)continue;
		int ch = g[v][i];
		if(ord[ch]==-1){
			dfs(ch,v,d+1);
			low[v] = min(low[v],low[ch]);
		}else{
			low[v] = min(low[v],ord[ch]);
		}
	}
}
int main(){
	scanf("%d %d",&V,&E);
	vector<P> es(E);
	for(int i=0;i<E;i++){
		int s,t;
		scanf("%d %d",&s,&t);
		g[s].pb(t);
		g[t].pb(s);
		if(s>t)swap(s,t);
		es[i]=P(s,t);
	}
	memset(ord,-1,sizeof(ord));
	dfs(0,-1,0);
	vector<P> ans;
	for(int i=0;i<E;i++){
		int s = es[i].fi,t = es[i].sec;
		if(dep[s]>dep[t])swap(s,t);
		if(ord[s]<low[t])ans.pb(es[i]);	
	}
	sort(all(ans));
	for(int i=0;i<ans.size();i++)printf("%d %d\n",ans[i].fi,ans[i].sec);
	return 0;
}