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 <algorithm>
#include <vector>
#include <cfloat>
#include <string>
#include <cmath>
#include <set>
#include <cstdlib>
#include <map>
#include <ctime>
#include <iomanip>
#include <functional>
#include <deque>
#include <iostream>
#include <cstring>
#include <queue>
#include <cstdio>
#include <stack>
#include <climits>
#include <sys/time.h>
#include <cctype>

using namespace std;

typedef long long ll;

// ????????°????????§??°
#define MAX_V 100000

vector <int> graph[MAX_V];
bool vis[MAX_V];
int ord[MAX_V], parent[MAX_V], lowlink[MAX_V], timer;

vector <pair<int, int> > edges;
vector <pair<int, int> > bridge;

void dfs(int current, int prev) {
  ord[current] = lowlink[current] = timer;
  timer++;

  vis[current] = true;

  int next;
  for (int i = 0; i < graph[current].size(); i++) {
    next = graph[current][i];
    if (!vis[next]) {
      parent[next] = current;

      dfs(next, current);
      lowlink[current] = min(lowlink[current], lowlink[next]);
    }else if (next != prev) {
      lowlink[current] = min(lowlink[current], ord[next]);
    }
  }
}

bool is_bridge(int s, int t) {
  if (ord[s] > ord[t]) swap(s, t);
  return ord[s] < lowlink[t];
}

void init_bridge() {
  memset(vis, false, sizeof(vis));
  timer = 1;
  dfs(0, -1);
}

int main() {
  int v, e;
  cin >> v >> e;

  for (int i = 0; i < e; i++) {
    int s, t;
    cin >> s >> t;
    graph[s].push_back(t);
    graph[t].push_back(s);
    if (s > t) swap(s, t);
    edges.push_back(make_pair(s, t));
  }
  sort(edges.begin(), edges.end());
  init_bridge();
  for (int i = 0; i < e; i++) {
    int s = edges[i].first, t = edges[i].second;
    if (is_bridge(s, t)) {
      cout << s << " " << t << endl;
    }
  }
}