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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;
#pragma warning (disable: 4996)

int N, M, A[1 << 17], B[1 << 17], pre[1 << 17], low[1 << 17], cnts;
vector<int> G[1 << 17]; vector<pair<int, int>> E;

void dfs(int pos, int prevs) {
	cnts++; pre[pos] = cnts; low[pos] = cnts;

	for (int i = 0; i < G[pos].size(); i++) {
		if (pre[G[pos][i]] == 0) {
			dfs(G[pos][i], pos);
			if (low[G[pos][i]] == pre[G[pos][i]]) {
				int u1 = pos, u2 = G[pos][i]; if (u1 > u2) swap(u1, u2);
				E.push_back(make_pair(u1, u2));
			}
			low[pos] = min(low[pos], low[G[pos][i]]);
		}
		else {
			if (G[pos][i] != prevs) low[pos] = min(low[pos], low[G[pos][i]]);
		}
	}
}

int main() {
	scanf("%d%d", &N, &M);
	for (int i = 1; i <= M; i++) {
		scanf("%d%d", &A[i], &B[i]);
		G[A[i]].push_back(B[i]);
		G[B[i]].push_back(A[i]);
	}
	dfs(1, 0);
	sort(E.begin(), E.end());
	for (int i = 0; i < E.size(); i++) printf("%d %d\n", E[i].first, E[i].second);
	return 0;
}