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>
using Int = int64_t;
using UInt = uint64_t;
using C = std::complex<double>;
#define rep(i, n) for(Int i = 0; i < (Int)(n); ++i)
#define guard(x) if( not (x) ) continue;
#ifndef LOCAL_
#define fprintf if( false ) fprintf
#endif

int main() {
   Int v, e;
   std::cin >> v >> e;
   std::vector<Int> ss(e), ts(e);
   rep(i, e) std::cin >> ss[i] >> ts[i];
   std::vector<std::vector<Int>> nexts(v);
   rep(i, e) {
      Int s = ss[i], t = ts[i];
      nexts[s].emplace_back(t);
      nexts[t].emplace_back(s);
   }
   std::vector<Int> xs(v,-1);
   std::vector<Int> ys(v);
   std::vector<std::pair<Int,Int>> zs;
   xs[0] = 0;
   Int id = 1;
   std::function<Int(Int,Int)> dfs = [&](Int i, Int prev) {
      xs[i] = id;
      id += 1;
      Int res = 0;
      for(Int k : nexts[i]) {
         guard( k != prev );
         if( xs[k] == -1 ) {
            Int t = dfs(k, i);
            if( t == 0 ) {
               Int a = std::min(i, k);
               Int b = std::max(i, k);
               zs.emplace_back(a, b);
            }
            res += t;
         }
         else if( xs[k] < xs[i] ) {
            ys[i] += 1;
            ys[k] -= 1;
         }
      }
      res += ys[i];
      return res;
   };
   dfs(0, -1);
   std::sort(zs.begin(), zs.end());
   for(auto z : zs) {
      printf("%ld %ld\n", z.first, z.second);
   }
}