Problem: You are given a simple connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex A_i and Vertex B_i. Takahashi will assign one of the two possible directions to each of the edges in the graph to make a directed graph. Determine if it is possible to make a directed graph with an even number of edges going out from every vertex. If the answer is yes, construct one such graph.

Constraints

* 2 \leq N \leq 10^5
* N-1 \leq M \leq 10^5
* 1 \leq A_i,B_i \leq N (1\leq i\leq M)
* The given graph is simple and connected.

Input

Input is given from Standard Input in the following format:


N M
A_1 B_1
:
A_M B_M


Output

If it is impossible to assign directions to satisfy the requirement, print -1. Otherwise, print an assignment of directions that satisfies the requirement, in the following format:


C_1 D_1
:
C_M D_M


Here each pair (C_i, D_i) means that there is an edge directed from Vertex C_i to Vertex D_i. The edges may be printed in any order.

Examples

Input

4 4
1 2
2 3
3 4
4 1


Output

1 2
1 4
3 2
3 4


Input

5 5
1 2
2 3
3 4
2 5
4 5


Output

-1

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL_DEBUG
  #include "LOCAL_DEBUG.hpp"
#endif
#define int long long

signed main(){

  int n, m; cin >> n >> m;
  vector<vector<int>> G(n);
  for(int i = 0; i < m; i++){
    int a, b; cin >> a >> b;
    a--, b--;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  if(m % 2 == 1){
    cout << -1 << endl;
    return 0;
  }

  vector<pair<int, int>> ans;
  vector<int> depth(n, -1), deg(n, 0);
  function< void(int,int) > dfs =
  [&](int u, int pre){
    for(int v : G[u]){
      if(depth[v] == -1){
        depth[v] = depth[u] + 1;
        dfs(v, u);
      }else{
        if(depth[v] > depth[u]){
          ans.emplace_back(u, v);
          deg[u]++;
        }
      }
    }
    if(pre == -1) return;
    if(deg[u] % 2 == 1){
      ans.emplace_back(u, pre);
      deg[u]++;
    }else{
      ans.emplace_back(pre, u);
      deg[pre]++;
    }
  };
  depth[0] = 0;
  dfs(0, -1);
  for(auto p : ans){
    cout << p.first+1 << " " << p.second+1 << endl;
  }

  return 0;
}