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 <stdio.h>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <map>
using namespace std;
typedef long long ll;
#define N_MAX 100005

bool used[N_MAX];
vector<int> G[N_MAX];
int dep[N_MAX];
int deg[N_MAX];

void dfs(int v = 0, int p = -1, int d = 0){
	used[v] = true;
  	dep[v] = d;
  	for(int i = 0; i < G[v].size(); i++){
    	int to = G[v][i];
      	if(to != p){
        	if(!used[to]) dfs(to, v, d+1);
          	else if(dep[to] < dep[v]){
            	cout << v+1 << ' ' << to + 1 << endl;
              	deg[v]++;
            }
        }
    }
  	if(p!=-1){
    	if(deg[v]%2 != 0){
        	cout << v+1 << ' ' << p+1 << endl;
          	deg[v]++;
        } else {
        	cout << p+1 << ' ' << v+1 << endl;
        	deg[p]++;
        }
    }
}

int main(){
	int N, M;
  	cin >> N >> M;
  	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 != 0){
    	cout << -1 << endl;
      	return 0;
    }
	dfs();
  	return 0;
}