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:
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
typedef long long ll;
#define FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
using namespace std;
const ll MAX_N=1e5;
ll N,M,par[MAX_N],outdeg[MAX_N];
vector<ll> G[MAX_N];
void init(ll n){
	REP(i,n)par[i]=i;
}
ll fndpar(ll v){
	if(par[v]==v)return v;
	return par[v]=fndpar(par[v]);
}
void unite(ll a,ll b){
	a=fndpar(a);
	b=fndpar(b);
	par[a]=b;
}
bool same(ll a,ll b){
	a=fndpar(a);
	b=fndpar(b);
	return a==b;
}
void prtedge(ll v,ll u){
	cout<<v+1<<' '<<u+1<<endl;
}
void dfs(ll v,ll p){
	for(auto e:G[v]){
		if(e!=p)dfs(e,v);
	}
	if(p!=-1){
		if(outdeg[v]%2==0){
			prtedge(p,v);
			outdeg[p]++;
		}else{
			prtedge(v,p);
			outdeg[v]++;
		}
	}
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>N>>M;
	if(M%2==0){
		init(N);
		REP(i,M){
			ll a,b;
			cin>>a>>b;
			a--;
			b--;
			if(same(a,b)){
				prtedge(a,b);
				outdeg[a]++;
			}else{
				unite(a,b);
				G[a].push_back(b);
				G[b].push_back(a);
			}
		}
		dfs(0,-1);
	}else{
		cout<<-1<<endl;
	}
}