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;
typedef long long ll;
typedef bitset<35> sta;

struct node{
	int Next,y,v;
}Pth[200005];
int cnt,head[100005];
inline void add(int x,int y,int v){
	cnt++;
	Pth[cnt]={head[x],y,v};
	head[x]=cnt;
}

struct Edge{
	int x,y,dir; //dir {1: x->y  -1: y->x}
}E[100005];
int n,m;
bool tg[100005],vis[100005];

void dfs(int x,int inid,int pr){
	vis[x]=1;
	for (int i=head[x];i;i=Pth[i].Next){
		if (vis[Pth[i].y]) continue;
		dfs(Pth[i].y,Pth[i].v,x);
	}
	if (tg[x]){
		tg[x]^=1; tg[pr]^=1;
		E[inid].dir=-E[inid].dir;
	}
}

int main(){
	cin>>n>>m;
	if (m%2==1){
		cout<<-1<<endl;
		return 0;
	}
	for (int i=1;i<=m;++i){
		int x,y;
		scanf("%d%d",&x,&y);
		add(x,y,i); add(y,x,i);
		E[i]={x,y,1}; tg[x]^=1;
	}
	dfs(1,0,0);
	for (int i=1;i<=m;++i){
		if (E[i].dir==-1) swap(E[i].x,E[i].y);
		printf("%d %d\n",E[i].x,E[i].y);
	}
	return 0;
}