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<iostream>
#include<cstdio>
#include<vector>
using namespace std;
const int N=100005;
int n,m;
vector<int>G[N];
int d[N];
int x[N],y[N];
int fa[N];
int getf(int v)
{
	if(v==fa[v]) return v;
	fa[v]=getf(fa[v]);
	return fa[v];
}
bool merge(int u,int v)
{
	int f1=getf(u),f2=getf(v);
	if(f1!=f2)
	{
		fa[f2]=f1;
		return true;
	}
	else return false;
}
vector<pair<int,int> >res;
void kruskal()
{
	for(int i=1;i<=n;i++)
		fa[i]=i;
	for(int i=1;i<=m;i++)
		if(merge(x[i],y[i])) G[x[i]].push_back(y[i]),G[y[i]].push_back(x[i]);
		else res.push_back(make_pair(x[i],y[i])),d[x[i]]++;
	return;
}
void dfs(int u,int father)
{
	for(int v:G[u])
	{
		if(v==father) continue;
		dfs(v,u);
		if(d[v]&1) res.push_back(make_pair(v,u)),d[v]++;
		else res.push_back(make_pair(u,v)),d[u]++;
	}
	return;
}
int main()
{
	scanf("%d%d",&n,&m);
	if(m&1)
	{
		printf("-1");
		return 0;
	}
	for(int i=1;i<=m;i++)
		scanf("%d%d",&x[i],&y[i]);
	kruskal();
	dfs(1,0);
	for(auto [u,v]:res)
		printf("%d %d\n",u,v);
	return 0;
}