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 pair<int,int> ii;
vector<vector<int>> adj;
set<ii> edges;
vector<bool> vis;
vector<vector<int>> child;
vector<int> outdeg;
void dfs(int u,int e){
	vis[u] = true;
	for(auto v:adj[u])
	if(v!=e){
		if(!vis[v]){
			child[u].push_back(v);
			outdeg[u]++;
			dfs(v,u);
		}
		else{
			if(edges.count({u,v})==0&&edges.count({v,u})==0)
			{
				edges.insert({u,v});
				outdeg[u]++;
			}
		}
	}
}
void assdir(int u,int e){
	for(auto v:child[u])
	{
		assdir(v,u);
	}
	if(e!=-1)
	{
		if(outdeg[u]&1){
			outdeg[u]+=1;
			outdeg[e]-=1;
			edges.insert({u,e});
		}
		else edges.insert({e,u});
	}
}
int main(int argc, char *argv[]) {
	int n,m;
	cin>>n>>m;
	child.resize(n+1);
	if(m%2==1) return (cout<<-1),0;
	adj.resize(n+1);
	vis.resize(n+1);
	outdeg.resize(n+1);
	for(int i=0;i<m;i++){
		int u,v;
		cin>>u>>v;
		adj[u].push_back(v);
		adj[v].push_back(u);
	}
	dfs(1,-1);
	assdir(1, -1);
//	for(int i=1;i<=n;i++) assert(outdeg[i]%2==0);
	for(auto e:edges) cout<<e.first<<' '<<e.second<<endl;
}