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<algorithm>
#include<vector>
#include<queue>
#include<unordered_set>
#include<unordered_map>
using namespace std;
typedef long long ll;
#define mod 1000000007
#define mad(a,b) a=(a+b)%mod;
#define N 100010
unordered_map<ll,bool> mas[N];
vector<ll> g[N];
ll n,m;
bool p[N],vis[N];
void dfs(ll x,ll from){
    if(vis[x])return;
    vis[x]=1;
    for(auto y:g[x])if(y!=from){
	dfs(y,x);
    }
    if(p[x]==1){
	if(from==-1)cout<<1/0<<endl;
	mas[x][from]^=1;
	mas[from][x]^=1;
	p[x]^=1,p[from]^=1;
    }
}
int main(){
  cin>>n>>m;
  for(int i=1;i<=n;i++)p[i]=0,vis[i]=0;
  for(int i=0;i<m;i++){
      ll a,b;cin>>a>>b;
      g[a].push_back(b);
      g[b].push_back(a);
      p[a]^=1;
      mas[a][b]=1,mas[b][a]=0;
  }
  if(m%2==1){
      cout<<-1<<endl;
      return 0;
  }
  dfs(1,-1);
  for(int i=1;i<=n;i++){
      for(auto y:g[i]){
	  if(mas[i][y]==1){
	      cout<<i<<" "<<y<<endl;
	  }
      }
  }
  return 0;
}