#include<bits/stdc++.h>
typedef long long int ll;
#define INF 0x3f3f3f3f
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
using namespace std;
const int sz=1e5+10, mod =1e9+7;
vector<int> g[sz];
vector<pair<int,int>> ans;
bool visited[sz];
int out[sz];
map<pair<int,int>,int> mp;

int dfs(int u,int p){
    visited[u]=true;
    int c=out[u]&1;

    for(auto v:g[u]){
        if(visited[v] ) continue;
        c^=dfs(v,u);
    }

    if(p==-1) return c;

    if(c&1){
        mp[{p,u}]^=1;
        mp[{u,p}]^=1;
    }
    return c;
}

int main(){
    ios_base::sync_with_stdio(0); cin.tie(0);
    memset(out,0,sizeof(out));
    memset(visited,false,sizeof(visited));

    int n,m,i,j,u,v;
    cin>>n>>m;
    for(i=0;i<m;i++){
        cin>>u>>v;
        g[u].pb(v);
        g[v].pb(u);
        mp[{u,v}]=true;
        mp[{v,u}]=false;
        out[u]++;
    }

    int zz=dfs(1,-1);

    if(zz&1)cout<<"-1";
    else{
        for(auto x:mp){
            if(x.yy) cout<<x.xx.xx<<" "<<x.xx.yy<<"\n";
        }
    }

}

### Prompt

Please formulate a Cpp solution to the following 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

### Response

```cpp
#include<bits/stdc++.h>
typedef long long int ll;
#define INF 0x3f3f3f3f
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
using namespace std;
const int sz=1e5+10, mod =1e9+7;
vector<int> g[sz];
vector<pair<int,int>> ans;
bool visited[sz];
int out[sz];
map<pair<int,int>,int> mp;

int dfs(int u,int p){
    visited[u]=true;
    int c=out[u]&1;

    for(auto v:g[u]){
        if(visited[v] ) continue;
        c^=dfs(v,u);
    }

    if(p==-1) return c;

    if(c&1){
        mp[{p,u}]^=1;
        mp[{u,p}]^=1;
    }
    return c;
}

int main(){
    ios_base::sync_with_stdio(0); cin.tie(0);
    memset(out,0,sizeof(out));
    memset(visited,false,sizeof(visited));

    int n,m,i,j,u,v;
    cin>>n>>m;
    for(i=0;i<m;i++){
        cin>>u>>v;
        g[u].pb(v);
        g[v].pb(u);
        mp[{u,v}]=true;
        mp[{v,u}]=false;
        out[u]++;
    }

    int zz=dfs(1,-1);

    if(zz&1)cout<<"-1";
    else{
        for(auto x:mp){
            if(x.yy) cout<<x.xx.xx<<" "<<x.xx.yy<<"\n";
        }
    }

}

```