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;

typedef long long ll;

ll n, m;
vector<ll> ve[100005];
bool v[100005];
bool vv[100005];
bool vvv[100005];

void f(ll p, ll q)
{
    v[p] = true;
    for(ll i = 0; i < ve[p].size(); i++)
    {
        if(ve[p][i] == q) continue;
        if(vvv[ve[p][i]]) continue;
        if(v[ve[p][i]])
        {
            cout<<p<<' '<<ve[p][i]<<endl;
            vv[p] ^= 1;
        }
        else
        {
            f(ve[p][i], p);
            if(vv[ve[p][i]]) cout<<ve[p][i]<<' '<<p<<endl;
            else cout<<p<<' '<<ve[p][i]<<endl;
            vv[p] ^= !vv[ve[p][i]];
            vv[ve[p][i]] = false;
        }
    }
    vvv[p] = true;
}

int main()
{
    scanf("%lld%lld", &n, &m);
    if(m % 2 == 1)
    {
        cout<<-1<<endl;
        return 0;
    }
    for(ll i = 0; i < m; i++)
    {
        ll t1, t2;
        scanf("%lld%lld", &t1, &t2);
        ve[t1].push_back(t2), ve[t2].push_back(t1);
    }
    f(1, 0);
    return 0;
}