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;

const int maxn = 1e5 + 20;

bool visited[maxn];
int n, m, a, b, outDegree[maxn], dis[maxn];
vector<int> graph[maxn];

void dfs(int i) {
    visited[i] = 1;
    for (int x : graph[i]) {
        if (!visited[x]){
            dis[x] = dis[i] + 1; 
            dfs(x);
        }
        if (dis[x] > dis[i]) {
            if (outDegree[x] % 2 == 0){
                outDegree[i]++;
                cout << i << " " << x << endl;
            }
            else{
                outDegree[x] ++;
                cout << x << ' '  << i << endl;
            }
        }
    }
}
int main() {
    int n, m;
    cin >> n >> m;
    if (m % 2 == 1)
        return cout << -1 << endl, 0;
    for (int i = 0; i < m; i++) {
        cin >> a >> b;
        graph[a].push_back(b);
        graph[b].push_back(a);
    }

    dfs(1);    
}