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;
#define Maxn 200007
int n,m;
int last[Maxn],pre[Maxn],other[Maxn],cnt=1;
int deg[Maxn];
bool vis[Maxn],flag[Maxn];
void insert(int u,int v)
{
    other[++cnt]=v,pre[cnt]=last[u],last[u]=cnt;
}
void dfs(int u,int fa)
{
    vis[u]=true;
    for (int q=last[u];q;q=pre[q])
    {
        if (flag[q]) continue;
        int v=other[q];
        if (v!=fa)
        {
            if (vis[v])
            {
                printf("%d %d\n",u,v);
                ++deg[u];
            } else dfs(v,u);
            flag[q]=true;
            flag[q^1]=true;
        }
    }
    if (deg[u]%2!=0)
    {
        printf("%d %d\n",u,fa);
        ++deg[u];
    } else if (u!=1)
    {
        printf("%d %d\n",fa,u);
        ++deg[fa];
    }
}
int main()
{
    scanf("%d%d",&n,&m);
    if (m%2!=0)
    {
        printf("%d\n",-1);
        return 0;
    }
    for (int i=1;i<=m;i++)
    {
        int u,v;
        scanf("%d%d",&u,&v);
        insert(u,v),insert(v,u);
    }
    dfs(1,-1);
    return 0;
}