#include <bits/stdc++.h>
#define pb push_back
using namespace std;

vector<pair<int, int> > adj[100005];
pair<int, int> edge[100005];
bool dir[100005];
bool used[100005];
int deg[100005];
int sz[100005];
void dfs(int node)
{
	used[node]=true;
	sz[node]+=deg[node];
	for(auto i:adj[node])
	{
		if(!used[i.first])
		{
			dfs(i.first);
			if(sz[i.first]%2==1)
			{
				dir[i.second]^=1;
			}
			sz[node]+=sz[i.first];
		}
	}
}

signed main()
{
	int n, m;
	cin>>n>>m;
	for(int i=1; i<=m; i++)
	{
		int u, v;
		cin>>u>>v;
		edge[i]={u,v};
		deg[u]++;
		adj[u].pb({v,i});
		adj[v].pb({u,i});
	}
	int cut=0;
	for(int i=1; i<=n; i++)
	{
		deg[i]%=2;
		if(deg[i]==1)
		{
			cut++;
		}
	}
	if(cut%2==1)
	{
		cout<<-1;
		return 0;
	}
	dfs(1);
	for(int i=1; i<=m; i++)
	{
		if(dir[i])
		{
			cout<<edge[i].second<<" "<<edge[i].first<<endl;
		}
		else
		{
			cout<<edge[i].first<<" "<<edge[i].second<<endl;
		}
	}
}
### 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>
#define pb push_back
using namespace std;

vector<pair<int, int> > adj[100005];
pair<int, int> edge[100005];
bool dir[100005];
bool used[100005];
int deg[100005];
int sz[100005];
void dfs(int node)
{
	used[node]=true;
	sz[node]+=deg[node];
	for(auto i:adj[node])
	{
		if(!used[i.first])
		{
			dfs(i.first);
			if(sz[i.first]%2==1)
			{
				dir[i.second]^=1;
			}
			sz[node]+=sz[i.first];
		}
	}
}

signed main()
{
	int n, m;
	cin>>n>>m;
	for(int i=1; i<=m; i++)
	{
		int u, v;
		cin>>u>>v;
		edge[i]={u,v};
		deg[u]++;
		adj[u].pb({v,i});
		adj[v].pb({u,i});
	}
	int cut=0;
	for(int i=1; i<=n; i++)
	{
		deg[i]%=2;
		if(deg[i]==1)
		{
			cut++;
		}
	}
	if(cut%2==1)
	{
		cout<<-1;
		return 0;
	}
	dfs(1);
	for(int i=1; i<=m; i++)
	{
		if(dir[i])
		{
			cout<<edge[i].second<<" "<<edge[i].first<<endl;
		}
		else
		{
			cout<<edge[i].first<<" "<<edge[i].second<<endl;
		}
	}
}
```