Problem: Given is a directed graph G with N vertices and M edges.
The vertices are numbered 1 to N, and the i-th edge is directed from Vertex A_i to Vertex B_i.
It is guaranteed that the graph contains no self-loops or multiple edges.

Determine whether there exists an induced subgraph (see Notes) of G such that the in-degree and out-degree of every vertex are both 1. If the answer is yes, show one such subgraph.
Here the null graph is not considered as a subgraph.

Constraints

* 1 \leq N \leq 1000
* 0 \leq M \leq 2000
* 1 \leq A_i,B_i \leq N
* A_i \neq B_i
* All pairs (A_i, B_i) are distinct.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
A_1 B_1
A_2 B_2
:
A_M B_M


Output

If there is no induced subgraph of G that satisfies the condition, print `-1`. Otherwise, print an induced subgraph of G that satisfies the condition, in the following format:


K
v_1
v_2
:
v_K


This represents the induced subgraph of G with K vertices whose vertex set is \\{v_1, v_2, \ldots, v_K\\}. (The order of v_1, v_2, \ldots, v_K does not matter.) If there are multiple subgraphs of G that satisfy the condition, printing any of them is accepted.

Examples

Input

4 5
1 2
2 3
2 4
4 1
4 3


Output

3
1
2
4


Input

4 5
1 2
2 3
2 4
1 4
4 3


Output

-1


Input

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2


Output

4
2
3
4
5

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

#define ll long long int
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
#define INF 0x3f3f3f3f
#define show(x) cerr<<#x<<" : "<<x<<'\n';
#define yogeshk972() cerr<<"\nTime Taken : "<<(float)(clock()-time_p)/CLOCKS_PER_SEC<<"\n";
clock_t time_p=clock();

using namespace std;
const int N=1e3+1, mod= 1e9+7;
vector<int> g[N];

int main(){
	ios_base::sync_with_stdio(0);	cin.tie(0);
	vector<pair<int,int>> e;
	int n,m;
	cin>>n>>m;
	for(int i=0;i<m;i++){
		int u,v;
		cin>>u>>v;
		g[u].pb(v);
		e.pb({u,v});
	}
	vector<int> res;
	for(auto x:e){
		priority_queue< pair<int,int> , vector<pair<int,int>> , greater<pair<int,int>> > pq;
		// x.yy -> x.xx
		pq.push({0,x.yy}); vector<int> dist(n+1,INF);
		dist[x.yy]=0;  unordered_map<int,int> par;
		par[x.yy]=-1;
		while(!pq.empty()){
			int u= pq.top().yy;
			pq.pop();
			for(auto v:g[u]){
				if( dist[v]>dist[u]+1 ){
					par[v]=u;
					dist[v]=dist[u]+1;
					pq.push({dist[v],v});
				}
			}
		}
		if( dist[x.xx]!=INF ){
			vector<int> v;

			int cur=x.xx;
			while(cur!=-1){
				v.pb(cur);
				cur=par[cur];
			}
			if(v.size()<res.size() || res.size()==0 )res=v;
		}
	}
	if(res.size()){
		cout<<res.size()<<"\n";
		for(auto x:res)cout<<x<<"\n";	
	}
	else cout<<"-1";
    yogeshk972();
}