Problem:
Score : 600 points

Problem Statement

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.

Notes

For a directed graph G = (V, E), we call a directed graph G' = (V', E') satisfying the following conditions an induced subgraph of G:

V' is a (non-empty) subset of V.

E' is the set of all the edges in E that have both endpoints in V'.

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.

Sample Input 1

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

Sample Output 1

3
1
2
4

The induced subgraph of G whose vertex set is \{1, 2, 4\} has the edge set \{(1, 2), (2, 4), (4, 1)\}. The in-degree and out-degree of every vertex in this graph are both 1.

Sample Input 2

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

Sample Output 2

-1

There is no induced subgraph of G that satisfies the condition.

Sample Input 3

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

Sample Output 3

4
2
3
4
5

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma GCC optimize(2)
#include<bits/stdc++.h>
#define ll long long
#define maxn 1000005
#define inf 1e9
#define eps 1e-10
using namespace std;

inline int read()
{
	int x=0,w=1; char c=getchar();
	while(c<'0'||c>'9') {if(c=='-') w=-1; c=getchar();}
	while(c<='9'&&c>='0') {x=(x<<1)+(x<<3)+c-'0'; c=getchar();}
	return w==1?x:-x;
}

int n,m,vis[maxn],pre[maxn];
vector <int> mp[maxn],ans,tmp;
queue <int> q;

inline void bfs(int nw)
{
	for(int i=1;i<=n;i++) vis[i]=0; ans.clear();
	while(!q.empty()) q.pop(); q.push(nw),vis[nw]=1;
	while(!q.empty())
	{
		int u=q.front(); q.pop(); //cout<<nw<<" "<<u<<endl;
		for(int i=0;i<mp[u].size();i++)
		{
			int v=mp[u][i];
			if(v==nw)
			{
				int x=u; ans.push_back(nw);
				while(x!=nw) ans.push_back(x),x=pre[x];
				if(ans.size()<tmp.size()||tmp.size()==0) tmp=ans;
				return;
			}
			if(!vis[v]) q.push(v),pre[v]=u,vis[v]=1;
		}
	}
}

int main()
{
	n=read(); m=read();
	for(int i=1;i<=m;i++)
	{
		int u=read(),v=read();
		mp[u].push_back(v);
	}
	for(int i=1;i<=n;i++) bfs(i);
	if(tmp.size()==0) puts("-1");
	else
	{
		cout<<tmp.size()<<endl;
		for(int i=0;i<tmp.size();i++) printf("%d\n",tmp[i]);
	}
	
	return 0;
}