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: Runtime Error)

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

int fa[2005];
vector<int>B;
int find(int x,int &cnt)
{
	++cnt;
	B.push_back(x);
	if(x==fa[x]) return x;
	return find(fa[x],cnt);
}

int main()
{
	int n,m; cin>>n>>m;
	int cnt = 0;
	vector<int>A;
	int ans = INT_MAX;
	for(int i=0;i<=n;++i) fa[i] = i;
	for(int i=0;i<m;++i)
	{
		int u,v;
		cin>>u>>v;
		cnt = 0;
		B.clear();
		if(find(v,cnt)==u)
		{
			ans = min(ans,cnt);
			A.clear();
			for(int i=0;i<B.size();++i)
			{
				A.push_back(B[i]);
			}
		}
		else fa[u] = v;
		
	}
	if(ans==INT_MAX) {
		cout<<"-1"<<"\n"; return 0;
	}
	cout<<ans<<"\n";
	for(int i=0;i<ans;++i) cout<<A[i]<<"\n";
}