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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int M = int.Parse(str[1]);
		int[,]A = new int[M,2];
		int[]B1 = new int[N];
		int[]B2 = new int[N];
		for(var i=0;i<M;i++){
			string[] str2 = Console.ReadLine().Split();
			A[i,0] = int.Parse(str2[0]);
			A[i,1] = int.Parse(str2[1]);
			B1[A[i,0]-1]++;
			B2[A[i,0]-1]++;
		}
		var hs = new HashSet<int>();
		for(var i=0;i<M;i++){
			hs.Add(i);
		}
		while(hs.Count>0){
			var hs2 = new HashSet<int>(hs);
			hs.Clear();
			bool flag = false;
			int[] BA = new int[N];
			int[] BB = new int[N];
			foreach(var i in hs2){
				BA[A[i,0]-1]++;
				BB[A[i,1]-1]++;
			}
			foreach(var i in hs2){
				if(BA[A[i,0]-1]>0 && BA[A[i,1]-1]>0 && BB[A[i,0]-1]>0 && BB[A[i,1]-1]>0){
					hs.Add(i);
				} else {
					flag = true;
				}
			}
			if(!flag){
				break;
			}
		}
		if(hs.Count==0){
			Console.WriteLine("-1");
		} else {
			var list = new List<int>();
			int a = -1;
			int b = -1;
			foreach(var i in hs){
				a = A[i,0];
				b = A[i,1];	
			}
			list.Add(a);
			list.Add(b);
			int listAns = -1;
			while(true){
				foreach(var i in hs){
					if(A[i,0]==b){
						int a2 = A[i,1];
						for(var j=0;j<list.Count;j++){
							if(list[j]==a2){
								listAns = list[j];
								break;
							}
						}
						if(listAns == -1){
							list.Add(a2);
							b = a2;
						}
						break;
					}
				}
				if(listAns>=0){
					break;
				}
			}
			Console.WriteLine(list.Count);
			for(var i=0;i<list.Count;i++){
				Console.WriteLine(list[i]);
			}
		}
	}
}