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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			Scanner cin = new Scanner();
			int n = cin.Int();
			int m = cin.Int();
			List<int>[] to = new List<int>[n];
			for (int i = 0; i < n; i++) {
				to[i] = new List<int>();
			}

			for (int i = 0; i < m; i++) {
				int a = cin.Int() - 1;
				int b = cin.Int() - 1;
				to[a].Add(b);
			}

			int inf = n + 1;
			List<int> ans = null;
			for (int i = 0; i < n; i++) {
				var q = new Queue<int>();
				var dist = new int[n];
				var prev = new int[n];
				for (int j = 0; j < n; j++) {
					dist[j] = inf;
					prev[j] = -1;
				}
				dist[i] = 0;
				q.Enqueue(i);

				while (q.Count > 0) {
					var next = q.Dequeue();
					for (int j = 0; j < to[next].Count(); j++) {
						int toi = to[next][j];
						if (dist[toi] != inf) {
							continue;
						}

						dist[toi] = dist[next] + 1;
						prev[toi] = next;
						q.Enqueue(toi);
					}
				}

				var min = new Tuple<int, int>(inf, 0);
				for (int j = 0; j < n; j++) {
					foreach (int k in to[j]) {
						if (k == i) {
							if (dist[j] < min.Item1) {
								min = new Tuple<int, int>(dist[j], j);
							}
						}
					}
				}

				if (min.Item1 != inf) {
					int v = min.Item2;
					var temp = new List<int>();
					while (v != -1) {
						temp.Add(v);
						v = prev[v];
					}

					if (ans == null || temp.Count < ans.Count) {
						ans = temp;
					}
				}
			}

			if (ans == null) {
				Console.WriteLine(-1);
			} else {
				var sb = new StringBuilder();
				sb.AppendLine(ans.Count.ToString());
				for (int i = 0; i < ans.Count; ++i) {
					sb.AppendLine($"{ans[i] + 1}");
				}

				Console.WriteLine(sb.ToString());
			}
		}
	}

	public class Scanner
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private string[] buf_;
		private int index_;

		public Scanner()
		{
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = Console.ReadLine();
			while (st == "") {
				st = Console.ReadLine();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}
	}
}