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: Runtime Error)

#region いつもの
#pragma warning disable
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using static AtCoderProject.Global;

namespace AtCoderProject
{
    static class Global
    {
        private class ComparerReverseImpl<T> : Comparer<T> where T : IComparable<T> { public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); }
        public static IComparer<T> ComparerReverse<T>() where T : IComparable<T> => new ComparerReverseImpl<T>();
        public static BigInteger ParseBigInteger(string s)
        {
            // MonoのBigInteger.Parseが遅いので自前実装
            var res = BigInteger.Zero;
            var splited = new string[(s.Length + 7) / 8];
            for (int i = 0; i < splited.Length - 1; i++)
            {
                splited[i] = s.Substring(8 * i, 8);
            }
            splited[splited.Length - 1] = s.Substring(8 * (splited.Length - 1));
            foreach (var sp in splited)
            {
                res *= (int)Math.Pow(10, sp.Length);
                res += int.Parse(sp);
            }
            return res;
        }
        public static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        public static string AllJoin<T>(IEnumerable<T> source) => string.Join(" ", source);
    }
    static class Ext
    {
        public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public int Int0 => Int - 1; public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public IEnumerable<string> String => this.Select(cr => cr.String); public IEnumerable<int> Int => this.Select(cr => cr.Int); public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1); public IEnumerable<long> Long => this.Select(cr => cr.Long); public IEnumerable<double> Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    public class Program
    {
        [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc());

        #endregion
        public object Calc()
        {
            var N = consoleReader.Int;
            var M = consoleReader.Int;
            var graph = new GraphBuilder(N, consoleReader, M).ToArray();
            var cycle = new GraphSearch(graph).GetCycleBFS();
            Console.WriteLine(cycle.Length - 1);
            return AllLines(cycle.Skip(1));
        }
        class GraphBuilder
        {
            private List<int>[] roots;
            private List<int>[] children;
            public GraphBuilder(int count, bool isOriented = true)
            {
                this.roots = new List<int>[count];
                this.children = new List<int>[count];
                for (int i = 0; i < count; i++)
                {
                    if (isOriented)
                    {
                        this.roots[i] = new List<int>();
                        this.children[i] = new List<int>();
                    }
                    else
                    {
                        this.roots[i] = this.children[i] = new List<int>();
                    }
                }
            }
            public GraphBuilder(int count, ConsoleReader cr, int edgeCount, bool isOriented = true) : this(count, isOriented)
            {
                for (int i = 0; i < edgeCount; i++)
                    this.Add(cr.Int - 1, cr.Int - 1);
            }
            public void Add(int from, int to)
            {
                children[from].Add(to);
                roots[to].Add(from);
            }
            public Node[] ToArray() =>
                Enumerable
                .Zip(roots, children, (r, c) => Tuple.Create(r, c))
                .Select((t, i) => new Node(i, t.Item1.ToArray(), t.Item2.ToArray()))
                .ToArray();
        }
        public class Node : IEquatable<Node>
        {
            public Node(int i, int[] roots, int[] children)
            {
                this.index = i;
                this.roots = roots;
                this.children = children;
            }
            public int index;
            public int[] roots;
            public int[] children;

            public override string ToString() => $"children: {string.Join(",", children)}";
            public override bool Equals(object obj)
            {
                if (obj is Node)
                    return this.Equals((Node)obj);
                else
                    return false;
            }
            public bool Equals(Node other) => this.index == other.index;
            public override int GetHashCode() => this.index;
        }

        class GraphSearch
        {
            enum Status
            {
                None,
                Active,
                Done
            }
            Node[] graph;
            Status[] statuses;
            public GraphSearch(Node[] graph)
            {
                this.graph = graph;
                this.statuses = new Status[graph.Length];
            }
            public int[] GetCycleBFS()
            {
                for (int i = 0; i < graph.Length; i++)
                {
                    if (statuses[i] == Status.None)
                    {
                        var res = GetCycleBFS(i);
                        if (res != null)
                            return res;
                    }
                }
                return null;
            }
            int[] GetCycleBFS(int v)
            {
                int[] res = null;
                statuses[v] = Status.Active;
                var queue = new Queue<int[]>();
                queue.Enqueue(new[] { v });
                while (queue.Count > 0)
                {
                    var currentArr = queue.Dequeue();
                    foreach (var child in graph[currentArr[currentArr.Length - 1]].children)
                    {
                        switch (statuses[child])
                        {
                            case Status.None:
                                if (res == null)
                                {
                                    statuses[child] = Status.Active;
                                    var next = new int[currentArr.Length + 1];
                                    Array.Copy(currentArr, next, currentArr.Length);
                                    next[next.Length - 1] = child;
                                    queue.Enqueue(next);
                                }
                                break;
                            case Status.Active:
                                var index = Array.IndexOf(currentArr, child);
                                if (res == null || res.Length > currentArr.Length + 1 - index)
                                {
                                    res = new int[currentArr.Length + 1 - index];
                                    Array.Copy(currentArr, index, res, 0, currentArr.Length - index);
                                    res[res.Length - 1] = child;
                                }
                                break;
                        }
                    }
                }
                if (res != null)
                    return res;

                for (int i = 0; i < statuses.Length; i++)
                    if (statuses[i] == Status.Active)
                        statuses[i] = Status.Done;
                return null;
            }
        }
    }
}