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.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
public static class P
{
    public static void Main()
    {
        var nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var n = nm[0];
        var m = nm[1];
        List<int>[] graph = Enumerable.Repeat(0, n).Select(_ => new List<int>()).ToArray();
        for (int i = 0; i < m; i++)
        {
            var st = Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray();
            graph[st[0]].Add(st[1]);
        }
        ImmutableStack<int> resStack = null;
        for (int i = 0; i < n; i++)
        {
            ImmutableStack<int>[] istacks = new ImmutableStack<int>[n];
            istacks[i] = new ImmutableStack<int>().Push(i);
            Queue<int> queue = new Queue<int>();
            queue.Enqueue(i);
            while (queue.Count > 0)
            {
                var item = queue.Dequeue();
                foreach (var adj in graph[item])
                {
                    if (adj == i)
                    {
                        if (resStack == null || resStack.Count > istacks[item].Count) resStack = istacks[item];
                        goto end;
                    }
                    if (istacks[adj] != null) continue;
                    istacks[adj] = istacks[item].Push(adj);
                    queue.Enqueue(adj);
                }
            }
            end:;
        }
        if (resStack == null) Console.WriteLine(-1);
        else
        {
            Console.WriteLine(resStack.Count);
            while (resStack.Count > 0)
            {
                Console.WriteLine(resStack.Top + 1);
                resStack = resStack.Pop();
            }
        }
    }
}


class ImmutableStack<T>
{
    readonly ImmutableStack<T> previousStack;
    public readonly T Top;
    public readonly int Count;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ImmutableStack() : this(null, default(T), 0) { }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private ImmutableStack(ImmutableStack<T> prev, T top, int count)
    {
        previousStack = prev;
        Top = top;
        Count = count;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ImmutableStack<T> Push(T value) => new ImmutableStack<T>(this, value, Count + 1);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ImmutableStack<T> Pop() => previousStack == null ? null : previousStack;
}