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.Generic;
using System.Linq;

public class Solution
{
    static List<int> GetCycle(int n, List<int>[] edges)
    {
        for (int i = 1; i <= n; i++)
        {
            var cycle = GetCycle(n, edges, i);
            if (cycle != null)
            {
                return cycle;
            }
        }
        return null;
    }

    static List<int> GetCycle(int n, List<int>[] edges, int start)
    {
        var prev = new int[n + 1];
        var currents = new List<int>() { start };

        do
        {
            var nexts = new List<int>();
            foreach (var cur in currents)
            {
                foreach (var next in edges[cur].Where(v => prev[v] == 0))
                {
                    nexts.Add(next);
                    prev[next] = cur;
                }
            }

            currents = nexts;
        } while (currents.Count > 0 && prev[start] == 0);
        if (prev[start] == 0)
        {
            return null;
        }

        var way = new Stack<int>();
        for (int v = prev[start]; v != start; v = prev[v])
        {
            way.Push(v);
        }
        way.Push(start);
        return way.ToList();
    }

    static void DeleteExtraEdge(List<int>[] edges, List<int> cycle)
    {
        var vertex = new HashSet<int>(cycle);
        foreach (var v in cycle)
        {
            edges[v] = edges[v].Where(x => vertex.Contains(x)).ToList();
        }
    }

    static List<int> GetInducedSubgraph(int n, List<int>[] edges, List<int> cycle)
    {
        while (true)
        {
            DeleteExtraEdge(edges, cycle);
            var ex = 0;
            for (int i = 0; i < cycle.Count; i++)
            {
                var cur = cycle[i];
                if (edges[cur].Count > 1)
                {
                    var next = cycle[(i + 1) % cycle.Count];
                    ex = edges[cur].First(v => v != next);
                    break;
                }
            }
            if (ex == 0)
            {
                return cycle;
            }
            cycle = GetCycle(n, edges, ex);
        }
    }

    public static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var N = vals[0];
        var M = vals[1];
        var edges = Enumerable.Range(0, N + 1).Select(_ => new List<int>()).ToArray();
        for (int i = 0; i < M; i++)
        {
            vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            edges[vals[0]].Add(vals[1]);
        }

        var cycle = GetCycle(N, edges);
        if (cycle == null)
        {
            Console.WriteLine(-1);
            return;
        }
        cycle = GetInducedSubgraph(N, edges, cycle);
        Console.WriteLine(cycle.Count);
        Console.WriteLine(string.Join(Environment.NewLine, cycle));
    }
}