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.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static List<int>[] li;
	static bool[] b;
	static int[] h;
	static void Main(){
		Sc sc=new Sc();
		int[] s=sc.Ia;
		int n=s[0],m=s[1];
		li=new List<int>[n+1];
		h=new int[n+1];
		for(int i=1;i<=n;i++){li[i]=new List<int>();}
		for(int i=0;i<m;i++){
			int[] e=sc.Ia;
			li[e[0]].Add(e[1]);
		}
		int ans=int.MaxValue,t=-1;
		for(int i = 1;i<=n;i++) {
			b=new bool[n+1];
			var qu=new Queue<Tuple<int,int>>();
			qu.Enqueue(Tuple.Create(i,0));
			while(qu.Count>0&&!b[0]){
				var e=qu.Dequeue();
				if(e.Item2>=ans){break;}
				b[e.Item1]=true;
				for(int j=0;j<li[e.Item1].Count;j++){
					if(!b[li[e.Item1][j]]){
						qu.Enqueue(Tuple.Create(li[e.Item1][j],e.Item2+1));
						b[e.Item1]=true;
					}
					else if(li[e.Item1][j]==i){
						ans=e.Item2+1;
						t=i;
						b[0]=true;
						break;
					}
				}
			}
		}
		if(t!=-1){
			Console.WriteLine("{0}",ans);
			b=new bool[n+1];
			var qu=new Queue<Tuple<int,string>>();
			qu.Enqueue(Tuple.Create(t,t.ToString()));
			while(qu.Count>0&&!b[0]){
				var e=qu.Dequeue();
				b[e.Item1]=true;
				for(int j=0;j<li[e.Item1].Count;j++){
					if(!b[li[e.Item1][j]]){
						qu.Enqueue(Tuple.Create(li[e.Item1][j],e.Item2+" "+li[e.Item1][j].ToString()));
						b[e.Item1]=true;
					}
					else if(li[e.Item1][j]==t){
						Console.WriteLine(String.Join("\n",Array.ConvertAll(e.Item2.Split(),int.Parse)));
						b[0]=true;
						break;
					}
				}
			}
		}
		else{Console.WriteLine(-1);}
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}