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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;
import static java.lang.System.in;

public class Main {
    ArrayList<Integer>[] graph;

    PrintWriter out = new PrintWriter(System.out);
    // no self-loop or multiple edges
    public static void main(String[] args) throws Exception {
        Main main = new Main();
//        main.solve();
        System.out.println(main.solve());
    }
    long solve(){
        // binary search
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(), m = sc.nextInt();
        graph = new ArrayList[n+1];
        for(int i=0;i<=n;i++) graph[i] = new ArrayList<>();
        for(int i=0;i<m;i++){
            int a = sc.nextInt(), b = sc.nextInt();
            graph[a].add(b);
        }
        for(int start=1;start <=n;start++){
            Set<Integer> rec = new HashSet<>(n);
//            rec.add(start);
            HashMap<Integer,Integer> forbid = new HashMap<>();
            for(int t:graph[start]){
//                rec.add(t);
                dfs(start,start,rec, forbid);
//                rec.remove(t);
            }
            rec.remove(start);
        }
        return -1;
    }
    void dfs(int cur, int start, Set<Integer> visited, HashMap<Integer,Integer> forbid){
        if(forbid.containsKey(cur)) return;
        if(cur==start&&visited.size()>1){
            //
            for(int a:visited){
                if(forbid.containsKey(a)) return;
            }
            // find a loop as wanted
            out.println(visited.size());
            for(int v:visited) out.println(v);
            out.flush();
            System.exit(0);
        }
        if(!visited.add(cur)) return;
        for(int to:graph[cur]){
            AddElement(to,forbid);
        }
        for(int to:graph[cur]){
            decreaseElement(to,forbid);
            if(!forbid.containsKey(to)){
                dfs(to,start,visited,forbid);
            }
            AddElement(to,forbid);
        }
        for(int to:graph[cur]) decreaseElement(to, forbid);
        visited.remove(cur);
    }
    void AddElement(int target, HashMap<Integer,Integer> forbidden){
        forbidden.put(target,1+forbidden.getOrDefault(target,0));
    }
    void decreaseElement(int target, HashMap<Integer,Integer> forbidden){
        Integer val = forbidden.getOrDefault(target,0);
        if(val>1) forbidden.put(target,val-1);
        else forbidden.remove(target);
    }
}