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: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Deque;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;

public class Main {

	static PrintWriter out;
	static InputReader ir;
	static int x=-1;

	static void solve() {
		int n=ir.nextInt();
		int m=ir.nextInt();
		Graph[] g=new Graph[n];
		Graph[] f=new Graph[n];
		boolean[][] e=new boolean[n][n];
		for(int i=0;i<n;i++){
			g[i]=new Graph();
			f[i]=new Graph();
		}
		for(int i=0;i<m;i++){
			int u=ir.nextInt()-1;
			int v=ir.nextInt()-1;
			g[u].add(v);
			f[v].add(u);
			e[u][v]=true;
		}
		int[] tp=TopologicalSort(g);
		if(x<0){
			out.println(-1);
		}
		else{
			long[] d=dijkstra(x, g);
			ArrayList<Integer> l=new ArrayList<>();
			for(int i=0;i<n;i++){
				if(d[i]<1L<<60&&e[i][x]){
					int cur=i;
					while(cur!=x){
						l.add(cur);
						for(int to : f[cur]){
							if(d[to]+1==d[cur]){
								cur=to;
								break;
							}
						}
					}
					l.add(x);
					out.println(l.size());
					for(int j=0;j<l.size();j++){
						out.println(l.get(j)+1);
					}
					return;
				}
			}
			out.println(-1);
		}
	}

	public static long[] dijkstra(int s, Graph[] g) {
		long[] d = new long[g.length];
		PriorityQueue<long[]> pq = new PriorityQueue<long[]>(new Comparator<long[]>() {
			public int compare(long[] a, long[] b) {
				return Long.compare(a[1], b[1]);
			}
		});
		Arrays.fill(d, 1L << 60);
		d[s] = 0;
		pq.offer(new long[] { s, 0 });
		while (!pq.isEmpty()) {
			long[] p = pq.poll();
			int from = (int) p[0];
			if (d[from] != p[1])
				continue;
			for (int i = 0; i < g[from].size(); i++) {
				int e = g[from].get(i);
				int to = (int) e;
				if (d[to] > d[from] + 1) {
					d[to] = d[from] + 1;
					pq.offer(new long[] { to, d[to] });
				}
			}
		}
		return d;
	}

	static int[] TopologicalSort(Graph[] g) {
		int n = g.length;
		int[] in = new int[n];
		int[] ord = new int[n];
		for (int i = 0; i < n; i++) {
			for (int to : g[i])
				in[to]++;
		}
		Deque<Integer> s = new ArrayDeque<Integer>();
		for (int i = 0; i < n; i++) {
			if (in[i] == 0) {
				s.offerFirst(i);
			}
		}
		int p = 0;
		while (!s.isEmpty()) {
			int from = s.pollFirst();
			ord[p++] = from;
			for (int j = 0; j < g[from].size(); j++) {
				int to = g[from].get(j);
				in[to]--;
				if (in[to] == 0) {
					s.offerFirst(to);
				}
			}
		}
		for (int i = 0; i < n; i++)
			if (in[i] != 0){
				x=i;
				return ord;
			}
		return ord;
	}

	static class Graph extends ArrayList<Integer>{}

	public static void main(String[] args) {
		ir = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	static class InputReader {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}

	static void tr(Object... o) {
		out.println(Arrays.deepToString(o));
	}
}