Problem: 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.

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.

Examples

Input

4 5
1 2
2 3
2 4
4 1
4 3


Output

3
1
2
4


Input

4 5
1 2
2 3
2 4
1 4
4 3


Output

-1


Input

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2


Output

4
2
3
4
5

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main
{
    PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tok;

    ArrayList<Integer> ans;

    public void go() throws IOException
    {
        ntok();
        int n = ipar();
        int m = ipar();
        Vertex[] vertices = new Vertex[n];
        for (int i = 0; i < n; i++)
        {
            vertices[i] = new Vertex(i);
        }
        for (int i = 0; i < m; i++)
        {
            ntok();
            int a = ipar()-1;
            int b = ipar()-1;
            vertices[a].add(vertices[b]);
        }
        for (int i = 0; i < n; i++)
        {
            if (!vertices[i].visit)
            {
                dfs(vertices[i], new ArrayList<>());
            }
            for (Vertex v : vertices)
            {
                v.finish = false;
                v.visit = false;
            }
        }
        if (ans != null)
        {
            out.println(ans.size());
            for (int x : ans)
            {
                out.println(x+1);
            }
        }
        else
        {
            out.println(-1);
        }

        out.flush();
        in.close();
    }

    public void dfs(Vertex curr, ArrayList<Vertex> path)
    {
        if (curr.visit)
        {
            if (!curr.finish)
            {
                ArrayList<Integer> temp = new ArrayList<>();
                temp.add(curr.i);
                for (int i = path.size()-1; i >= 0; i--)
                {
                    if (path.get(i).i == curr.i)
                    {
                        break;
                    }
                    temp.add(path.get(i).i);
                }
                if (ans == null || temp.size() < ans.size())
                {
                    ans = temp;
                }
            }
            return;
        }
        curr.visit = true;
        path.add(curr);
        for (Vertex v : curr.neighbors)
        {
            dfs(v, path);
        }
        path.remove(path.size()-1);
        curr.finish = true;
    }

    private class Vertex
    {
        int i;
        ArrayList<Vertex> neighbors;
        boolean visit, finish;

        public Vertex(int i)
        {
            this.i = i;
            neighbors = new ArrayList<>();
        }

        public void add(Vertex other)
        {
            neighbors.add(other);
        }
    }

    public void ntok() throws IOException
    {
        tok = new StringTokenizer(in.readLine());
    }

    public int ipar()
    {
        return Integer.parseInt(tok.nextToken());
    }

    public int[] iapar(int n)
    {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
        {
            arr[i] = ipar();
        }
        return arr;
    }

    public long lpar()
    {
        return Long.parseLong(tok.nextToken());
    }

    public long[] lapar(int n)
    {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
        {
            arr[i] = lpar();
        }
        return arr;
    }

    public double dpar()
    {
        return Double.parseDouble(tok.nextToken());
    }

    public String spar()
    {
        return tok.nextToken();
    }

    public static void main(String[] args) throws IOException
    {
        new Main().go();
    }
}