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++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <functional>
using namespace std;

int main()
{
    int N, M;
    cin>>N>>M;

    vector<vector<int>> E(N);
    for (int i=0; i<M; i++)
    {
        int A, B;
        cin>>A>>B;
        E[A-1].push_back(B-1);
    }

    vector<int> C;
    vector<bool> F(N);
    bool f = false;

    function<void(int)> BT = [&](int c)
    {
        if (F[c])
        {
            if (c==0)
                f = true;
            return;
        }

        C.push_back(c);
        F[c] = true;

        for (int e: E[c])
        {
            BT(e);
            if (f)
                break;
        }

        if (!f)
            C.pop_back();
    };

    for (int s=0; s<N && !f; s++)
    {
        for (int i=0; i<N; i++)
            F[i] = false;
        BT(s);
    }

    if (C.size()<=1)
    {
        cout<<-1<<endl;
        return 0;
    }

    vector<bool> F2(N);
    vector<int> C2;

    while (true)
    {
        for (int i=0; i<N; i++)
            F2[i] = false;
        for (int c: C)
            F2[c] = true;

        int ef = -1;
        int et = -1;
        for (int i=0; i<(int)C.size() && ef==-1; i++)
            for (int e: E[C[i]])
                if (F2[e] &&
                    e!=C[(i+1)%C.size()])
                {
                    ef = C[i];
                    et = e;
                    break;
                }

        if (ef==-1)
            break;

        C2.clear();
        for (int c: C)
        {
            if (c==ef)
            {
                int s = 0;
                for (int c: C)
                {
                    if (s==0)
                        C2.push_back(c);
                    if (c==ef)
                        s=1;
                    if (c==et)
                        s=2;
                    if (s==2)
                        C2.push_back(c);
                }
                break;
            }
            else if (c==et)
            {
                int s = 0;
                for (int c: C)
                {
                    if (c==et)
                        s = 1;
                    if (s==1)
                        C2.push_back(c);
                    if (c==ef)
                        s = 2;
                }
                break;
            }
        }
        C.swap(C2);
    }

    cout<<C.size()<<endl;
    for (int c: C)
        cout<<c+1<<endl;
}