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 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
 
using namespace std;
 
typedef vector<int> vi;
typedef queue<int> qi;
 
int main() {
    ios::sync_with_stdio(false);
 
    int n, m;
    cin >> n >> m;
    vi e[n];
    for (int i = 0; i < m; i++) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        e[a].push_back(b);
    }
 
    vi ans;
    for (int i = 0; i < n; i++) {
        int v[n];
        fill(v, v + n, -1);
        qi q;
        for (int y : e[i]) {
            v[y] = i;
            q.push(y);
        }
        while (!q.empty()) {
            int x = q.front();
            q.pop();
 
            if (x == i) {
                vi t;
                x = v[x];
                while (x != i) {
                    t.push_back(x);
                    x = v[x];
                }
                t.push_back(i);
                
                if (ans.size() == 0 || t.size() < ans.size()) {
                    ans = t;
                }
                
                break;
            }
 
            for (int y : e[x]) {
                if (v[y] == -1) {
                    v[y] = x;
                    q.push(y);
                }
            }
        }
    }
 
    if (ans.size()) {
        cout << ans.size() << endl;
        for (int i = ans.size() - 1; i >= 0; i--) {
            cout << ans[i] + 1 << endl;
        }
    } else {
        cout << -1 << endl;
    }
 
    return 0;
}