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: Wrong Answer)

//
// Created by Mahmoud Rashad on 11/27/19.
//

#include <bits/stdc++.h>


using namespace std;

typedef vector<int> vi;
typedef pair<int, int> ii;
typedef vector<pair<ii, ii>> vii;

const int MAXN = 1003;
int vis[MAXN];
vector<int> adjList[MAXN];
vector<int> ans;

void dfs(int u) {
    vis[u] = 1;
    for (int v : adjList[u]) {
        if (vis[v] == 1) {
//            cout << v << ' ' << u << endl;
            ans.push_back(v);
            ans.push_back(u);
            return;
        } else if (vis[v] == 0) {
            dfs(v);
            if (!ans.empty() && ans.back() != ans[0]) {
                ans.push_back(u);
                return;
            }
        }
    }
    vis[u] = 2;
}

int main() {
#ifndef ONLINE_JUDGE
//    freopen("input.txt", "r", stdin);
//    freopen("output.out", "w", stdout);
#endif
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0), cout.precision(10), cout << fixed;


    int n, m;
    cin >> n >> m;
    for (int i = 0; i < m; ++i) {
        int u, v;
        cin >> u >> v;
        adjList[u].push_back(v);
    }

    for (int i = 1; i <= n; ++i) {
        if (!vis[i]) {
            dfs(i);
            if (ans.size()) {
                cout << ans.size() - 1 << '\n';
                for (int i = (int)ans.size() - 1; i > 0; --i) {
                    cout << ans[i] << '\n';
                }
                return 0;
            }
        }
    }

    cout << -1 << '\n';

    return 0;
}