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)

#include <iostream>
#include <fstream>
#include <cmath>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <set>
#include <unordered_set>
#include <bitset>
#include <limits>
#include <algorithm>

#define MOD_BIG 1000000007
using std::string;
using std::cin;
using std::cout;
using std::cerr;
using std::endl;
using ll = long long;
using std::vector;

template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) {
    vec.resize(len);
    for (auto &v : vec) ndarray(v, args...);
}

//////////////////////////////////////

enum Status {
    Not = 0,
    Now,
    End,
};

template<typename T>
struct Edge {
    int to;
    int from;
    T weight;
    Edge(int from, int to, T weight) : from(from), to(to), weight(weight) {}
};

template<typename T, typename D>
struct Graph {
    int n;
    vector<vector<Edge<T>>> g;
    vector<D> data;
    vector<Status> s;
    
    Graph(int N) : n(N), g(N+1), data(N+1), s(N+1) {}
    
    void add_edge(int from, Edge<T> e) {
        g[from].push_back(e);
    }
    void set_data(int node, D value) {
        data[node] = value;
    }
    
    //改変して使うか、削除する
    vector<Edge<T>> dfs(int now, int par, int depth, vector<Edge<T>> route) {
        //std::cout << "searching now: " << now << std::endl;
        if (g[now].empty()) {
            //終端ノード
            return {};
        }
        s[now] = Status::Now;
        vector<Edge<T>> res;
        for (auto e : g[now]) {
            int chi = e.to;
            if (s[chi] == Status::Now) {
                //閉路あり
                auto r = route;
                r.push_back(e);
                if (r.size() == n) {
                    return {};
                }
                return r;
            } else {
                //未探索
                auto r = route;
                r.push_back(e);
                auto tmp = dfs(chi, now, depth+1, r);
                if (tmp.size() != 0) {
                    return tmp;
                }
            }
        }
        s[now] = Status::End;
        return res;
    }
    
    //出力
    void print() {
        for (auto v: g) {
            for (auto e: v) {
                std::cout << e.from << "-(" << e.weight << ")->" << e.to << ", ";
            }
            std::cout << std::endl;
        }
    }
};

//////////////////////////////////////

int main() {
    
    int N, M;
    cin >> N >> M;
    
    Graph<int, int> g(N);
    
    for (int i = 0; i < M; i++) {
        int a, b;
        cin >> a >> b;
        g.add_edge(a, Edge<int>(a, b, 1));
    }
    
    //g.print();
    vector<Edge<int>> ans;
    for (int i = 1; i <= N; i++) {
        auto tmp = g.dfs(i, -1, 1, {});
        if (tmp.size() != 0) {
            ans = tmp;
            break;
        }
    }
    if (ans.size() == 0) {
        cout << -1 << endl;
        return 0;
    }
    cout << ans.size() << endl;
    for (auto e: ans) {
        cout << e.from << endl;
    }
    
    return 0;
}