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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

using graph = vector<vector<int>>;

int main() {
    int n, m; cin >> n >> m;
    graph g(n);
    for(int i = 0; i < m; ++i) {
        int a, b; cin >> a >> b;
        a--, b--;
        g[a].push_back(b);
    }

    vector<int> used(n);
    function<vector<int>(vector<int> const&)> find_cycle = [&] (vector<int> path) {
        assert(!path.empty());
        for(auto to : g[path.back()]) {
            if(used[to] == 2) continue;
            if(used[to] == 1) {
                reverse(path.begin(), path.end());
                while(path.back() != to) path.pop_back();
                reverse(path.begin(), path.end());
                return path;
            } else {
                used[to] = 1;
                path.push_back(to);
                auto vs = find_cycle(path);
                if(!vs.empty()) {
                    return vs;
                }
                path.pop_back();
                used[to] = 2; // searched
            }
        }
        return std::vector<int>{};
    };

    vector<int> cycle, nxt(n, -1);
    for(int i = 0; i < n; ++i) {
        fill(used.begin(), used.end(), 0);
        used[i] = 1;
        cycle = find_cycle({i});
        if(!cycle.empty()) {
            for(int j = 0; j < (int)cycle.size(); ++j) {
                nxt[cycle[j]] = cycle[(j + 1) % n];
            }
            break;
        }
    }

    if(cycle.empty()) {
        cout << -1 << endl;
        return 0;
    }

    // remove
    bool update = true;
    while(update) {
        update = false;
        vector<int> nnxt(n, -1);
        //for(int i = 0; i < n; ++i) {
        //    cout << nxt[i] << " \n"[i + 1 == n];
        //}
        for(int from = 0; from < n && !update; ++from) {
            if(nxt[from] == -1) continue;
            for(auto to : g[from]) {
                if(nxt[to] == -1) continue;
                if(nxt[from] == to) continue; // on cycle
                nxt[from] = to;
                update = true;
                int cur = from;
                do {
                    nnxt[cur] = nxt[cur];
                    cur = nxt[cur];
                } while(cur != from);
                break;
            }
        }
        if(update) {
            nxt = move(nnxt);
        }
    }

    vector<int> ans;
    for(int i = 0; i < n; ++i) {
        if(nxt[i] == -1) continue;
        ans.push_back(i);
    }
    cout << ans.size() << endl;
    for(auto v : ans) {
        cout << v + 1 << endl;
    }
}