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)

#define _USE_MATH_DEFINES
#include <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <algorithm>
#include <functional>
#include <bitset>
#include <iterator>
#include <valarray>
#include <complex>
#include <utility>
#include <string>
#include <sstream>
#include <tuple>
#include <initializer_list>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cctype>
#include <cmath>
#include <cassert>
#include <unordered_map>
#include <unordered_set>
#include <iomanip>
#include <fstream>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rep1(i, n) for (int i = 1; i <= (int)(n); ++i)
#define all(c) (c).begin(),(c).end()
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using tii = tuple<int, int>;
using tll = tuple<ll, ll>;
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; }
#ifdef DBG
template<typename T> ostream &operator<<(ostream &os, set<T> const &s) { if (s.size() == 0) return os << "{}"; os << "{"; decltype(s.begin()) iter; for (iter = s.begin(), ++iter; iter != s.end(); ++iter) { --iter; os << *iter << ", "; ++iter; } --iter; os << *iter << '}'; return os; }
template<typename T> ostream &operator<<(ostream &os, multiset<T> const &s) { if (s.size() == 0) return os << "{}"; os << "{"; decltype(s.begin()) iter; for (iter = s.begin(), ++iter; iter != s.end(); ++iter) { --iter; os << *iter << ", "; ++iter; } --iter; os << *iter << '}'; return os; }
template<typename T, typename U> ostream &operator<<(ostream &os, map<T, U> const &mp) { if (mp.size() == 0) return os << "{}"; os << "{" << endl; decltype(mp.begin()) iter; for (iter = mp.begin(), ++iter; iter != mp.end(); ++iter) { --iter; os << "  {" << iter->first << ", " << iter->second << "}," << endl; ++iter; } --iter; os << "  {" << iter->first << ", " << iter->second << "}" << endl << '}'; return os; }
template<typename T> ostream &operator<<(ostream &os, unordered_set<T> const &s) { if (s.size() == 0) return os << "{}"; os << "{"; decltype(s.begin()) iter; for (iter = s.begin(), ++iter; iter != s.end(); ++iter) { --iter; os << *iter << ", "; ++iter; } --iter; os << *iter << '}'; return os; }
template<typename T> ostream &operator<<(ostream &os, unordered_multiset<T> const &s) { if (s.size() == 0) return os << "{}"; os << "{"; decltype(s.begin()) iter; for (iter = s.begin(), ++iter; iter != s.end(); ++iter) { --iter; os << *iter << ", "; ++iter; } --iter; os << *iter << '}'; return os; }
template<typename T, typename U> ostream &operator<<(ostream &os, unordered_map<T, U> const &mp) { if (mp.size() == 0) return os << "{}"; os << "{" << endl; decltype(mp.begin()) iter; for (iter = mp.begin(), ++iter; iter != mp.end(); ++iter) { --iter; os << "  {" << iter->first << ", " << iter->second << "}," << endl; ++iter; } --iter; os << "  {" << iter->first << ", " << iter->second << "}" << endl << '}'; return os; }
template<typename T> ostream &operator<<(ostream &os, vector<T> const &v) { os << '['; rep(i, v.size()-1) os << v[i] << ", "; if (v.size() > 0) os << v[v.size()-1]; cerr << ']'; return os; }
template<typename T, unsigned N, unsigned Last> struct TuplePrinter { static void print(ostream &os, T const& v) { os << std::get<N>(v) << ", "; TuplePrinter<T, N + 1, Last>::print(os, v); } };
template<typename T, unsigned N> struct TuplePrinter<T, N, N> { static void print(ostream &os, T const &v) { os << std::get<N>(v); } };
template<typename... Types> ostream& operator<<(ostream &os, tuple<Types...> const &v) { os << "("; TuplePrinter<tuple<Types...>, 0, sizeof...(Types) - 1>::print(os, v); os << ")"; return os; }
template<typename T> void _dbg(T const &t) { cerr << t << endl; }
template<typename T, typename... Args> void _dbg(T const &t, Args... args) { cerr << t << " "; _dbg(args...); }
template<typename... Args> void __dbg(const char *fn, int l, Args... args) { cerr << "[" << fn << ":" << l << "] "; _dbg(args...); }
#define dbg(...) __dbg(__func__, __LINE__, __VA_ARGS__)
#else
#define dbg(...)
#endif
const ll infty = 1223372036854775807LL;
const double eps = 1e-8;

enum Flag {
    NEW = 0,
    CUR = 1,
    FINISHED = 2
};

bool dfs(const vvi& g, vector<Flag>& flag, int node, vi& loop) {
    if (flag[node] == FINISHED) return false; // visited node
    else if (flag[node] == CUR) return true; // loop close point
    else { // unvisited node
        flag[node] = CUR;
        for (int to: g[node]) {
            if (dfs(g, flag, to, loop)) {
                loop.push_back(node);
                return true;
            }
        }
        flag[node] = FINISHED;
        return false;
    }
}

vi find_loop(const vvi& g) {
    int n = g.size();
    vector<Flag> flag(n, NEW);
    vi res;
    rep(i, n) {
        if (dfs(g, flag, i, res)) {
            break;
        }
    }
    return vi(res.rbegin(), res.rend());
}

void solve() {
    int n, m;
    cin >> n >> m;
    vvi g(n);
    rep(i, m) {
        int a, b;
        cin >> a >> b;
        --a; --b;
        g[a].push_back(b);
    }
    auto loop = find_loop(g);
    if (loop.size() == 0) {
        cout << -1 << endl;
        return;
    }
    // compress loop
    for (;;) {
        vector<int> index_of(n, -1);
        bool updated = false;
        dbg(loop);
        rep(i, loop.size()) index_of[loop[i]] = i;
        rep(i, loop.size()-1) {
            int node = loop[i];
            int next = loop[i+1];
            for (int to : g[node]) if (to != next && index_of[to] != -1) {
                int idx = index_of[to];
                if (idx < i) {
                    loop = vi(loop.begin()+idx, loop.begin()+i+1);
                } else {
                    loop.erase(loop.begin()+i+1, loop.begin()+idx);
                }
                updated = true;
                break;
            }
            if (updated) break;
        }
        if (!updated) break;
    }
    cout << loop.size() << endl;
    for (int node : loop) cout << node + 1 << endl;
}

int main() {
#ifdef DBG
    ifstream cin("in.txt");
    std::cin.rdbuf(cin.rdbuf());
    //ofstream cout("out.txt");
    //std::cout.rdbuf(cout.rdbuf());
#else
    ios_base::sync_with_stdio(false);
    std::cin.tie(0);
#endif
    solve();
    return 0;
}