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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdint>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

#ifdef _DEBUG
#define DUMP(x) std::cerr << (#x) << " = " << (x) << "\n"
#else
#define DUMP(x)
#endif
#define REP(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define EREP(i, a, b) for (int i = (int)(a); i <= (int)(b); ++i)
#define RREP(i, a, b) for (int i = (int)(a)-1; i >= (int)(b); --i)
#define rep(i, n) REP(i, 0, n)
#define erep(i, n) EREP(i, 0, n)
#define rrep(i, n) RREP(i, n, 0)
#define ALL(r) (r).begin(), (r).end()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    os << "{";
    rep(i, v.size()) os << v[i] << (i == (int)v.size() - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    return (os << "(" << p.first << ", " << p.second << ")");
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &m) {
    bool first = true;
    os << "{";
    for (const auto &e : m) {
        if (!first)
            os << ", ";
        os << "{" << e.first << ": " << e.second << "}";
        first = false;
    }
    os << "}";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &s) {
    os << "{";
    bool first = true;
    for (const auto &e : s) {
        if (!first)
            os << ", ";
        os << e;
        first = false;
    }
    os << "}";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, const multiset<T> &s) {
    os << "{";
    bool first = true;
    for (const auto &e : s) {
        if (!first)
            os << ", ";
        os << e;
        first = false;
    }
    os << "}";
    return os;
}
template <typename T>
T dup(T x, T y) {
    return (x + y - 1) / y;
};
template <typename A, size_t N, typename T>
inline void arrayFill(A (&array)[N], const T &val) {
    std::fill((T *)array, (T *)(array + N), val);
}
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;
}
struct in {
    const size_t n = 0;
    in() = default;
    in(size_t n) : n(n){};
    template <typename T>
    operator T() {
        T ret;
        cin >> ret;
        return ret;
    }
    template <typename T>
    operator vector<T>() {
        assert(n != 0);
        vector<T> ret(n);
        for (T &x : ret) {
            T tmp = in();
            x = tmp;
        }
        return ret;
    }
    template <typename T, typename U>
    operator pair<T, U>() {
        pair<T, U> ret;
        ret.first = in();
        ret.second = in();
        return ret;
    }
};

namespace fiore::impl {
template <typename T>
inline void out_impl(const T &x, char end_char) {
    std::cout << x << end_char;
}
template <typename T>
inline void out_impl(const vector<T> &x, char end_char) {
    bool first = true;
    for (const auto &e : x) {
        if (!first)
            std::cout << ' ';
        std::cout << e;
        first = false;
    }
    std::cout << end_char;
}
} // namespace fiore::impl
template <typename T>
inline void out(const T &x) {
    fiore::impl::out_impl(x, '\n');
};
template <typename T, typename U, typename... Args>
inline void out(const T &x, const U &y, const Args &... args) {
    fiore::impl::out_impl(x, ' ');
    out(y, args...);
}

using ll = int64_t;
using vint = vector<int32_t>;
using vvint = vector<vint>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vstr = vector<string>;
using pint = pair<int32_t, int32_t>;
using vpint = vector<pint>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;
using setint = set<int32_t>;
using qint = queue<int32_t>;
using qpint = queue<pint>;

constexpr std::int32_t INF = 1001001001;
constexpr std::int64_t LINF = 1001001001001001001;

template <typename T = int>
struct Edge {
    int from, to;
    T cost;
    int idx;
    Edge() = default;
    Edge(const int from, const int to, const T cost = 1, const int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
};
template <typename T = int>
using Edges = vector<Edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;

template <typename T = int>
struct Graph {
    vector<vector<Edge<T>>> g;
    int es;

    Graph() = default;

    explicit Graph(const int n) : g(n), es(0){};

    size_t size() const { return g.size(); }

    void add_directed_edge(const int from, const int to, const T cost = 1) {
        g[from].emplace_back(from, to, cost, es++);
    }
    void add_edge(const int from, const int to, const T cost = 1) {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }
};

vint findCycle(const UnWeightedGraph &g) {
    const int n = g.size();
    vint seen(n, 0), depth(n), cycle;
    int min_depth_nv = -1;
    auto dfs = [&g, &seen, &depth, &cycle, &min_depth_nv](auto &&self,
                                                          const int v) {
        for (const auto nv : g[v]) {
            if (seen[nv] == 1) { // 後退辺が存在
                if (min_depth_nv == -1 || depth[min_depth_nv] > depth[nv]) {
                    min_depth_nv = nv;
                }
            }
        }
        if (min_depth_nv != -1) {
            cycle.push_back(v);
            return false;
        }
        for (const auto nv : g[v]) {
            seen[nv] = 1;
            if (self(self, nv))
                return true;
            if (min_depth_nv != -1) {
                cycle.push_back(v);
                return min_depth_nv == v;
            }
            seen[nv] = 2;
        }
        return false;
    };
    rep(s, n) {
        if (seen[s] != 0)
            continue;
        if (dfs(dfs, s))
            return cycle;
    }
    return vint();
}

void Main() {
    int n = in(), m = in();
    vvint g(n);
    rep(i, m) {
        int a = in(), b = in();
        --a, --b;
        g[a].pb(b);
    }
    auto cycle = findCycle(g);
    sort(ALL(cycle));

    if (cycle.empty())
        out(-1);
    else {
        out(cycle.size());
        for (auto e : cycle)
            out(e + 1);
    }
}

signed main() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(15);
    Main();
    return 0;
}