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: Runtime Error)

#define DEBUG 0
/**
 * File    : F.cpp
 * Author  : Kazune Takahashi
 * Created : 2/10/2020, 11:29:02 AM
 * Powered by Visual Studio Code
 */
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>
// ----- boost -----
#include <boost/rational.hpp>
#include <boost/multiprecision/cpp_int.hpp>
// ----- using directives and manipulations -----
using namespace std;
using boost::rational;
using boost::multiprecision::cpp_int;
using ll = long long;
template <typename T>
using max_heap = priority_queue<T>;
template <typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
// ----- constexpr for Mint and Combination -----
constexpr ll MOD{1000000007LL};
// constexpr ll MOD{998244353LL}; // be careful
constexpr ll MAX_SIZE{3000010LL};
// constexpr ll MAX_SIZE{30000010LL}; // if 10^7 is needed
// ----- ch_max and ch_min -----
template <typename T>
void ch_max(T &left, T right)
{
  if (left < right)
  {
    left = right;
  }
}
template <typename T>
void ch_min(T &left, T right)
{
  if (left > right)
  {
    left = right;
  }
}
// ----- Mint -----
template <ll MOD = MOD>
class Mint
{
public:
  ll x;
  Mint() : x{0LL} {}
  Mint(ll x) : x{(x % MOD + MOD) % MOD} {}
  Mint operator-() const { return x ? MOD - x : 0; }
  Mint &operator+=(const Mint &a)
  {
    if ((x += a.x) >= MOD)
    {
      x -= MOD;
    }
    return *this;
  }
  Mint &operator-=(const Mint &a) { return *this += -a; }
  Mint &operator++() { return *this += 1; }
  Mint &operator++(int)
  {
    Mint tmp{*this};
    ++*this;
    return tmp;
  }
  Mint &operator--() { return *this -= 1; }
  Mint &operator--(int)
  {
    Mint tmp{*this};
    --*this;
    return tmp;
  }
  Mint &operator*=(const Mint &a)
  {
    (x *= a.x) %= MOD;
    return *this;
  }
  Mint &operator/=(const Mint &a)
  {
    Mint b{a};
    return *this *= b.power(MOD - 2);
  }
  Mint operator+(const Mint &a) const { return Mint(*this) += a; }
  Mint operator-(const Mint &a) const { return Mint(*this) -= a; }
  Mint operator*(const Mint &a) const { return Mint(*this) *= a; }
  Mint operator/(const Mint &a) const { return Mint(*this) /= a; }
  bool operator<(const Mint &a) const { return x < a.x; }
  bool operator<=(const Mint &a) const { return x <= a.x; }
  bool operator>(const Mint &a) const { return x > a.x; }
  bool operator>=(const Mint &a) const { return x >= a.x; }
  bool operator==(const Mint &a) const { return x == a.x; }
  bool operator!=(const Mint &a) const { return !(*this == a); }
  const Mint power(ll N)
  {
    if (N == 0)
    {
      return 1;
    }
    else if (N % 2 == 1)
    {
      return *this * power(N - 1);
    }
    else
    {
      Mint half = power(N / 2);
      return half * half;
    }
  }
};
template <ll MOD>
Mint<MOD> operator+(ll lhs, const Mint<MOD> &rhs)
{
  return rhs + lhs;
}
template <ll MOD>
Mint<MOD> operator-(ll lhs, const Mint<MOD> &rhs)
{
  return -rhs + lhs;
}
template <ll MOD>
Mint<MOD> operator*(ll lhs, const Mint<MOD> &rhs)
{
  return rhs * lhs;
}
template <ll MOD>
Mint<MOD> operator/(ll lhs, const Mint<MOD> &rhs)
{
  return Mint<MOD>{lhs} / rhs;
}
template <ll MOD>
istream &operator>>(istream &stream, Mint<MOD> &a)
{
  return stream >> a.x;
}
template <ll MOD>
ostream &operator<<(ostream &stream, const Mint<MOD> &a)
{
  return stream << a.x;
}
// ----- Combination -----
template <ll MOD = MOD, ll MAX_SIZE = MAX_SIZE>
class Combination
{
public:
  vector<Mint<MOD>> inv, fact, factinv;
  Combination() : inv(MAX_SIZE), fact(MAX_SIZE), factinv(MAX_SIZE)
  {
    inv[1] = 1;
    for (auto i = 2LL; i < MAX_SIZE; i++)
    {
      inv[i] = (-inv[MOD % i]) * (MOD / i);
    }
    fact[0] = factinv[0] = 1;
    for (auto i = 1LL; i < MAX_SIZE; i++)
    {
      fact[i] = Mint<MOD>(i) * fact[i - 1];
      factinv[i] = inv[i] * factinv[i - 1];
    }
  }
  Mint<MOD> operator()(int n, int k)
  {
    if (n >= 0 && k >= 0 && n - k >= 0)
    {
      return fact[n] * factinv[k] * factinv[n - k];
    }
    return 0;
  }
  Mint<MOD> catalan(int x, int y)
  {
    return (*this)(x + y, y) - (*this)(x + y, y - 1);
  }
};
// ----- for C++14 -----
using mint = Mint<MOD>;
using combination = Combination<MOD, MAX_SIZE>;
template <typename T>
T gcd(T x, T y) { return y ? gcd(y, x % y) : x; }
template <typename T>
T lcm(T x, T y) { return x / gcd(x, y) * y; }
// ----- for C++17 -----
template <typename T>
int popcount(T x) // C++20
{
  int ans{0};
  while (x != 0)
  {
    ans += x & 1;
    x >>= 1;
  }
  return ans;
}
// ----- frequently used constexpr -----
// constexpr double epsilon{1e-10};
// constexpr ll infty{1000000000000000LL}; // or
// constexpr int infty{1'000'000'010};
// constexpr int dx[4] = {1, 0, -1, 0};
// constexpr int dy[4] = {0, 1, 0, -1};
// ----- Yes() and No() -----
void Yes()
{
  cout << "Yes" << endl;
  exit(0);
}
void No()
{
  cout << "No" << endl;
  exit(0);
}
// ----- main() -----

using Edge = tuple<int, int>;

class Solve
{
  int N, M;
  vector<vector<int>> V;
  vector<Edge> W;

public:
  Solve(int N, int M, vector<vector<int>> const &V, vector<Edge> const &W) : N{N}, M{M}, V(V), W(W) {}

  void flush()
  {
    vector<int> ans(N + 1);
    for (auto i = 0; i < N; ++i)
    {
      auto tmp{mini_close_path(i)};
      if (tmp.size() < ans.size())
      {
        swap(ans, tmp);
      }
    }
    if (static_cast<int>(ans.size()) > N)
    {
      cout << -1 << endl;
    }
    else
    {
      cout << ans.size() << endl;
      sort(ans.begin(), ans.end());
      for (auto x : ans)
      {
        cout << x + 1 << endl;
      }
    }
  }

private:
  vector<int> mini_close_path(int k)
  {
    int A, B;
    tie(A, B) = W[k];
#if DEBUG == 1
    cerr << "A = " << A << ", B = " << B << endl;
#endif
    vector<int> P(N, -1);
    using Info = tuple<int, int>;
    queue<Info> Q;
    Q.push(Info(B, A));
    while (!Q.empty())
    {
      int now, par;
      tie(now, par) = Q.front();
      Q.pop();
      if (P[now] == -1)
      {
        P[now] = par;
#if DEBUG == 1
        cerr << "P[" << now << "] = " << P[now] << endl;
#endif
        for (auto x : V[now])
        {
          if (P[x] == -1)
          {
            Q.push(Info(x, now));
          }
        }
      }
    }
    vector<int> res;
    if (P[A] == -1)
    {
      res.resize(N + 1);
      return res;
    }
    int now{A};
    while (now != B)
    {
      res.push_back(now);
      now = P[now];
    }
    res.push_back(now);
    return res;
  }
};

int main()
{
  int N, M;
  cin >> N >> M;
  vector<vector<int>> V(N);
  vector<Edge> W;
  for (auto i = 0; i < M; ++i)
  {
    int A, B;
    cin >> A >> B;
    --A;
    --B;
    V[A].push_back(B);
    W.emplace_back(A, B);
  }
  Solve solve(N, M, V, W);
  solve.flush();
}