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 <bits/stdc++.h>
using namespace std;
#define ll long long
#define REP(i,m,n) for(int i=(int)(m); i<(int)(n); i++)
#define rep(i,n) REP(i,0,n)
#define RREP(i,m,n) for(int i=(int)(m); i>=(int)(n); i--)
#define rrep(i,n) RREP(i,n-1,0)
#define all(v) v.begin(), v.end()
const int inf = 1e9+7;
const ll longinf = 1LL<<60;
const ll mod = 1e9+7;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N, M;
  cin >> N >> M;
  vector<vector<int>> G(N);
  rep(i, M) {
    int a, b;
    cin >> a >> b;
    --a, --b;
    G[a].push_back(b);
  }
  vector<bool> vis(N);
  vector<int> path;
  vector<int> ans;
  function<void(int, int)> dfs = [&](int tmp, int par) {
    if(vis[tmp]) {
      if(ans.size() == 0) {
        auto from = find(all(path), tmp);
        int size = path.end() - from;
        if(size != 0) {
          vector<int> loop(size);
          copy(from, path.end(), loop.begin());
          ans = vector<int>(size);
          copy(all(loop), ans.begin());
        }
      }
      return;
    }
    path.push_back(tmp);
    vis[tmp] = true;
    for(int ne: G[tmp]) dfs(ne, tmp);
    path.pop_back();
  };
  rep(i, N) dfs(i, -1);
  if(ans.size() == 0) {
    cout << -1 << endl;
  } else {
    auto check = [&](vector<int>& path) {
      set<int> se;
      for(int v: path) se.insert(v);
      int n = path.size();
      rep(i, n) {
        for(int ne: G[path[i]]) {
          if(se.count(ne) && ne != path[(i+1)%n]) {
            return make_pair(path[i], ne);
          }
        }
      }
      return make_pair(-1, -1);
    };

    while(true) {
      auto ret = check(ans);
      if(ret.first == -1) break;
      vector<int> newPath;
      int n = ans.size();
      int begin = find(all(ans), ret.second) - ans.begin();
      int end = find(all(ans), ret.first) - ans.begin();
      for(int i=begin; i!=end; i=(i+1)%n) {
        newPath.push_back(path[i]);
      }
      newPath.push_back(path[end]);
      ans = vector<int>(newPath.size());
      copy(all(newPath), ans.begin());
    }
    cout << ans.size() << endl;
    for(int a: ans) cout << a+1 << endl;
  }
  return 0;
}