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>
#define rep(i, n) for (int i = 0; i < n; ++i)
using namespace std;

const int inf = 1e9;
int G[1000][1000];
int D[1000][1000];
int main() {
  int n, m;
  cin >> n >> m;
  rep(i, n) rep(j, n) D[i][j] = inf;
  rep(z, m) {
    int a, b;
    cin >> a >> b;
    --a; --b;
    G[a][b] = D[a][b] = 1;
  }
  
  rep(k, n) rep(i, n) rep(j, n)
    D[i][j] = min(D[i][j], D[i][k] + D[k][j]);
  
  int l = inf;
  int s = 0;
  rep(i, n) {
    if (D[i][i] < l) {
      l = D[i][i];
      s = i;
    }
  }
  
  cout << l << endl;
  int c = s;
  while (true) {
    cout << c + 1 << endl;
    int nxt = -1;
    for (int i = 0; i < n; ++i) {
      if (c == i) continue;
      if (G[c][i] + D[i][s] == D[c][s]) {
        nxt = i;
        break;
      }
    }
    if (nxt == -1) break;
    c = nxt;
  }
}