Problem: 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.

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.

Examples

Input

4 5
1 2
2 3
2 4
4 1
4 3


Output

3
1
2
4


Input

4 5
1 2
2 3
2 4
1 4
4 3


Output

-1


Input

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2


Output

4
2
3
4
5

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main() {
  const int inf = 1e9;
  int n, m;
  cin >> n >> m;
  vector<vector<int>> to(n);
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    to.at(a - 1).push_back(b - 1);
  }
  int shortest = inf;
  for (int i = 0; i < n; i++) {
    vector<bool> seen(n);
    queue<pair<int, int>> q;
    q.emplace(i, 0);
    while (!q.empty()) {
      int present = q.front().first, d = q.front().second;
      q.pop();
      seen.at(present) = true;
      for (int next : to.at(present)) {
        if (seen.at(next)) {
          if (next == i) {
            shortest = min(shortest, d + 1);
          }
          continue;
        }
        q.emplace(next, d + 1);
      }
    }
  }
  if (shortest == inf) {
    cout << -1 << endl;
    return 0;
  }
  cout << 0 << endl;
}