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;
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
//const ll mod=998244353;
const ll inf=1LL<<61;
 
int main() {
  ll n,m;
  cin >> n >> m;
  mat G(n),GG(n);
  for(ll i=0;i<m;i++) {
    ll a,b;
    cin >> a >> b;
    a--,b--;
    G[a].push_back(b);
    GG[b].push_back(a);
  }
  ll ans=inf;
  vec ansv(n);
  for(ll i=0;i<n;i++) {
    queue<ll> q;
    ll id=-1;
    vec d(n,-1);
    d[i]=0;
    q.push(i);
    while(q.size()) {
      ll f=q.front();
      ll td=d[f];
      q.pop();
      for(ll t:G[f]) {
        ll nd=td+1;
        if(t==i) {
          id=f;
          break;
        }
        if(d[t]>-1) continue;
        d[t]=nd;
        q.push(t);
      }
      if(id>-1) break;
    }
    if(id>-1) {
      if(ans>d[id]+1) {
        ans=d[id]+1;
        for(ll j=0;j<ans;j++) {
          ansv[j]=id+1;
          for(ll f:GG[id]) {
            if(d[f]+1==d[id]) {
              id=f;
              break;
            }
          }
        }
      }
    }
    while(q.size()) q.pop();
  }
  if(ans==inf) ans=-1;
  cout << ans << endl;
  for(ll i=0;i<ans;i++) {
    cout << ansv[i] << endl;
  }
}