#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

//template
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(a);i>(b);i--)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll; const int inf = 0x3fffffff; const ll INF = 0x3fffffffffffffff;
template<class T> inline bool chmax(T& a,T b){ if(a<b){a=b;return 1;}return 0; }
template<class T> inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; }
//template end



int main(){
    int n,m; scanf("%d%d",&n,&m);
    vector<int> g[1010]; int cnt[1010];
    rep(i,0,m){
        int a,b; scanf("%d%d",&a,&b); a--; b--;
        g[a].push_back(b); cnt[b]++;
    }
    queue<int> q;
    rep(i,0,n)if(!cnt[i])q.push(i);
    int val=0;
    while(q.size()){
        int v=q.front(); q.pop();
        val++;
        for(int to:g[v]){
            cnt[to]--;
            if(!cnt[to])q.push(to);
        }
    }
    printf("%d\n",-(val==n));
    return 0;
}
### Prompt

Your challenge is to write a CPP solution to the following 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

### Response

```cpp
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

//template
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(a);i>(b);i--)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll; const int inf = 0x3fffffff; const ll INF = 0x3fffffffffffffff;
template<class T> inline bool chmax(T& a,T b){ if(a<b){a=b;return 1;}return 0; }
template<class T> inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; }
//template end



int main(){
    int n,m; scanf("%d%d",&n,&m);
    vector<int> g[1010]; int cnt[1010];
    rep(i,0,m){
        int a,b; scanf("%d%d",&a,&b); a--; b--;
        g[a].push_back(b); cnt[b]++;
    }
    queue<int> q;
    rep(i,0,n)if(!cnt[i])q.push(i);
    int val=0;
    while(q.size()){
        int v=q.front(); q.pop();
        val++;
        for(int to:g[v]){
            cnt[to]--;
            if(!cnt[to])q.push(to);
        }
    }
    printf("%d\n",-(val==n));
    return 0;
}
```