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:
// ※※※ 解答不能 ※※※
// kotatsugame氏.
// https://atcoder.jp/contests/abc142/submissions/7825341
#include <bits/stdc++.h>
using namespace std;
int N, M;
vector<int> G[1000];
int cnt[1000];
int main(){
    scanf("%d %d", &N, &M);
    for(int i = 0; i < M; i++){
        int u, v;
        scanf("%d %d", &u, &v);
        u--, v--;
        G[u].push_back(v);
        cnt[v]++;
    }
    queue<int> q;
    for(int i = 0; i < N; i++) if(cnt[i] == 0) q.push(i);
    int sz = 0;
    while(!q.empty()){
        sz++;
        int u = q.front(); q.pop();
        for(int v : G[u]) if(--cnt[v] == 0) q.push(v);
    }
    printf("%d\n", -(sz == N));
    return 0;
}