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> vl;
typedef vector<vl> vvl;
typedef pair<ll,ll> pll;
typedef vector<bool> vb;
const ll oo = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;
#define sz(c) ll((c).size())
#define all(c) begin(c), end(c)
#define FOR(i,a,b) for (ll i = (a); i < (b); i++)
#define FORD(i,a,b) for (ll i = (b)-1; i >= (a); i--)
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
#define TR(X) ({ if(1) cerr << "TR: " << (#X) << " = " << (X) << endl; })

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	ll n, m;
	cin >> n >> m;

	vvl adj(n);
	while (m--) {
		ll a, b;
		cin >> a >> b;
		a--, b--;
		adj[a].pb(b);
	}
	
	vl res;
	FOR(s,0,n) {
		vl pred(n,-1);
		queue<ll> q;
		q.push(s);

		while (sz(q)) {
			ll i = q.front();
			q.pop();
			for (ll j: adj[i]) {
				if (j == s) {
					vl cur = {i};
					while (i != s) i = pred[i], cur.pb(i);
					if (sz(res) == 0 || sz(cur) < sz(res)) res = cur;
					while (sz(q)) q.pop();
					break;
				}
				if (pred[j] != -1) continue;
				pred[j] = i;
				q.push(j);
			}
		}
	}

	if (sz(res)) {
		cout << sz(res) << endl;
		for (ll x: res) cout << x+1 << endl;
	} else {
		cout << -1 << endl;
	}
}