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;

constexpr const int maxn = 1024;
vector<int> adj[maxn], dag[maxn];
int die[maxn], deg[maxn];

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);
	int n, m;
	cin >> n >> m;
	while (m--) {
		int a, b;
		cin >> a >> b;
		adj[a].push_back(b);
		++deg[b];
	}
	vector<int> topo;
	for (int u = 1; u <= n; ++u) if (!deg[u]) topo.push_back(u);
	for (int i = 0; i != int(topo.size()); ++i) for (int u : adj[topo[i]]) if (!--deg[u]) topo.push_back(u);
	if (int(topo.size()) == n) return cout << -1 << endl, 0;
	for (int i = 1; i <= n; ++i) {
		die[i] = 1;
		vector<int> node;
		memset(deg, 0, maxn << 2);
		for (int u = 1; u <= n; ++u) dag[u].resize(0);
		for (int u = 1; u <= n; ++u) if (!die[u]) {
			node.push_back(u);
			for (int v : adj[u]) if (!die[v]) dag[u].push_back(v);
			for (int v : dag[u]) ++deg[v];
		}
		topo.resize(0);
		for (int u : node) if (!deg[u]) topo.push_back(u);
		for (int j = 0; j != int(topo.size()); ++j) for (int u : dag[topo[j]]) if (!--deg[u]) topo.push_back(u);
		if (topo.size() == node.size()) die[i] = 0;
	}
	vector<int> res;
	for (int i = 1; i <= n; ++i) if (!die[i]) res.push_back(i);
	cout << res.size() << endl;
	for (int ans : res) cout << ans << '\n';
}