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 <iostream>
#include <vector>

using namespace std;

int s;
bool Find;
vector<int> vl,cu;
vector< vector<int> > el;

void dfs(int v, int nov) {
	if (nov > 0 && v == s) {
		cout << nov << endl;
		for (int i = 0; i < nov; ++i) {
			cout << vl[i]+1 << endl;
		}
		Find = true;
		return;
	}
	if (!Find) {
		bool ca = true;
		for (int i = 0; i < el[v].size(); ++i) {
			if (cu[el[v][i]] == 1) {
				cu[el[v][i]] = -v;
			}
			else if (cu[el[v][i]] > 1) {
				for (int j = 0; j < nov; ++j) {
					if (vl[j] == el[v][i]) {
						cout << nov-j << endl;
						for (int k = j; k < nov; ++k) {
							cout << vl[k]+1 << endl;
						}
						Find = true;
						return;
					}
				}
			}
		}
		for (int i = 0; i < el[v].size(); ++i) {
			if (cu[el[v][i]] == -v) {
				cu[el[v][i]] = 2;
				vl[nov] = el[v][i];
				dfs(vl[nov],nov+1);
				cu[el[v][i]] = -v;
			}
		}
		for (int i = 0; i < el[v].size(); ++i) {
			if (cu[el[v][i]] == -v) {
				cu[el[v][i]] = 1;
			}
		}
	}
	return;
}

int main(void) {
	int u,v,N,M;
	cin >> N >> M;
	el = vector< vector<int> >(N);
	for (int i = 0; i < M; ++i) {
		cin >> u >> v;
		el[u-1].push_back(v-1);
	}
	s = 0;
	cu = vector<int>(N,1);
	vl = vector<int>(N,-1);
	Find = false;
	while (!Find && s < N) {
		dfs(s,0);
		++s;
	}
	if (!Find) {
		cout << -1 << endl;
	}
	return 0;
}