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:
#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <functional>
#include <map>

#define M 1001

using namespace std;

int n, m, minl = 0x7fffffff;
bool mapp[M][M];
bool visit[M];
int ans[M];
int real[M];

void dfs(int x, int num)
{
	if (num > minl)
		return;

	if (visit[x] == true)
	{
		int p;
		for (int i = 1; i <= num; i++)
			if (ans[i] == x)
			{
				p = i;
				break;
			}
		minl = num - p;
		int tmp = 1;
		for (int i = p + 1; i <= num; i++)
			real[i - p] = ans[i];

		return;
	}

	visit[x] = true;

	for (int i = 1; i <= n; i++)
	{
		if (mapp[x][i] == true)
		{
			num++;
			ans[num] = i;

			dfs(i, num);
			num--;
		}
	}

	visit[x] = false;
	return;
}

int main()
{
	cin >> n >> m;
	for (int i = 1; i <= m; i++)
	{
		int x, y;
		cin >> x >> y;
		mapp[x][y] = true;
	}

	for (int i = 1; i <= n; i++)
	{
		ans[1] = i;
		dfs(i, 1);

		memset(visit, 0, sizeof(visit));
	}

	if (minl == 0x7fffffff)
		cout << -1 << endl;
	else
	{
		cout << minl << endl;
		for (int i = 1; i <= minl; i++)
			cout << real[i] << endl;
	}

	return 0;
}