#include "bits/stdc++.h"

using namespace std;

void solve(void)
{
	int n, m, s, t;
	cin >> n >> m;
	vector<int> g[3*n];
	while(m--)
	{
		int u, v;
		cin >> u >> v;
		u--, v--;
		g[u].push_back(v+n);
		g[u+n].push_back(v+2*n);
		g[u+2*n].push_back(v);
	}
	cin >> s >> t;
	s--, t--;
	vector<int> ds(3*n, -1);
	queue<int> q;
	ds[s] = 0;
	q.push(s);

	while(!q.empty())
	{
		int v = q.front();
		q.pop();
		for (int nv : g[v])
		{
			if (ds[nv] != -1) continue;
			ds[nv] = ds[v] + 1;
			q.push(nv);
		}
	}
	int ans = ds[t] == -1 ? -1 : ds[t] / 3;
	cout << ans << endl;

}

int main()
{
	solve();
	//cout << "yui(*-v・)yui" << endl;
	return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

Ken loves ken-ken-pa (Japanese version of hopscotch). Today, he will play it on a directed graph G. G consists of N vertices numbered 1 to N, and M edges. The i-th edge points from Vertex u_i to Vertex v_i.

First, Ken stands on Vertex S. He wants to reach Vertex T by repeating ken-ken-pa. In one ken-ken-pa, he does the following exactly three times: follow an edge pointing from the vertex on which he is standing.

Determine if he can reach Vertex T by repeating ken-ken-pa. If the answer is yes, find the minimum number of ken-ken-pa needed to reach Vertex T. Note that visiting Vertex T in the middle of a ken-ken-pa does not count as reaching Vertex T by repeating ken-ken-pa.

Constraints

* 2 \leq N \leq 10^5
* 0 \leq M \leq \min(10^5, N (N-1))
* 1 \leq u_i, v_i \leq N(1 \leq i \leq M)
* u_i \neq v_i (1 \leq i \leq M)
* If i \neq j, (u_i, v_i) \neq (u_j, v_j).
* 1 \leq S, T \leq N
* S \neq T

Input

Input is given from Standard Input in the following format:


N M
u_1 v_1
:
u_M v_M
S T


Output

If Ken cannot reach Vertex T from Vertex S by repeating ken-ken-pa, print -1. If he can, print the minimum number of ken-ken-pa needed to reach vertex T.

Examples

Input

4 4
1 2
2 3
3 4
4 1
1 3


Output

2


Input

3 3
1 2
2 3
3 1
1 2


Output

-1


Input

2 0
1 2


Output

-1


Input

6 8
1 2
2 3
3 4
4 5
5 1
1 4
1 5
4 6
1 6


Output

2

### Response

```cpp
#include "bits/stdc++.h"

using namespace std;

void solve(void)
{
	int n, m, s, t;
	cin >> n >> m;
	vector<int> g[3*n];
	while(m--)
	{
		int u, v;
		cin >> u >> v;
		u--, v--;
		g[u].push_back(v+n);
		g[u+n].push_back(v+2*n);
		g[u+2*n].push_back(v);
	}
	cin >> s >> t;
	s--, t--;
	vector<int> ds(3*n, -1);
	queue<int> q;
	ds[s] = 0;
	q.push(s);

	while(!q.empty())
	{
		int v = q.front();
		q.pop();
		for (int nv : g[v])
		{
			if (ds[nv] != -1) continue;
			ds[nv] = ds[v] + 1;
			q.push(nv);
		}
	}
	int ans = ds[t] == -1 ? -1 : ds[t] / 3;
	cout << ans << endl;

}

int main()
{
	solve();
	//cout << "yui(*-v・)yui" << endl;
	return 0;
}

```