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
#include <bits/stdc++.h>
using namespace std;

#define mp make_pair
typedef long long ll;
typedef pair<int,int>pii;
const int N = 3e5;
vector<int>graph[N+100];
int dist[N+100];

int main()
{
	int n,m,s,t;
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++){
		int u,v;
		scanf("%d%d",&u,&v);
		graph[u].push_back(v+n);
		graph[u+n].push_back(v+2*n);
		graph[u+2*n].push_back(v);
	}
	scanf("%d%d",&s,&t);
	queue<int>q;
	memset(dist,-1,sizeof dist);
	dist[s] = 0;
	q.push(s);
	while(!q.empty())
	{
		int u = q.front();
		q.pop();
		for(auto it:graph[u])
		{
			if(dist[it]==-1){
				dist[it] = dist[u]+1;
				q.push(it);
			}
		}
	}
	if(dist[t]==-1){
		printf("-1\n");
	}
	else printf("%d\n",dist[t]/3);
}
