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


import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	static ArrayList<Integer>[] adj;
	public static void main(String args[])
	{
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int m=scan.nextInt();
		adj=new ArrayList[n];
		for(int i=0;i<n;i++)
		{
			adj[i]=new ArrayList<Integer>();
		}
		for(int i=0;i<m;i++)
		{
			int u=scan.nextInt();
			int v=scan.nextInt();
			u--;v--;
			adj[u].add(v);
		}
//		System.out.println(adj[0].get(0));
		int dist[][]=new int[n][3];
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<3;j++)
				dist[i][j]=Integer.MAX_VALUE-10;
		}
		Queue<fok> que=new LinkedList<fok>();
		int s=scan.nextInt()-1;
		int t=scan.nextInt()-1;
		que.add(new fok(s,0));
		dist[s][0]=0;
		while(!que.isEmpty())
		{
			
			fok cur=que.poll();
//			System.out.println(cur.a);
			int pos=cur.a;
			int rem=cur.b;
			for(int to:adj[pos])
			{
//				System.out.println("LOL");
				if(dist[to][(rem+1)%3]>dist[pos][rem]+1) {
					dist[to][(rem+1)%3]=dist[pos][rem]+1;
					que.add(new fok(to,(rem+1)%3));
				}
			}
			
		}
	
		if(dist[t][0]==Integer.MAX_VALUE-10) {
			dist[t][0]=-3;
		}
		System.out.println(dist[t][0]/3);
	}
}
class fok{
	int a;int b;
	fok(int x,int y)
	{
		a=x;
		b=y;
		
	}
}
