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.*;
public class Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		List<Integer>[] edge = new ArrayList[N*3];
		for(int i = 0; i < N*3; i++)
			edge[i] = new ArrayList<>();
		for(int i = 0; i < M; i++) {
			int u = sc.nextInt()-1;
			int v = sc.nextInt()-1;
			edge[u].add(v+N);
			edge[u+N].add(v+2*N);
			edge[u+2*N].add(v);
		}
		int S = sc.nextInt()-1;
		int T = sc.nextInt()-1;
		long[] d = new long[N*3];
		int INF = Integer.MAX_VALUE;
		Arrays.fill(d, INF);
		d[S] = 0;
		Queue<Integer> q = new ArrayDeque<>();
		for(int i : edge[S]) {
		    q.offer(i);
		    d[i] = 1;
		}
		while(q.size() > 0) {
		    int x = q.poll();
		    for(int i : edge[x]) {
		        if(d[i] > d[x] + 1) {
		            d[i] = d[x] + 1;
		            q.offer(i);
		        }
		    }
		}
		System.out.println(d[T] != INF ? d[T]/3 : -1);
	}

}
