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.*;

class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());
		int M = Integer.parseInt(sc.next());
		int[][] flag = new int[N][3];
		ArrayList<ArrayList<Integer>> edge = new ArrayList<ArrayList<Integer>>();
		for (int i=0;i<N;i++) {
			ArrayList<Integer> add = new ArrayList<Integer>();
			edge.add(add);
		}
		for (int i=0;i<M;i++) {
			int u = Integer.parseInt(sc.next())-1;
			int v = Integer.parseInt(sc.next())-1;
			edge.get(u).add(v);
		}
		int S = Integer.parseInt(sc.next())-1;
		int T = Integer.parseInt(sc.next())-1;

		LinkedList<Integer> dfs = new LinkedList<Integer>();
		dfs.add(S);
		dfs.add(0);
		dfs.add(0);
		dfs.add(0);

		int ans=-1;
		while (dfs.size()>0) {
			Integer rem = dfs.remove(0);
			Integer index = dfs.remove(0);
			Integer steps = dfs.remove(0);
			Integer before = dfs.remove(0);
			if (rem==T && index==0) {
				System.out.println(steps/3);
				ans=0;
				break;
			}
			if (flag[rem][index]==1) {
				continue;
			}
			flag[rem][index]=1;
			for (Integer element : edge.get(rem)) {
				int add_index;
				if (index==2) {
					add_index=0;
				} else {
					add_index=index+1;
				}
				dfs.add(element);
				dfs.add(add_index);
				dfs.add(steps+1);
				dfs.add(rem);
			}
		}
		if (ans==-1) {
			System.out.println(-1);
		}
	}
}