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.HashMap;
import java.util.HashSet;
import java.util.Scanner;

public class Main {


	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();

		HashMap<Integer, ArrayList<Integer>> graph = new HashMap<>();

		for (int i=1;i<=n;i++) {
			graph.put(i, new ArrayList<Integer>());
		}
		for (int i=0;i<m;i++) {
			int u = sc.nextInt();
			int v = sc.nextInt();

			graph.get(u).add(v);
		}

		int s = sc.nextInt();
		int t = sc.nextInt();

		HashMap<Integer, Integer> dist = new HashMap<>();


		HashSet<Integer> set = new HashSet<>();


		set.add(s);
		int i=0;
		while(!set.isEmpty()) {
			for (Integer intg : set) {
				dist.put(intg, i);
			}
			HashSet<Integer> first = new HashSet<>();
			HashSet<Integer> second = new HashSet<>();
			HashSet<Integer> third = new HashSet<>();
			for (Integer intg : set) {
				for (Integer intg2 : graph.get(intg)) {
					first.add(intg2);
				}
			}
			for (Integer intg2 : first) {
				for (Integer intg3 : graph.get(intg2)) {
					second.add(intg3);
				}
			}
			for (Integer intg3 : second) {
				for (Integer intg4 : graph.get(intg3)) {
					if (!dist.containsKey(intg4)) {
						third.add(intg4);
					}
				}
			}

			set=third;
			i++;
		}
		if(dist.containsKey(t)) {
			System.out.println(dist.get(t));
		} else {
			System.out.println("-1");
		}
	}






}