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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] first = br.readLine().split(" ", 2);
        int n = Integer.parseInt(first[0]);
        int m = Integer.parseInt(first[1]);
        HashSet<Integer>[] orgGraph = new HashSet[n + 1];
        for (int i = 1; i <= n; i++) {
            orgGraph[i] = new HashSet<>();
        }
        for (int i = 0; i < m; i++) {
            String[] line = br.readLine().split(" ", 2);
            int a = Integer.parseInt(line[0]);
            int b = Integer.parseInt(line[1]);
            orgGraph[a].add(b);
        }
        boolean[][] cost = new boolean[3][n + 1];
        ArrayDeque<Integer> deq = new ArrayDeque<>();
        ArrayDeque<Integer> next = new ArrayDeque<>();
        String[] last = br.readLine().split(" ", 2);
        int s = Integer.parseInt(last[0]);
        int t = Integer.parseInt(last[1]);
        deq.add(s);
        int idx = 0;
        while (deq.size() > 0) {
            while (deq.size() > 0) {
                int x = deq.poll();
                if (x == t && idx % 3 == 0) {
                    System.out.println(idx / 3);
                    return;
                }
                if (cost[idx % 3][x]) {
                    continue;
                }
                cost[idx % 3][x] = true;
                next.addAll(orgGraph[x]);
            }
            ArrayDeque<Integer> tmp = next;
            next = deq;
            deq = tmp;
            idx++;
        }
        System.out.println(-1);
    }
}