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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
import java.util.concurrent.ArrayBlockingQueue;
import java.util.concurrent.BlockingQueue;

public class Main {
    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int n = in.nextInt();
        final int m = in.nextInt();
        final Map<Integer, List<Integer>> edges = new HashMap<>();
        final int[][] cost = new int[n][3];
        // -1 means not visited.
        for (int i = 0; i < n; i++) {
            Arrays.fill(cost[i], Integer.MIN_VALUE);
        }


        for (int i = 0; i < m; i++) {
            final int from = in.nextInt();
            final int to = in.nextInt();
            edges.compute(from - 1, (key, list) -> {
                if (list == null) {
                    list = new ArrayList<>();
                }
                list.add(to - 1);
                return list;
            });
        }
        final int s0 = in.nextInt() - 1;
        final int t0 = in.nextInt() - 1;
        final List<int[]> nodes = new ArrayList<>();
        nodes.add(new int[]{s0, 0});
        cost[s0][0] = 0;
        while (!nodes.isEmpty()) {
            final int[] from = nodes.remove(0);
            if (from[0] == t0 && from[1] == 0) {
                System.out.println(cost[from[0]][0] / 3);
                return;
            }

            for (Integer to : edges.getOrDefault(from[0], new ArrayList<>())) {
                final int state = from[1];
                final int nextState = (state + 1) % 3;
                if (cost[to][nextState] == Integer.MIN_VALUE) {
                    cost[to][nextState] = cost[from[0]][state] + 1;
                    nodes.add(new int[]{to, nextState});
                }
            }
        }
        System.out.println(-1);
    }
}
