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.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        HashMap<Integer, ArrayList<Integer>> adj = new HashMap<>();
        StringTokenizer st = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        for (int i = 0; i < m; i++) {
            st = new StringTokenizer(in.readLine());
            int u = Integer.parseInt(st.nextToken());
            int v = Integer.parseInt(st.nextToken());
            if (adj.containsKey(u)) {
                ArrayList<Integer> list = adj.get(u);
                list.add(v);
                adj.put(u, list);
            } else {
                ArrayList<Integer> list = new ArrayList<>();
                list.add(v);
                adj.put(u, list);
            }
        }
        st = new StringTokenizer(in.readLine());
        int start = Integer.parseInt(st.nextToken());
        int end = Integer.parseInt(st.nextToken());

        Queue<Node> queue = new LinkedList<>();
        boolean[][] vis = new boolean[n + 1][3];
        queue.offer(new Node(start, 0, 0));
        int min = Integer.MAX_VALUE;
        while (!queue.isEmpty()) {
            Node x = queue.poll();
            if (x.id == end) {
                if (x.hops == 0) {
                    min = Math.min(x.dist, min);
                }
            }
            if (adj.containsKey(x.id)) {
                for (int y : adj.get(x.id)) {
                    if (!vis[y][(x.hops + 1) % 3]) {
                        queue.offer(new Node(y, (x.hops + 1) % 3, x.dist + 1));
                        vis[y][(x.hops+1)%3] = true;
                    }
                }
            }
            vis[x.id][x.hops] = true;
        }
        if (min == Integer.MAX_VALUE) {
            System.out.println("-1");
        } else {
            System.out.println(min / 3);
        }
    }

    static class Node {
        int id, hops, dist;

        public Node(int id, int hops, int dist) {
            this.id = id;
            this.hops = hops;
            this.dist = dist;
        }
    }
}
/*


 */