Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

4 4
1 2
2 3
3 4
4 1
1 3

Sample Output 1

2

Ken can reach Vertex 3 from Vertex 1 in two ken-ken-pa, as follows: 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 in the first ken-ken-pa, then 4 \rightarrow 1 \rightarrow 2 \rightarrow 3 in the second ken-ken-pa. This is the minimum number of ken-ken-pa needed.

Sample Input 2

3 3
1 2
2 3
3 1
1 2

Sample Output 2

-1

Any number of ken-ken-pa will bring Ken back to Vertex 1, so he cannot reach Vertex 2, though he can pass through it in the middle of a ken-ken-pa.

Sample Input 3

2 0
1 2

Sample Output 3

-1

Vertex S and Vertex T may be disconnected.

Sample Input 4

6 8
1 2
2 3
3 4
4 5
5 1
1 4
1 5
4 6
1 6

Sample Output 4

2

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.List;
import java.util.Collection;
import java.util.Scanner;
import java.util.Queue;
import java.util.ArrayDeque;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Eric
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EHopscotchAddict solver = new EHopscotchAddict();
        solver.solve(1, in, out);
        out.close();
    }

    static class EHopscotchAddict {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            EHopscotchAddict.Vertex[] vertices = new EHopscotchAddict.Vertex[n];
            for (int i = 0; i < n; i++) {
                vertices[i] = new EHopscotchAddict.Vertex();
            }
            for (int i = 0; i < m; i++) {
                vertices[in.nextInt() - 1].next.add(vertices[in.nextInt() - 1]);
            }
            EHopscotchAddict.Vertex s = vertices[in.nextInt() - 1];
            EHopscotchAddict.Vertex t = vertices[in.nextInt() - 1];
            Queue<EHopscotchAddict.Vertex> queue = new ArrayDeque<>();
            queue.add(s);
            s.isAdded = true;
            boolean found = false;
            int nbSteps = -1;
            while (!queue.isEmpty()) {
                EHopscotchAddict.Vertex current = queue.poll();
                for (EHopscotchAddict.Vertex vertex : current.next) {
                    for (EHopscotchAddict.Vertex vertex2 : vertex.next) {
                        for (EHopscotchAddict.Vertex vertex3 : vertex2.next) {
                            if (vertex3.isAdded)
                                continue;
                            vertex3.nbSteps = current.nbSteps + 1;
                            vertex3.isAdded = true;
                            queue.add(vertex3);
                            if (vertex3 == t) {
                                nbSteps = vertex3.nbSteps;
                                found = true;
                                break;
                            }
                        }
                    }
                }
                if (found)
                    break;
            }
            out.println(nbSteps);
        }

        public static class Vertex {
            List<EHopscotchAddict.Vertex> next = new ArrayList<>();
            boolean isAdded;
            int nbSteps;

        }

    }
}