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.*;
import java.util.*;
public class Main{
    public static void main(String[] args) throws IOException{
        MyReader r = new MyReader();  
        int N, M;
        {int[] a = r.ii(); N = a[0]; M = a[1];}

        ArrayList<Integer>[] nb = new ArrayList[N+1];
        for(int i = 1; i < N+1; i++)
            nb[i] = new ArrayList<>();

        for(int i = 0; i < M; i++){
            int u, v;
            {int[] a = r.ii(); u = a[0]; v = a[1];}
            nb[u].add(v);
        }

        ArrayList<Integer>[] next = new ArrayList[N+1];
        for(int i = 1; i < N+1; i++){
            ArrayList<Integer> A = new ArrayList<>();
            A.add(i);
            for(int j = 0; j < 3; j++){
                HashSet<Integer> hs = new HashSet<>();
                for(int a : A)
                    hs.addAll(nb[a]);
                A.clear();
                A.addAll(hs);
            }
            next[i] = A;
        }

        int S, T;
        {int[] a = r.ii(); S = a[0]; T = a[1];}
        ArrayList<Integer> A = new ArrayList<>();
        Set<Integer> B = new HashSet<>();
        A.add(S);
        for(int i = 1; !A.isEmpty(); i++){
            ArrayList<Integer> C = new ArrayList<>();
            for(int v : A){
                B.add(v);
                for(int u : next[v]){                  
                    if(u == T){
                        println(i);
                        return;
                    }
                    if(!B.contains(u))
                        C.add(u);                
                }   
            }
            A = C;
        }
        println(-1);
    }

    static void print(Object o){
        System.out.print(o.toString());
    }

    static void println(Object o){
        System.out.println(o.toString());
    }

    static int Int(String s){
        return Integer.parseInt(s);
    }

    static long Long(String s){
        return Long.parseLong(s);
    }
    static class MyReader extends BufferedReader{
        MyReader(){
            super(new InputStreamReader(System.in));
        }

        String s() throws IOException{
            return readLine();
        }

        String[] ss() throws IOException{
            return s().split(" ");
        }

        int i() throws IOException{
            return Int(s());
        }

        int[] ii() throws IOException{
            String[] ss = ss();
            int size = ss.length;
            int[] ii = new int[size];
            for(int j = 0; j < size; j++) ii[j] = Integer.parseInt(ss[j]);
            return ii;
        }

        long l() throws IOException{
            return Long(s());
        }

        long[] ll() throws IOException{
            String[] ss = ss();
            int size = ss.length;
            long[] ll = new long[size];
            for(int j = 0; j < size; j++) ll[j] = Long.parseLong(ss[j]);            
            return ll;
        }
    }
}