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: Runtime Error)

import java.util.*;


class Main{
    static int[][] dp;
    static int[][] map;
    static int n,m,T,S;
    public static void main(String argv[]) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        dp = new int[n+1][n+1];
        map = new int[n+1][3];
        for(int i=0;i<m;i++){
            dp[sc.nextInt()][sc.nextInt()]=1;
        }
        for(int i=0;i<n+1;i++){
            map[i][0]=999999999;
            map[i][1]=999999999;
            map[i][2]=999999999;
        }
        S = sc.nextInt();
        T = sc.nextInt();
        search(S, 0);
        // /dump();
        int result = -1;
        if(map[T][0]!=999999){
            result = map[T][0]/3;
        }
        System.out.println(result);
    }

    public static void search(int node, int hosu) {
        if(hosu<=map[node][hosu%3]){
            map[node][hosu%3]=hosu;
        }
        else{
            return;
        }
        if(map[T][0] < hosu)return;
        for(int i=0;i<n+1;i++){
            if(dp[node][i]==1){
                search(i, hosu+1);
            }
        }
        return;
    }

    public static void dump() {
        for(int i=0;i<n+1;i++){
            for(int j=0;j<n+1;j++){
                System.out.print(dp[i][j] + " ");
            }
            System.out.println();
        }
        for(int i=0;i<n+1;i++){
            System.out.println(map[i]);

        }
    }
}