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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC132E3
{
    class Program
    {
        static int count = 0;
        static int N;
        static int S;
        static int T;
        static int[] table;
        static List<int>[] dp;

        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split();
            N = int.Parse(input[0]);
            int M = int.Parse(input[1]);
            if (M == 0)
            {
                Console.WriteLine("-1");
            }
            else
            {
                dp = new List<int>[N + 1];
                for (int i = 0; i < N + 1; i++)
                {
                    dp[i] = new List<int>();
                }
                for (long i = 1; i <= M; i++)
                {
                    string[] input2 = Console.ReadLine().Split();
                    dp[int.Parse(input2[0])].Add(int.Parse(input2[1]));
                }
                string[] input3 = Console.ReadLine().Split();
                S = int.Parse(input3[0]);
                T = int.Parse(input3[1]);
                table = new int[N + 1];
                trace(T);
                /*
                for (int i = 1; i <= N; i++)
                {
                    Console.WriteLine(i+" "+table[i]);
                }
                */
                Console.WriteLine(table[S]/3);
            }
        }
        static void trace(int goal)
        {
            if (table[T]!=0&&table[T]%3==0)
            {
                //Console.WriteLine("Loop");
                table[S] = -3;
                return;
            }
            if (table[S] != 0 && table[S] % 3 == 0)
            {
                //Console.WriteLine("Goal");
                return;
            }
            else
            {
                for (int i = 1; i <= N; i++)
                {
                    if (dp[i].Contains(goal))
                    {
                        count++;
                        table[i] = count;
                        trace(i);
                    }
                }
            }
        }
    }
}