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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ABC132E
{
    class Program
    {
        static void Main(string[] args)
        {
            var NM = ReadInt();
            int N = NM[0];
            int M = NM[1];

            List<int>[] edges = new List<int>[N].Select(x => new List<int>()).ToArray();
            for (int i = 0; i < M; i++)
            {
                var input = ReadInt();
                int u = input[0] - 1;
                int v = input[1] - 1;
                edges[u].Add(v);
            }

            var ST = ReadInt();
            int S = ST[0] - 1;
            int T = ST[1] - 1;

            //3頂点先を登録
            List<int>[] edgesto3 = new List<int>[N];
            for (int i = 0; i < N; i++)
            {
                Queue<int> que = new Queue<int>();
                que.Enqueue(i);

                for (int j = 0; j < 3; j++)
                {
                    int count = que.Count;
                    for (int k = 0; k < count; k++)
                    {
                        int from = que.Dequeue();
                        foreach (var to in edges[from])
                        {
                            que.Enqueue(to);
                        }
                    }
                }

                edgesto3[i] = que.ToList();
            }

            //幅優先探索
            Queue<int> que1 = new Queue<int>();
            que1.Enqueue(S);
            int[] distance = new int[N].Select(x => int.MaxValue).ToArray();
            distance[S] = 0;

            while (que1.Count > 0)
            {
                int q = que1.Dequeue();

                foreach (var to in edgesto3[q])
                {
                    int dis = distance[q] + 1;
                    if (dis < 0) Console.WriteLine("error");
                    if (distance[to] > dis)
                    {
                        distance[to] = dis;
                        que1.Enqueue(to);
                    }
                }
            }

            if (distance[T] != int.MaxValue) Console.WriteLine(distance[T]);
            else Console.WriteLine(-1);
            Console.ReadKey();
        }

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}