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;

class ABC_132_E
{
    static void Main(string[] args)
    {
        string[] input = Console.ReadLine().Split(' ');
        int N = int.Parse(input[0]);
        int M = int.Parse(input[1]);

        Node[] nodes = new Node[N];
        for (int i = 0; i < N; i++)
        {
            nodes[i] = new Node(i);
        }
        for (int i = 0; i < M; i++)
        {
            string[] input2 = Console.ReadLine().Split(' ');
            int from = int.Parse(input2[0]) - 1;
            int to = int.Parse(input2[1]) - 1;
            nodes[from].AddNextNode(nodes[to]);
        }

        string[] input3 = Console.ReadLine().Split(' ');
        int S = int.Parse(input3[0]) - 1;
        int T = int.Parse(input3[1]) - 1;

        nodes[S].MinAccess = 0;

        Queue<Node> queue = new Queue<Node>();
        queue.Enqueue(nodes[S]);

        Queue<Node> queue1 = new Queue<Node>();
        Queue<Node> queue2 = new Queue<Node>();

        while (queue.Count>0)
        {
            Node n0 = queue.Dequeue();
            List<Node> nextNode0 = n0.nextNode;
            for (int i = 0; i < nextNode0.Count; i++)
            {
                queue1.Enqueue(nextNode0[i]);
            }

            while (queue1.Count > 0)
            {
                Node n1 = queue1.Dequeue();
                List<Node> nextNode1 = n1.nextNode;
                for (int i = 0; i < nextNode1.Count; i++)
                {
                    queue2.Enqueue(nextNode1[i]);
                }

                while (queue2.Count > 0)
                {
                    Node n2 = queue2.Dequeue();

                    List<Node> nextNode2 = n2.nextNode;
                    for (int i = 0; i < nextNode2.Count; i++)
                    {
                        bool b = nextNode2[i].Step(n0.MinAccess);
                        if (b)
                        {
                            queue.Enqueue(nextNode2[i]);
                        }
                    }
                }
            }
        }

        if (nodes[T].MinAccess < 0)
        {
            Console.WriteLine("-1");
        }
        else
        {
            Console.WriteLine(nodes[T].MinAccess);
        }
    }

    class Node
    {
        public List<Node> nextNode = new List<Node>();

        public Node(int index)
        {
            Index = index;
            MinAccess = -1;
        }

        public void AddNextNode(Node node)
        {
            nextNode.Add(node);
        }

        public bool Step(int count)
        {
            int nextCount = count + 1;
            if (MinAccess==-1 || MinAccess > nextCount)
            {
                MinAccess = nextCount;
                return true;
            }
            return false;
        }

        public int Index=-1;
        public int MinAccess;
    }
}