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: Runtime Error)

using System;
using System.Collections.Generic;
using System.IO;

namespace Sandbox
{
    internal class Program
    {
        static Dictionary<int, SortedSet<int>> v2uX1 = new Dictionary<int, SortedSet<int>>();
        static Dictionary<int, SortedSet<int>> v2uX2 = new Dictionary<int, SortedSet<int>>();
        static Dictionary<int, SortedSet<int>> v2uX3 = new Dictionary<int, SortedSet<int>>();

        private static void Main(string[] args)
        {
            var scanner = new Scanner();
            var n = scanner.GetNextAsInt();
            var m = scanner.GetNextAsInt();
            var uv = new int[m,2];

            for (var i = 0; i < m; i++)
            {
                var ui = scanner.GetNextAsInt();
                var vi = scanner.GetNextAsInt();
                uv[i, 0] = ui;
                uv[i, 1] = vi;

                if (!v2uX1.ContainsKey(vi))
                {
                    v2uX1[vi] = new SortedSet<int>();
                }

                v2uX1[vi].Add(ui);
            }

            var s = scanner.GetNextAsInt();
            var t = scanner.GetNextAsInt();

            foreach (var kv in v2uX1)
            {
                var vi = kv.Key;

                foreach (var u1 in kv.Value)
                {
                    if (!v2uX1.ContainsKey(u1))
                    {
                        continue;
                    }

                    foreach (var ui2 in v2uX1[u1])
                    {
                        if (!v2uX2.ContainsKey(vi))
                        {
                            v2uX2[vi] = new SortedSet<int>();
                        }

                        v2uX2[vi].Add(ui2);
                    }
                }
            }

            foreach (var kv in v2uX2)
            {
                var vi = kv.Key;

                foreach (var u1 in kv.Value)
                {
                    if (!v2uX2.ContainsKey(u1))
                    {
                        continue;
                    }

                    foreach (var ui2 in v2uX1[u1])
                    {
                        if (!v2uX3.ContainsKey(vi))
                        {
                            v2uX3[vi] = new SortedSet<int>();
                        }

                        v2uX3[vi].Add(ui2);
                    }
                }
            }

            throw new InvalidOperationException();

            var count = 0;
            var isOk = false;
            var visited = new HashSet<int>();

            var currentList = new HashSet<int>();

            currentList.Add(t);
            visited.Add(t);

            while (true)
            {
                var nextList = new HashSet<int>();

                foreach (var current in currentList)
                {
                    visited.Add(current);
                    if (!v2uX3.ContainsKey(current))
                    {
                        break;
                    }

                    foreach (var next in v2uX3[current])
                    {
                        if (next == s)
                        {
                            isOk = true;
                            break;
                        }

                        if (visited.Contains(next))
                        {
                            continue;
                        }
                        nextList.Add(next);
                    }

                    if (isOk)
                    {
                        break;
                    }
                }

                count++;
                currentList = nextList;

                if (isOk)
                {
                    break;
                }

                if (nextList.Count == 0)
                {
                    break;
                }
            }

            if (!isOk)
            {
                count = -1;
            }

            Console.WriteLine(count);
        }

        #region String Scanner

        public class Scanner
        {
            private const char Separator = ' ';
            private readonly StreamReader _Stream = new StreamReader(Console.OpenStandardInput());
            private int _Pos;
            private string[] _Line = new string[0];

            #region get a element

            public string GetNext()
            {
                // ReSharper disable once InvertIf
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                    this._Pos = 0;
                }

                return this._Line[this._Pos++];
            }

            public int GetNextAsInt()
            {
                return int.Parse(this.GetNext());
            }

            public long GetNextAsLong()
            {
                return long.Parse(this.GetNext());
            }

            public double GetNextAsDouble()
            {
                return double.Parse(this.GetNext());
            }

            #endregion

            #region get array

            public string[] ToArrayFromNextLine()
            {
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                }

                this._Pos = this._Line.Length;
                return this._Line;
            }

            public int[] ToIntArrayFromNextLine()
            {
                return ToIntArray(this.ToArrayFromNextLine());
            }

            public long[] ToLongArrayFromNextLine()
            {
                return ToLongArray(this.ToArrayFromNextLine());
            }

            public double[] ToDoubleArrayFromNextLine()
            {
                return ToDoubleArray(this.ToArrayFromNextLine());
            }

            #endregion

            #region convert array

            private static int[] ToIntArray(string[] array)
            {
                var result = new int[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = int.Parse(array[i]);
                }

                return result;
            }

            private static long[] ToLongArray(string[] array)
            {
                var result = new long[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = long.Parse(array[i]);
                }

                return result;
            }

            private static double[] ToDoubleArray(string[] array)
            {
                var result = new double[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = double.Parse(array[i]);
                }

                return result;
            }

            #endregion
        }

        #endregion
    }
}