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;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;

namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        //static List<List<int>> G = new List<List<int>>();
        static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
       
        
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var input = cin.SplitRead();
            int N = input[0];
            int M = input[1];
            var used = new bool[N, 3];
            for (var i = 0; i < N; i++) for (var j = 0; j < 3; j++) used[i, j] = false;
            for (var i = 0; i < N; i++) G.Add(new List<Edge>());

            for(var i = 0; i < M; i++)
            {
                var p = cin.SplitRead();
                G[p[0] - 1].Add(new Edge(p[1] - 1, 1));
            }

            var st = cin.SplitRead();
            int S = st[0] - 1;
            int T = st[1] - 1;

            var bfs = new Queue<Pair<int, long>>();
            bfs.Enqueue(new Pair<int, long>(S, 0));

           
            while (bfs.Any())
            {
                var now = bfs.Dequeue();
                var v = now.first;
                var d = now.second;

                used[v, d % 3] = true;
                if (v == T && d % 3 == 0)
                {
                    Console.WriteLine(d / 3);
                    return;
                }

                foreach(var ed in G[v])
                {
                    if (used[ed.to, (d + 1) % 3]) { continue; }
                    bfs.Enqueue(new Pair<int, long>(ed.to, d + 1));
                }

            }
            Console.WriteLine(-1);


             

            //Console.Out.Flush();
        }

        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
        struct Pair<T, U> : IComparable<Pair<T, U>>
        where T : IComparable<T>
        where U : IComparable<U>
        {
            public T first;
            public U second;
            private readonly bool CompWithFirst;

            public Pair(T f, U s, int comp)
            {
                first = f;
                second = s;
                CompWithFirst = comp == 1;
            }
            public Pair(T f,U s)
            {
                first = f;
                second = s;
                CompWithFirst = true;
            }

            public int CompareTo(Pair<T, U> other)
            {
                return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
            }
        }
    }
    public class PriorityQueue<T> where T : IComparable<T>
    {

        private List<T> Q;
        private readonly int r;

        public PriorityQueue(bool ascending)
        {
            if (ascending)
            {
                r = 1;
            }
            else
            {
                r = -1;
            }
            Q = new List<T>();
        }


        private void PushHeap(List<T> list, T item)
        {
            int n = list.Count();
            list.Add(item);

            while (n != 0)
            {
                int pIndex = (n - 1) / 2;

                if (list[n].CompareTo(list[pIndex]) * r > 0)
                {
                    Swap(Q, n, pIndex);
                }
                else { break; }

                n = pIndex;
            }
        }

        private void PopHeap(List<T> list)
        {
            int n = list.Count() - 1;
            list[0] = list[n];
            list.RemoveAt(n);

            int cur = 0;
            int comp;

            while (2 * cur + 1 <= n - 1)
            {
                int c1 = 2 * cur + 1;
                int c2 = 2 * (cur + 1);
                if (c1 == n - 1)
                {
                    comp = c1;
                }
                else
                {

                    comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                }

                if (list[cur].CompareTo(list[comp]) * r < 0)
                {
                    Swap(Q, cur, comp);
                }
                else { break; }

                cur = comp;
            }
        }

        private void Swap(List<T> list, int a, int b)
        {
            T keep = list[a];
            list[a] = list[b];
            list[b] = keep;
        }



        public void Enqueue(T value)
        {
            PushHeap(Q, value);
        }

        public T Dequeue()
        {
            T ret = Q[0];
            PopHeap(Q);
            return ret;
        }

        public T Peek()
        {
            return Q[0];
        }

        public int Count()
        {
            return Q.Count();
        }

        public bool Contains(T search)
        {
            return Q.Contains(search);
        }
    }
    public class Scanner
    {
        public int[] SplitRead()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReadL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }

        static public T MaxLot<T>(params T[] val) where T : IComparable<T>
        {
            T ret = val[0];
            for (var i = 1; i < val.Count(); i++)
            {
                if (ret.CompareTo(val[i]) < 0) { ret = val[i]; }
            }
            return ret;
        }
        static public T MinLot<T>(params T[] val) where T : IComparable<T>
        {
            T ret = val[0];
            for (var i = 1; i < val.Count(); i++)
            {
                if (ret.CompareTo(val[i]) > 0) { ret = val[i]; }
            }
            return ret;
        }

        static void Swap<T>(T[] a, int i, int j)
        {
            T k = a[i];
            a[i] = a[j];
            a[j] = k;
        }

        static T chmax<T>(T val1, T val2) where T : IComparable<T>
        {
            return val1.CompareTo(val2) >= 0 ? val1 : val2;
        }

        static T chmin<T>(T val1,T val2) where T : IComparable<T>
        {
            return val1.CompareTo(val2) < 0 ? val1 : val2;
        }
    }

}