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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

namespace ABC132E
{
    class Program
    {
        static void Solve(Input input)
        {
            var n = input.NextInt();
            var m = input.NextInt();

            var dj = new Dijkstra(n);
            for (int i = 0; i < m; i++)
            {
                var u = input.NextInt() - 1;
                var v = input.NextInt() - 1;

                dj.AddPath(u, v, 1);
            }

            var s = input.NextInt() - 1;
            var t = input.NextInt() - 1;
            var cost = dj.ShortestPath(s, t);

            Console.WriteLine(cost);
        }

        /// <summary>
        /// 重み付き・有向グラフの単一始点最短経路
        /// 辺の重みは非負数だけ
        /// </summary>
        class Dijkstra
        {
            class PriorityQueue<T> where T : IComparable<T>
            {
                List<T> Heap;
                Func<T, T, bool> compare;

                public PriorityQueue(int capacity, bool isMinHeap = true)
                {
                    this.Heap = new List<T>(capacity);

                    if (isMinHeap)
                    {
                        compare = (x, y) => x.CompareTo(y) < 0;
                    }
                    else
                    {
                        compare = (x, y) => x.CompareTo(y) > 0;
                    }
                }

                public PriorityQueue() : this(0) { }

                static void pushHeap(List<T> heap, Func<T, T, bool> compare, T item)
                {
                    var n = heap.Count();
                    heap.Add(item);

                    while (n != 0)
                    {
                        var parent = (n - 1) / 2;

                        if (compare(heap[n], heap[parent]))
                        {
                            var temp = heap[n];
                            heap[n] = heap[parent];
                            heap[parent] = temp;
                        }

                        n = parent;
                    }
                }

                static T popHeap(List<T> heap, Func<T, T, bool> compare)
                {
                    if (!heap.Any())
                    {
                        throw new Exception();
                    }
                    var item = heap[0];

                    var n = heap.Count() - 1;
                    heap[0] = heap.Last();
                    heap.RemoveAt(n);

                    var parent = 0;
                    var child = 2 * parent + 1;
                    while (child < n)
                    {
                        if ((child != n - 1) && compare(heap[child + 1], heap[child]))
                        {
                            child++;
                        }

                        if (compare(heap[child], heap[parent]))
                        {
                            var temp = heap[parent];
                            heap[parent] = heap[child];
                            heap[child] = temp;
                        }

                        parent = child;
                        child = 2 * parent + 1;
                    }

                    return item;
                }

                /// <summary>
                /// 要素追加
                /// </summary>
                /// <param name="item"></param>
                public void Push(T item)
                {
                    pushHeap(this.Heap, this.compare, item);
                }

                /// <summary>
                /// 先頭の値取得し削除する
                /// </summary>
                /// <returns></returns>
                public T Pop()
                {
                    return popHeap(this.Heap, this.compare);
                }

                /// <summary>
                /// 先頭の値取得（削除はしない）
                /// </summary>
                /// <returns></returns>
                public T Peek()
                {
                    if (!this.Heap.Any())
                    {
                        throw new Exception();
                    }

                    return this.Heap[0];
                }

                /// <summary>
                /// ヒープに格納されているアイテム数
                /// </summary>
                /// <returns></returns>
                public int Count() => this.Heap.Count();

                /// <summary>
                /// 一つでの値が格納されているか
                /// </summary>
                /// <returns></returns>
                public bool Any() => this.Heap.Any();
            }

            struct Edge : IComparable<Edge>
            {
                public int To;
                public int Cost;

                public Edge(int to, int cost)
                {
                    this.To = to;
                    this.Cost = cost;
                }

                public int CompareTo(Edge other)
                {
                    return this.Cost - other.Cost;
                }
            }

            // 接続情報
            List<List<Edge>> es;
            // ノード数
            int V;

            /// <summary>
            /// 
            /// </summary>
            /// <param name="v">ノード数</param>
            public Dijkstra(int v)
            {
                es = Enumerable.Repeat(0, v)
                    .Select(_ => new List<Edge>())
                    .ToList();
                V = v;
            }

            /// <summary>
            /// 経路追加
            /// </summary>
            /// <param name="from"></param>
            /// <param name="to"></param>
            /// <param name="cost"></param>
            public void AddPath(int from, int to, int cost)
                => es[from].Add(new Edge(to, cost));

            public int ShortestPath(int s, int t)
            {
                var pq = new PriorityQueue<Edge>();

                pq.Push(new Edge(s, 0));

                while (pq.Any())
                {
                    var p = pq.Pop();
                    var v = p.To;

                    // 始点に3の倍数で戻ってきたら削除する
                    if (v == s && p.Cost != 0) continue;
                    if (v == t) return p.Cost;

                    foreach (var e1 in es[v])
                    {
                        foreach (var e2 in es[e1.To])
                        {
                            foreach (var e3 in es[e2.To])
                            {
                                pq.Push(new Edge(e3.To, p.Cost + 1));
                            }
                        }
                    }
                }

                return -1;
            }
        }

        #region Competitive Template
        static readonly int MOD = (int)1e9 + 7;

        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // その場合は出力がボトルネックになっていないので、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();
            // 仮想的に標準入力をセットする
            //input.SetText("4 4 1 2 2 3 3 4 4 1 1 3");

            Solve(input);

            Console.Out.Flush();
        }

        class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            Queue<string> q { get; set; }
            StreamReader sr;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            /// <param name="path"></param>
            public Input(string path = "")
            {
                q = new Queue<string>();

                if (string.IsNullOrEmpty(path))
                {
                    sr = new StreamReader(Console.OpenStandardInput());
                }
                else
                {
                    sr = new StreamReader(path);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="items"></param>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="s"></param>
            /// <returns></returns>
            public bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            /// <returns></returns>
            bool read()
            {
                var s = sr.ReadLine();
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                if (!q.Any()) return read();

                return true;
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            /// <returns></returns>
            public string Next()
            {
                if (!q.Any())
                {
                    if (!read())
                    {
                        return "";
                    }
                }

                return q.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            bool accumulate(int n)
            {
                while (q.Count() < n)
                {
                    if (!read()) return false;
                }

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="n"></param>
            /// <param name="offset"></param>
            /// <param name="parse"></param>
            /// <param name="add"></param>
            /// <returns></returns>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(q.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static void Print<T>(IEnumerable<T> ie, string sep = " ") => Console.WriteLine(string.Join(sep, ie));
            public static void Print<T>(params T[] objs) => Print(objs);
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            public static void Swap<T>(ref T x, ref T y) where T : struct { var t = x; x = y; y = t; }
            public static void Swap<T>(IList<T> list, int i, int j) where T : struct { var t = list[i]; list[i] = list[j]; list[j] = t; }

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="d1"></param>
            /// <param name="d2"></param>
            /// <param name="v"></param>
            /// <returns></returns>
            public static T[][] Create2DArray<T>(int d1, int d2, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="d1"></param>
            /// <param name="d2"></param>
            /// <param name="d3"></param>
            /// <param name="v"></param>
            /// <returns></returns>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                     Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}