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 BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var line = consoleReader.Split.Int;
            var N = line[0];
            var M = line[1];
            graph = new GraphBuilder(N, consoleReader.Repeat(M).SplitInt).ToArray();
            line = consoleReader.Split.Int;
            var S = line[0] - 1;
            var T = line[1] - 1;

            v = new int[N, 3];
            for (int i = 0; i < N; i++)
                for (int j = 0; j < 3; j++)
                    v[i, j] = -1;

            v[S, 0] = 0;
            Update(S, 0);
            return v[T, 0];
        }

        int[][] graph;
        int[,] v;
        void Update(int index, int step)
        {
            int nextStep, nextValue;
            if (step < 2)
            {
                nextValue = v[index, step];
                nextStep = step + 1;
            }
            else
            {
                nextValue = v[index, step] + 1;
                nextStep = 0;
            }
            var nexts = new List<int>(graph[index].Length);
            foreach (var to in graph[index])
            {
                if (v[to, nextStep] < 0 || nextValue < v[to, nextStep])
                {
                    nexts.Add(to);
                    v[to, nextStep] = nextValue;
                }
            }
            foreach (var to in nexts)
            {
                Update(to, nextStep);
            }
        }

        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader()).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        #endregion
    }
    class GraphBuilder
    {
        private List<int>[] lists;
        public GraphBuilder(int count)
        {
            this.lists = new List<int>[count];
            for (int i = 0; i < count; i++)
                this.lists[i] = new List<int>();
        }
        public GraphBuilder(int count, IEnumerable<int[]> arrays) : this(count)
        {
            foreach (var item in arrays)
                this.Add(item[0] - 1, item[1] - 1);
        }
        public void Add(int from, int to)
        {
            this.lists[from].Add(to);
        }
        public int[][] ToArray()
        {
            var N = this.lists.Length;
            var res = new int[N][];
            for (int i = 0; i < N; i++)
                res[i] = this.lists[i].ToArray();
            return res;
        }
    }

    struct Mod : IEquatable<Mod>
    {
        public const long mod = 1000000007;
        public readonly long val;
        public Mod(long val) { this.val = val; }
        public override bool Equals(object obj) => (obj is Mod) ? this == ((Mod)obj) : false;
        public bool Equals(Mod obj) => this == obj;
        public override int GetHashCode() => val.GetHashCode();
        public override string ToString() => val.ToString();
        public static implicit operator Mod(long x) => new Mod(x);
        public static Mod operator +(Mod x, Mod y) => (x.val + y.val) % mod;
        public static Mod operator -(Mod x, Mod y) => x.val >= y.val ? (x.val - y.val) % mod : (x.val - y.val) % mod + mod;
        public static Mod operator *(Mod x, Mod y) => (x.val * y.val) % mod;
        public static Mod operator /(Mod x, Mod y) => x * y.Inverse();
        public static bool operator ==(Mod x, Mod y) => x.val == y.val;
        public static bool operator !=(Mod x, Mod y) => x.val != y.val;
        public Mod Inverse()
        {
            long a = val, b = mod, u = 1, v = 0;
            while (b > 0)
            {
                long t = a / b;
                var b2 = a - t * b;
                a = b; b = b2;
                var v2 = u - t * v;
                u = v; v = v2;
            }
            u %= mod;
            if (u < 0) u += mod;
            return u;
        }
        public static Mod Pow(Mod x, int y)
        {
            Mod res = 1;
            for (; y > 0; y >>= 1)
            {
                if ((y & 1) == 1) res *= x;
                x *= x;
            }
            return res;
        }

        public static Factor CreateFactor(int max) => new Factor(max);
        public class Factor
        {
            private readonly Mod[] fac, finv;
            public Factor(int max)
            {
                var inv = new Mod[max];
                fac = new Mod[max]; finv = new Mod[max];
                fac[0] = fac[1] = 1;
                finv[0] = finv[1] = 1;
                inv[1] = 1;
                for (int i = 2; i < max; i++)
                {
                    fac[i] = fac[i - 1] * i;
                    inv[i] = mod - inv[mod % i].val * (mod / i) % mod;
                    finv[i] = finv[i - 1] * inv[i];
                }
            }

            // 二項係数計算
            public Mod Combine(int n, int k)
            {
                if (n < k) return 0;
                if (n < 0 || k < 0) return 0;
                return fac[n] * finv[k] * finv[n - k];
            }

            public Mod Factorial(int n) => fac[n];
            public Mod FactorialInvers(int n) => finv[n];
        }
    }

#pragma warning disable
    public class ConsoleReader { public class SplitLine { string[] splited; public SplitLine(string line) { splited = line.Split(); } public string[] String => splited.ToArray(); public int[] Int => splited.Select(int.Parse).ToArray(); public long[] Long => splited.Select(long.Parse).ToArray(); public ulong[] ULong => splited.Select(ulong.Parse).ToArray(); public double[] Double => splited.Select(double.Parse).ToArray(); } public class RepeatLine { ConsoleReader reader; int num; public RepeatLine(ConsoleReader reader, int num) { this.reader = reader; this.num = num; } public IEnumerable<string> String { get { for (int i = 0; i < num; i++) yield return reader.String; } } public IEnumerable<int> Int { get { for (int i = 0; i < num; i++) yield return reader.Int; } } public IEnumerable<long> Long { get { for (int i = 0; i < num; i++) yield return reader.Long; } } public IEnumerable<string[]> SplitString { get { for (int i = 0; i < num; i++) yield return reader.Split.String; } } public IEnumerable<int[]> SplitInt { get { for (int i = 0; i < num; i++) yield return reader.Split.Int; } } } public virtual string String => Console.ReadLine(); public int Int => int.Parse(String); public long Long => long.Parse(String); public ulong ULong => ulong.Parse(String); public double Double => double.Parse(String); public SplitLine Split => new SplitLine(String); public RepeatLine Repeat(int count) => new RepeatLine(this, count); }
}