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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;


namespace AtCoder
{
    partial class Program
    {
		static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }
        static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
		static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }
        static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }
		
        public static int[] ZAlgotithm(string s)
        {
            var len = s.Length;

            var a = new int[len];
            a[0] = len;
            var i = 1;
            var j = 0;
            while (i < len)
            {
                while (i + j < len && s[j] == s[i + j]) j++;
                a[i] = j;

                if (j == 0)
                {
                    i++;
                    continue;
                }

                var k = 1;
                while (i + k < len && k + a[k] < j)
                {
                    a[i + k] = a[k];
                    k++;
                }
                i += k;
                j -= k;
            }

            return a;
        }
        public class MaxHeap<T> : IEnumerable<T>
        {
            private List<T> _list;
            private Comparer<T> _comp;
			
            public int Count
            {
                get
                {
                    return _list.Count;
                }
            }
            public MaxHeap() : this(0) { }
            public MaxHeap(int capacity, Comparison<T> comp=null)
            {
                _list = new List<T>(capacity);

                if (comp == null)
                {
                    _comp = Comparer<T>.Default;
                }
                else
                {
                    _comp = Comparer<T>.Create(comp);
                }
            }
            
            public void Push(T elem)
            {
                Upheap(elem);
            }

            public T Pop()
            {
                return Downheap();
            }

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

            
            private void Swap(int i, int j)
            {
                var a = _list[j];
                _list[j] = _list[i];
                _list[i] = a;
            }

            private void Upheap(T elem)
            {
                _list.Add(elem);
                var i = _list.Count - 1;

                while (true)
                {
                    if (i == 0) return;
                    var j = (i - 1) / 2;

                    var e = _list[i];
                    var p = _list[j];

                    var c = _comp.Compare(e, p);
                    if (c > 0)
                    {
                        Swap(i, j);
                        i = j;
                        continue;
                    }
                    else
                    {
                        break;
                    }
                }
            }

            private T Downheap()
            {
                var result = _list[0];

                var last = _list.Count - 1;
                Swap(0, last);
                _list.RemoveAt(last);
                if (_list.Count == 0) return result;

                var i = 0;
                while (true)
                {
                    if (i == _list.Count - 1) return result;
                    var p = _list[i];

                    var j = i * 2 + 1;
                    if (j >= _list.Count) return result;

                    if(j+1 < _list.Count && _comp.Compare(_list[j], _list[j+1]) < 0)
                    {
                        j++;
                    }

                    if (_comp.Compare(_list[i], _list[j]) < 0)
                    {
                        Swap(i, j);
                        i = j;
                    }
                    else
                    {
                        return result;
                    }
                }
            }

            public IEnumerator<T> GetEnumerator()
            {
                return _list.GetEnumerator();
            }

            IEnumerator IEnumerable.GetEnumerator()
            {
                return GetEnumerator();
            }
        }
        public class PriorityQueue<T> where T : IComparable
        {
            private IComparer<T> _comparer = null;
            private int _type = 0;

            private T[] _heap;
            private int _sz = 0;

            private int _count = 0;

            /// <summary>
            /// Priority Queue with custom comparer
            /// </summary>
            public PriorityQueue(int maxSize, IComparer<T> comparer)
            {
                _heap = new T[maxSize];
                _comparer = comparer;
            }

            /// <summary>
            /// Priority queue
            /// </summary>
            /// <param name="maxSize">max size</param>
            /// <param name="type">0: asc, 1:desc</param>
            public PriorityQueue(int maxSize, int type = 0)
            {
                _heap = new T[maxSize];
                _type = type;
            }

            private int Compare(T x, T y)
            {
                if (_comparer != null) return _comparer.Compare(x, y);
                return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
            }

            public void Push(T x)
            {
                _count++;

                //node number
                var i = _sz++;

                while (i > 0)
                {
                    //parent node number
                    var p = (i - 1) / 2;

                    if (Compare(_heap[p], x) <= 0) break;

                    _heap[i] = _heap[p];
                    i = p;
                }

                _heap[i] = x;
            }

            public T Pop()
            {
                _count--;

                T ret = _heap[0];
                T x = _heap[--_sz];

                int i = 0;
                while (i * 2 + 1 < _sz)
                {
                    //children
                    int a = i * 2 + 1;
                    int b = i * 2 + 2;

                    if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                    if (Compare(_heap[a], x) >= 0) break;

                    _heap[i] = _heap[a];
                    i = a;
                }

                _heap[i] = x;

                return ret;
            }

            public int Count()
            {
                return _count;
            }

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

            public bool Contains(T x)
            {
                for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
                return false;
            }

            public void Clear()
            {
                while (this.Count() > 0) this.Pop();
            }

            public IEnumerator<T> GetEnumerator()
            {
                var ret = new List<T>();

                while (this.Count() > 0)
                {
                    ret.Add(this.Pop());
                }

                foreach (var r in ret)
                {
                    this.Push(r);
                    yield return r;
                }
            }

            public T[] ToArray()
            {
                T[] array = new T[_sz];
                int i = 0;

                foreach (var r in this)
                {
                    array[i++] = r;
                }

                return array;
            }
        }
        class InputLine
        {
            private string[] _inputs;
            private int _index = 0;

            InputLine(string input)
            {
                _inputs = input.Split();
                _index = 0;
            }

            public static InputLine Read()
            {
                return new InputLine(Console.ReadLine());
            }

            public int NextInt()
            {
                return int.Parse(_inputs[_index++]);
            }
            public long NextLong()
            {
                return long.Parse(_inputs[_index++]);
            }
            public double NextDouble()
            {
                return double.Parse(_inputs[_index++]);
            }
        }
        public static int GCD(int x, int y)
        {
            var a = Math.Max(x, y);
            var b = x + y - a;

            while (b != 0)
            {
                var c = b;
                b = a % b;
                a = c;
            }

            return a;
        }
        public static long GCD(long x, long y)
        {
            var a = Math.Max(x, y);
            var b = x + y - a;

            while (b != 0)
            {
                var c = b;
                b = a % b;
                a = c;
            }

            return a;
        }
        static long ModPower(long x, long y, long mod)
        {
            var bytes = BitConverter.GetBytes(y);
            var bits = new System.Collections.BitArray(bytes);

            var max2 = 0;
            for (int i = bits.Length - 1; i >= 0; i--)
            {
                if (bits[i])
                {
                    max2 = i;
                    break;
                }
            }

            long result = 1;
            for (int i = max2; i >= 0; i--)
            {
                result = (result * result) % mod;
                if (bits[i])
                {
                    result = (result * x) % mod;
                }
            }

            return result;
        }
        
        static long ModFact(long n, long mod)
        {
            long result = 1;

            for (int i = 1; i <= n; i++)
            {
                result = result * i % mod;
            }
            return result;
        }

        static long ModMal(long x, long y, long mod)
        {
            return ((x % mod) * (y % mod)) % mod;
        }

        static long ModDiv(long x, long y, long mod)
        {
            //フェルマーの小定理より、a^(-1) = a^(p-2)
            return ModMal(x, ModPower(y, mod - 2, mod), mod);
        }
        static long ModComb(long n, long r, long mod)
        {
            long numerator = 1;
            for (int i = 0; i < r; i++)
            {
                numerator = ModMal(numerator, n - i, mod);
            }

            long denominator = ModFact(r, mod);

            return ModDiv(numerator, denominator, mod);
        }
        class Graph
        {
            private int _size;
            private List<int>[] _map;

            public IEnumerable<int> this[int i]
            {
                get
                {
                    if (_map[i] == null) return Enumerable.Empty<int>();
                    return _map[i];
                }
            }

            public Graph(int size)
            {
                _size = size;
                _map = new List<int>[size];
            }

            public void Add(int from, int to)
            {
                if (_map[from] == null)
                {
                    _map[from] = new List<int>();
                }
                _map[from].Add(to);
            }
        }
        static long p1097 = 1000000007;
        static void Main(string[] args)
        {
			//↓

            var ins = InputLine.Read();
            var n = ins.NextInt();
            var m = ins.NextInt();
            var g = new Graph(n);
            for (int i = 0; i < m; i++)
            {
                var uv = ReadIntArray();
                g.Add(uv[0] - 1, uv[1] - 1);
            }

            ins = InputLine.Read();
            var s = ins.NextInt() - 1;
            var t = ins.NextInt() - 1;

            var min = new int[n];
            min[t] = -1;
            min[s] = 0;
            var count = 0;
            var q = new HashSet<int>();
            q.Add(s);
            while (q.Any())
            {
                var nexts = new HashSet<int>();
                foreach (var from in q)
                {
                    foreach (var next in g[from])
                    {
                        if (count % 3 == 2)
                        {
                            if (min[next] <= 0)
                            {
                                nexts.Add(next);
                                min[next] = (count + 1) / 3;
                            }
                        }
                        else
                        {
                            nexts.Add(next);
                        }
                    }
                }
                q = nexts;
                count++;

                if (min[t] > 0) break;
            }

            Console.WriteLine(min[t]);


			//↑
        }

	}
}