Problem:
Score : 400 points

Problem Statement

Takahashi will play a game using a piece on an array of squares numbered 1, 2, \cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1, 2, \cdots, N: P_1, P_2, \cdots, P_N.

Now, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):

In one move, if the piece is now on Square i (1 \leq i \leq N), move it to Square P_i. Here, his score increases by C_{P_i}.

Help him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game.)

Constraints

2 \leq N \leq 5000

1 \leq K \leq 10^9

1 \leq P_i \leq N

P_i \neq i

P_1, P_2, \cdots, P_N are all different.

-10^9 \leq C_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_1 P_2 \cdots P_N
C_1 C_2 \cdots C_N

Output

Print the maximum possible score at the end of the game.

Sample Input 1

5 2
2 4 5 1 3
3 4 -10 -8 8

Sample Output 1

8

When we start at some square of our choice and make at most two moves, we have the following options:

If we start at Square 1, making one move sends the piece to Square 2, after which the score is 4. Making another move sends the piece to Square 4, after which the score is 4 + (-8) = -4.

If we start at Square 2, making one move sends the piece to Square 4, after which the score is -8. Making another move sends the piece to Square 1, after which the score is -8 + 3 = -5.

If we start at Square 3, making one move sends the piece to Square 5, after which the score is 8. Making another move sends the piece to Square 3, after which the score is 8 + (-10) = -2.

If we start at Square 4, making one move sends the piece to Square 1, after which the score is 3. Making another move sends the piece to Square 2, after which the score is 3 + 4 = 7.

If we start at Square 5, making one move sends the piece to Square 3, after which the score is -10. Making another move sends the piece to Square 5, after which the score is -10 + 8 = -2.

The maximum score achieved is 8.

Sample Input 2

2 3
2 1
10 -7

Sample Output 2

13

Sample Input 3

3 3
3 1 2
-1000 -2000 -3000

Sample Output 3

-1000

We have to make at least one move.

Sample Input 4

10 58
9 1 6 7 8 4 3 2 10 5
695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719

Sample Output 4

29507023469

The absolute value of the answer may be enormous.

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;

namespace AtCoder
{
    static class Program_D
    {
        class Solver
        {
            int ri => sc.Integer();
            long rl => sc.Long();
            double rd => sc.Double();
            string rs => sc.Scan();
            public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
            private List<long[]> scores;
            private int k;
            private int[] p;
            private int[] c;
            long allMax = -10000000000;

            public void Solve()
            {
                var n = ri;
                k = ri;
                p = new int[n];
                c = new int[n];
                for(int i = 0; i < n; ++i)
                {
                    p[i] = ri - 1;
                }
                for (int i = 0; i < n; ++i)
                {
                    c[i] = ri;
                }
                scores = new List<long[]>();
                for(int i = 0; i < n; ++i)
                {
                    if (p[i] == -1) continue;
                    scores.Add(CreateScores(i));
                }
                //DumpScores();
                //Wl("---");

                foreach (var score in scores)
                {
                    CalcMaxScore(score);
                }
                Wl(allMax);

            }

            private void CalcMaxScore(long[] score)
            {
                var work = new long[score.Length];
                int end = Math.Min(k, score.Length);
                var scoreSum = score.Sum();
                //Wl($"scoreSum[{scoreSum}]");

                long maxScore = -1;
                int maxIndex = -1;

                for(int t = 0; t < end; ++t)
                {
                    long wTmp = work[0];
                    for (int i = 0; i < score.Length; ++i)
                    {
                        var nextIndex = (i + 1) % score.Length;
                        var wTmp2 = work[nextIndex];
                        work[nextIndex] = wTmp + score[nextIndex];
                        wTmp = wTmp2;
                    }
                    //Wl(string.Join(" ", work.Select(tmp => tmp.ToString())));
                    var currentMax = work.Max();
                    //Wl(currentMax);
                    int nokoriLoop = (k - (t + 1)) / score.Length;
                    long maxScoreMod = currentMax;
                    if (scoreSum > 0)
                    {
                        //Wl($"add nokoriLoop[{nokoriLoop}] * scoreSum[{scoreSum}]");
                        maxScoreMod = currentMax + nokoriLoop * scoreSum;
                    }
                    if (t == 0 || maxScoreMod > maxScore)
                    {
                        maxScore = maxScoreMod;
                        maxIndex = t;
                    }
                }

                
                //Wl($"maxIndex[{maxIndex}] maxScore[{maxScore}] ");
                allMax = Math.Max(allMax, maxScore);
            }

            private void DumpScores()
            {
                foreach (var score in scores)
                {
                    Wl(string.Join(" ", score.Select(s => s.ToString())));
                }
            }

            long[] CreateScores(int index)
            {
                var result = new List<long>();
                do
                {
                    if (p[index] == -1) return result.ToArray();
                    result.Add(c[p[index]]);
                    var newIndex = p[index];
                    p[index] = -1;
                    index = newIndex;
                } while (true);
            }



            // ----------------------------------------------------------------------------
            static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }


            string Rl()
            {
                return Console.ReadLine();
            }
            void Wl(UInt64 val)
            {
                Console.WriteLine(val);
            }
            void Wl(Int64 val)
            {
                Console.WriteLine(val);
            }
            void Wl(uint val)
            {
                Console.WriteLine(val);
            }
            void Wl(int val)
            {
                Console.WriteLine(val);
            }
            void Wl(double val)
            {
                Console.WriteLine(val);
            }
            void Wl(string mes)
            {
                Console.WriteLine(mes);
            }
            public int Int()
            {
                return int.Parse(Console.ReadLine());
            }

            public int[] Ints(int subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => int.Parse(s) - subtract).ToArray();
            }
            public Int64[] Int64s(Int64 subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => Int64.Parse(s) - subtract).ToArray();
            }
            public UInt64[] UInt64s(UInt64 subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => UInt64.Parse(s) - subtract).ToArray();
            }


        }



        static void Main(string[] args)
        {
            Console.SetOut(new Printer(Console.OpenStandardOutput()) { AutoFlush = false });
            new Solver().Solve();
            Console.Out.Flush();
        }
    }

    public class Printer : StreamWriter
    {
        public override IFormatProvider FormatProvider => CultureInfo.InvariantCulture;
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;

        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char()
        {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }

    struct ModInt
    {
        const int MOD = 1000000007;
        long Data;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public ModInt(long data) { if ((Data = data % MOD) < 0) Data += MOD; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator long(ModInt modInt) => modInt.Data;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator ModInt(long val) => new ModInt(val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator +(ModInt a, ModInt b)
        {
            long res = a.Data + b.Data;
            return new ModInt() { Data = res >= MOD ? res - MOD : res };
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator +(ModInt a, long b) => a.Data + b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator -(ModInt a, ModInt b)
        {
            long res = a.Data - b.Data;
            return new ModInt() { Data = res < 0 ? res + MOD : res };
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator -(ModInt a, long b) => a.Data - b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % MOD };
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator /(ModInt a, ModInt b) => a.Data * GetInverse(b);

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string ToString() => Data.ToString();

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static long GetInverse(long a)
        {
            long div;
            long p = MOD;
            long x1 = 1, y1 = 0, x2 = 0, y2 = 1;
            while (true)
            {
                if (p == 1) return x2;
                div = a / p;
                x1 -= x2 * div;
                y1 -= y2 * div;
                a %= p;
                if (a == 1) return x1;
                div = p / a;
                x2 -= x1 * div;
                y2 -= y1 * div;
                p %= a;
            }
        }
    }

}