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: Wrong Answer)

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

namespace AtCoder.D
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var (N, K) = Read2Longs();
            // インデックス変換
            var P = ReadLongs().Select(x => (int)x - 1).ToList();
            var C = ReadLongs();

            // すべて0以下の場合
            if (C.All(x => x <= 0))
            {
                // 一度だけ最大の場所に移動するのが最適
                return C.Max();
            }

            var took = new bool[N];
            var loops = new List<List<int>>();
            for (var i = 0; i < N; i++)
            {
                if (took[i]) continue;

                var loop = new List<int>();
                var next = P[i];
                while (!took[P[next]])
                {
                    loop.Add(next);
                    next = P[next];
                    took[next] = true;
                }
                loops.Add(loop);
            }

            var max = 0L;
            foreach (var loop in loops)
            {
                var score = GetScore(loop, C, K);
                max = Math.Max(max, score);
            }

            return max;
        }

        private static long GetScore(List<int> loop, List<long> c, long count)
        {
            var sum = loop.Select(x => c[x]).Sum();

            // 1周が最適な場合
            if (sum <= 0 || count < loop.Count)
            {
                var maxScrore = 0L;
                for (var start = 0; start < loop.Count; start++)
                {
                    var currentScoreSum = 0L;
                    var limit = Math.Min(loop.Count, count);
                    for (var i = 0; i < limit; i++)
                    {
                        var next = start + i;
                        if (next >= loop.Count)
                        {
                            next -= loop.Count;
                        }
                        currentScoreSum += c[loop[next]];

                        maxScrore = Math.Max(maxScrore, currentScoreSum);
                    }
                }
                return maxScrore;
            }

            // 1周以上が最適な場合
            var score = sum * (count / loop.Count);
            var nokoriCount = count % loop.Count;

            return score + GetScore(loop, c, nokoriCount);
        }

        #region Console.Read

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static (long, long) Read2Longs() { var ls = ReadLongs(); return (ls[0], ls[1]); }
        public static (long, long, long) Read3Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2]); }
        public static (long, long, long, long) Read4Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3]); }
        public static (long, long, long, long, long) Read5Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3], ls[4]); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
}