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.Numerics;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using System.Collections;

namespace debug
{
    class main
    {
        static void Main(string[] args)
        {
            //問題クラスを展開
            ProgramD a = new ProgramD();
            a.main();//実行する

        }

    }
    //ABC175
    class ProgramA
    {
        public void main()
        {
            //入力
            string s = Console.ReadLine();

            //30以上ならYes、それ以外はNoを出力
            if (s == "RRR")
                Console.WriteLine(3);
            else if(s == "RRS" || s == "SRR")
                Console.WriteLine(2);
            else if (s == "SSS")
                Console.WriteLine(0);
            else
                Console.WriteLine(1);

        }
    }

    class ProgramB
    {
        public void main()
        {
            //入力

            int n = int.Parse(Console.ReadLine());
            string[] s = Console.ReadLine().Split(' ');

            long count = 0;
            //それぞれの距離を求めて、距離がD以下なら1足す
            for (int i = 0; i < n; i++)
                for (int j = i + 1; j < n; j++)
                    for (int k = j + 1; k < n; k++)
                    {
                        long a = long.Parse(s[i]);
                        long b = long.Parse(s[j]);
                        long c = long.Parse(s[k]);
                        if (a == b || b == c || c == a)
                            continue;

                        if (a + b> c  && b + c > a && c +a > b)
                            count++;
                    }

            //答え出力
            Console.WriteLine(count);

        }
    }

    class ProgramC
    {
        public void main()
        {

            //入力
            string[] s = Console.ReadLine().Split(' ');
            long X = Math.Abs(long.Parse(s[0]));
            long k = long.Parse(s[1]);
            long D = long.Parse(s[2]);

            if(X == 0)
            {
                if(k % 2 == 0)
                    Console.WriteLine(0);
                else
                    Console.WriteLine(D);
                return;
            }

            if(X >= k * D)
            {
                Console.WriteLine(X - k * D);
                return;
            }

            long count = X / D;
            long ans1 = X - count * D; 
            long ans2 = Math.Abs(ans1 - D);

            

            if (count % 2 == 0)
            {
                if (k % 2 == 0)
                    Console.WriteLine(ans1);
                else
                    Console.WriteLine(ans2);
            }
            else
            {
                if (k % 2 == 1)
                    Console.WriteLine(ans1);
                else
                    Console.WriteLine(ans2);

            }



        }
    }

    class ProgramD
    {
        public void main()
        {

            //入力
            string[] s = Console.ReadLine().Split(' ');
            long n = long.Parse(s[0]);
            long k = long.Parse(s[1]);
            string[] p = Console.ReadLine().Split(' ');
            string[] c = Console.ReadLine().Split(' ');

            long[] flag = new long[n];
            long ans = 0;

            for (int i = 0; i < n; i++)
            {
                if (flag[i] != 0)
                    continue;

                List<long> list = new List<long>();
                int start = int.Parse(p[i]) - 1;
                while (start != i)
                {
                    flag[start]++;
                    list.Add(long.Parse(c[start]));
                    start = int.Parse(p[start])- 1;
                }

                for(int j = 0; j < list.Count();j++)
                {
                    if (k < j + 1)
                        continue;


                    long temp = 0;
                    for (int x = 0;x < j + 1; x++)
                    {
                        temp += list[x];
                    }

                    ans = Math.Max(ans, temp);

                    for(int y = j + 1; y < list.Count();y++)
                    {
                        temp -= list[y - j - 1];
                        temp += list[y];
                        ans = Math.Max(ans, temp);
                    }
                }


            }

            
            Console.WriteLine(ans);
            

        }

    }

    class ProgramE
    {

        public void main()
        {
            //入力
            string[] s = Console.ReadLine().Split(' ');
            long n = long.Parse(s[0]);
            long k = long.Parse(s[1]);

            long[] a = new long[n];

            string[] t = Console.ReadLine().Split(' ');

            for(int i = 0;i < n;i++)
                a[i] = long.Parse(t[i]);

            long min = 0;//最初を0にすると1に答えができる
            long max = 1000000000;//答候補の最大

            //二分探索（答えを決め打ちして、切る回数を数える。k回以下ならmax,そうでないならmin)
            //小さくした方が回数がかかるので、maxが満たす最小の丸太の長さ
            while(min + 1 != max)
            {
                long temp = (min + max) / 2;
                long cut = 0;
                //切る回数を数える
                for (int i = 0; i < n; i++)
                {
                    //tempが大きいなら切らない
                    if (a[i] < temp)
                        continue;
                    //割り切れるかどうかで回数は変わる
                    if(a[i] % temp == 0)
                        cut += a[i] / temp - 1;
                    else
                        cut += a[i] / temp;
                }

                //k回以下ならmax更新、そうでないならminを更新
                if (cut <= k)
                    max = temp;
                else
                    min = temp;

            }

            //答え出力
            Console.WriteLine(max);

        }


    }

}