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# (Mono-csc 3.5.0) (judge verdict: Accepted)

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

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC175.D();
    }
    class ABC175
    {
      public static void A()
      {
        var S = Read.Str();
        if (S == "RRR")
        {
          Console.WriteLine(3);
        }else if (S.Contains("RR"))
        {
          Console.WriteLine(2);
        }else if (S.Contains("R"))
        {
          Console.WriteLine(1);
        }
        else
        {
          Console.WriteLine(0);
        }
      }
      public static void B()
      {
        var N = Read.Int();
        var L = Read.LongN();
        long count = 0;
        for(int i = 0; i < N; ++i)
        {
          for (int j = i + 1; j < N; ++j)
          {
            for(int k = j + 1; k < N; ++k)
            {
              var x = new long[] { L[i], L[j], L[k] }.Distinct().OrderBy(x => x).ToArray();
              if (x.Length < 3) { continue; }
              if (x[0] + x[1] > x[2])
              {
                count++;
              }
            }
          }
        }
        Console.WriteLine(count);
      }
      public static void C()
      {
        var X = Read.Long();
        var K = Read.Long();
        var D = Read.Long();
        var diff = X / D;
        long min = (long)1e18;
        if ((double)K * (double)D < 1e18)
        {
          min = Math.Min(min, Math.Abs(X - D * K));
          min = Math.Min(min, Math.Abs(X + D * K));
        }
        for (long i = (K - diff) / 2 - 100; i < (K - diff) / 2 + 100; ++i)
        {
          var j = K - i;
          if (i < 0 || j < 0) { continue; }
          var Y = X + (i - j) * D;
          min = Math.Min(min, Math.Abs(Y));
        }
        Console.WriteLine(min);
      }
      public static void D()
      {
        var N = Read.Int();
        var K = Read.Long();
        var P = Read.IntN().Select(i => i - 1).ToArray();
        var C = Read.LongN();

        var uft = new Util.UnionFindTree(N);
        for(int i = 0; i < N; ++i)
        {
          uft.Unite(i, P[i]);
        }
        Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
        for (int i = 0; i < N; ++i)
        {
          var p = uft.Root(i);
          if (!dict.ContainsKey(p))
          { dict.Add(p, new HashSet<int>()); }
          dict[p].Add(i);
        }
        long max = C.Max();
        foreach(var kvp in dict)
        {
          var len = kvp.Value.Count;
          var sum = kvp.Value.Select(i => C[i]).Sum();
          var resK = K;
          long point = 0;
          if (sum > 0)
          {
            var loopCount = (K - 1) / len;
            point += sum * loopCount;
            resK -= len * loopCount;
          }
          resK = Math.Min(resK, len);
          List<long> cs = new List<long>();
          {
            var x = kvp.Value.ElementAt(0);
            for (int i = 0; i < len * 2; ++i)
            {
              cs.Add(C[x]);
              x = P[x];
            }
          }
          max = Math.Max(max, point + D_Max(cs.ToArray(), resK));
        }
        Console.WriteLine(max);
      }
      static long D_Max(long[] array, long K)
      {
        var asum = Util.ASum(array);
        long max = (long)-1e18;
        for(int k = 1; k <= K; ++k)
        {
          for(int i = 0; i < asum.Length; ++i)
          {
            if (i + k > array.Length) { continue; }
            max = Math.Max(max, asum[i + k] - asum[i]);
          }
        }
        return max;
      }
      public static void E()
      {
        var R = Read.Int();
        var C = Read.Int();
        var K = Read.Int();
        var dict = new Dictionary<int, Dictionary<int, long>>();
        for (int i = 0; i < K; ++i)
        {
          var RCV = Read.IntN();
          var r = RCV[0] - 1;
          var c = RCV[1] - 1;
          if (!dict.ContainsKey(r)) { dict.Add(r, new Dictionary<int, long>()); }
          dict[r].Add(c, RCV[2]);
        }
        var values = new long[4, R, C];
        for (int r = 0; r < R; ++r)
        {
          for (int c = 0; c < C; ++c)
          {
            var v = dict.ContainsKey(r) ? dict[r].ContainsKey(c) ? dict[r][c] : 0 : 0;
            if (r > 0)
            {
              var max = Math.Max(values[0, r - 1, c], Math.Max(values[1, r - 1, c], Math.Max(values[2, r - 1, c], values[3, r - 1, c])));
              values[0, r, c] = max;
              values[1, r, c] = max + v;
            }
            else
            {
              values[1, r, c] = Math.Max(values[1, r, c], v);
            }
            if (c > 0)
            {
              for (int k = 0; k <= 3; ++k)
              {
                values[k, r, c] = Math.Max(values[k, r, c], values[k, r, c - 1]);
                if (v > 0 && k < 3)
                {
                  values[k + 1, r, c] = Math.Max(values[k + 1, r, c], values[k, r, c - 1] + v);
                }
              }
            }
          }
        }
        Console.WriteLine(Math.Max(values[0, R - 1, C - 1], Math.Max(values[1, R - 1, C - 1], Math.Max(values[2, R - 1, C - 1], values[3, R - 1, C - 1]))));
      }
      public static void F()
      {

      }
    }

    class Bound
    {
      public static int Lowerbound<T1, T2>(SortedList<T1, T2> list, T1 x) where T1 : IComparable<T1>
      {
        return Lowerbound(list.Keys, x);
      }
      public static int Upperbound<T1, T2>(SortedList<T1, T2> list, T1 x) where T1 : IComparable<T1>
      {
        return Upperbound(list.Keys, x);
      }
      public static int Lowerbound<T>(IList<T> list, T x) where T : IComparable<T>
      {
        int min = 0;
        int max = list.Count;
        while (min < max)
        {
          var mid = (min + max) / 2;
          if (list[mid].CompareTo(x) >= 0)
          {
            max = mid;
          }
          else
          {
            min = mid + 1;
          }
        }
        return max;
      }
      public static int Upperbound<T>(IList<T> list, T x) where T : IComparable<T>
      {
        int min = 0;
        int max = list.Count;
        while (min < max)
        {
          var mid = (min + max) / 2;
          if (list[mid].CompareTo(x) > 0)
          {
            max = mid;
          }
          else
          {
            min = mid + 1;
          }
        }
        return max;
      }

    }


    class Util
    {
      public static T[,] Gen<T>(int r, int c, T v)
      {
        var matrix = new T[r, c];
        for (int i = 0; i < r; ++i)
        {
          for (int j = 0; j < c; ++j)
          {
            matrix[i, j] = v;
          }
        }
        return matrix;
      }
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static long[,] ASum(long[,] matrix)
      {
        var N = matrix.GetLength(0);
        var M = matrix.GetLength(1);
        var res = new long[N + 1, M + 1];
        for(int i = 0; i < N; ++i)
        {
          for(int j = 0; j < M; ++j)
          {
            res[i + 1, j + 1] = res[i, j + 1] + res[i + 1, j] - res[i, j] + matrix[i, j];
          }
        }
        return res;
      }
      public static MyDict<T, long> Frequency2<T>(T[] array)
      {
        var dict = new MyDict<T, long>();
        foreach (var a in array)
        {
          dict[a]++;
        }
        return dict;
      }
      public class MyDict<T1, T2> : Dictionary<T1, T2>
      {
        public new T2 this[T1 key]
        {
          get { if (!base.ContainsKey(key)) { base.Add(key, default(T2)); } return base[key]; }
          set { base[key] = value; }
        }
      }

      public class BIT
      {
        int N; long[] array;
        public BIT(int m) { for (int n = 1; ; n *= 2) { if (n >= m) { N = n; array = new long[N + 1]; break; } } }
        public void Add(int idx, int v) { for (int x = idx; x <= N; x += x & -x) { array[x] += v; } }
        public long Sum(int idx) { long ret = 0; for (int x = idx; x > 0; x -= x & -x) { ret += array[x]; } return ret; }
      }

      public class UnionFindTree
      {
        int[] parent; int[] count;
        public UnionFindTree(int n) { parent = new int[n]; count = new int[n]; for (int i = 0; i < n; ++i) { parent[i] = i; count[i] = 1; } }
        public int Root(int i) { if (parent[i] == i) { return i; } else { return parent[i] = Root(parent[i]); } }
        public int Count(int i) { return count[Root(i)]; }
        public bool Same(int i, int j) { return Root(i) == Root(j); }
        public void Unite(int i, int j) { var ri = Root(i); var rj = Root(j); if (ri != rj) { parent[ri] = rj; count[rj] += count[ri]; } }
      }
    }
    struct MOD
    {
      public static long P = 1000000007;
      public readonly long V;

      public MOD(long a) { this.V = a % P; }
      public static implicit operator MOD(long a) { return new MOD(a); }
      public static MOD operator +(MOD a, MOD b) { return new MOD((a.V + b.V) % P); }
      public static MOD operator -(MOD a, MOD b) { return new MOD((a.V - b.V + P) % P); }
      public static MOD operator *(MOD a, MOD b) { return new MOD((a.V * b.V) % P); }
      public static MOD operator /(MOD a, MOD b) { return new MOD((a.V * b.Inverse().V) % P); }
      public MOD Inverse()
      {
        long a = V, p = P; long b = p, c = 1, d = 0, e = 0, f = 0;
        while (b != 0) { e = a / b; f = b; b = a - e * b; a = f; f = d; d = c - e * d; c = f; }
        c %= p;
        return c + (c < 0 ? p : 0);
      }
      public MOD Power(long n)
      {
        long a = V, p = P; long res = 1; long mult = a;
        for (int i = 0; i < 63; ++i) { if ((n & ((long)1 << i)) > 0) { res = (res * mult) % p; } mult = (mult * mult) % p; }
        return res;
      }
      public override string ToString() { return V.ToString(); }
    }


    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M, bool isDirectional = false)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); if (!isDirectional) { dict[ab[1]].Add(ab[0], ab[2]); } }
return dict;
}
}
    }
}