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;
using System.Collections.Generic;
//using System.Collections.Immutable;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static Output;
using static Utils;

public class CP
{
    Input sc;
    public void Solve()
    {
        sc = new Input();
        bool multicases = false;
        var t = multicases ? sc.Int : 1;
        // var sw = new Stopwatch();
        // sw.Start();
        while (t-- > 0)
        {
            c1();
        }
        // sw.Stop();
        //Put(sw.ElapsedMilliseconds + "ms");
    }
    public void c1()
    {
        int n = sc.Int;
        var k = sc.Long;
        var p = sc.Intarr;
        var c = sc.Longarr;
        long ans = -INFL;
        for (int i = 0; i < n; ++i)
        {
            var arr = Enumerable.Repeat(-INFL, n).ToArray();
            int cnt = 0;
            long score = 0;
            int now = i;
            arr[now] = 0;
            var pre = new int[n];
            var time = new int[n];
            var max = Enumerable.Repeat(-INFL, n).ToArray();
            max[0] = 0;
            while (true)
            {
                int last = now;
                now = p[now] - 1;
                if (arr[now] != -INFL)
                {
                    var end = score;
                    var T = cnt - time[now];
                    var nk = k - cnt;
                    if (end - arr[pre[now]] > 0)
                    {
                        var scoree = arr[pre[now]] + (nk / T - 1) * (end - arr[pre[now]]);
                        var nt = nk % T;
                        scoree += Max(0, max[nt + time[now]] - arr[pre[now]]);
                        ans = Max(scoree, ans);
                    }
                    else ans = Max(ans, max[cnt]);
                    break;
                }
                pre[now] = last;
                score += c[now];
                if (cnt > 0)
                    max[cnt] = max[cnt - 1];
                if (score > max[cnt]) max[cnt] = score;
                time[now] = cnt + 1;
                arr[now] = score;
                if (cnt >= k - 1)
                {
                    ans = Max(ans, max[cnt]);
                    break;
                }
                ans = Max(ans, score);
                ++cnt;

            }
        }
        Put(ans);
    }

}





public class PriorityQueue<T>
{
    List<T> _item;
    public int Count { get { return _item.Count; } }
    bool _isascend { get; set; }
    public T Peek { get { return _item[0]; } }
    Comparison<T> Comp;
    public PriorityQueue(bool IsAscend = true, IEnumerable<T> list = null) : this(Comparer<T>.Default.Compare, IsAscend, list) { }
    public PriorityQueue(Comparison<T> cmp, bool IsAscend = true, IEnumerable<T> list = null)
    {
        _item = new List<T>();
        _isascend = IsAscend;
        this.Comp = cmp;
        if (list != null)
        {
            _item.AddRange(list);
            Build();
        }
    }

    private int Compare(int i, int j) => (_isascend ? -1 : 1) * Comp(_item[i], _item[j]);
    private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
    private int Parent(int i) => (i - 1) >> 1;
    private int Left(int i) => (i << 1) + 1;
    public T Enqueue(T val)
    {
        int i = _item.Count;
        _item.Add(val);
        while (i > 0)
        {
            int p = Parent(i);
            if (Compare(i, p) > 0)
                Swap(i, p);
            i = p;
        }
        return val;
    }
    private void Heapify(int index)
    {
        for (int i = index, j;
            (j = Left(i)) < _item.Count; i = j)
        {
            if (j != _item.Count - 1 && Compare(j, j + 1) < 0) j++;
            if (Compare(i, j) < 0)
                Swap(i, j);
        }
    }
    public T Dequeue()
    {
        T val = _item[0];
        _item[0] = _item[_item.Count - 1];
        _item.RemoveAt(_item.Count - 1);
        Heapify(0);
        return val;
    }
    private void Build()
    {
        for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
            Heapify(i);
    }
    public bool Any() => Count > 0;
}
public class BinarySearch
{
    public static int Lower_Bound<T>(IList<T> Array, T Target)
    {
        return Lower_Bound<T>(Array, Target, Comparer<T>.Default.Compare);
    }
    public static int Lower_Bound<T>(IList<T> Array, T Target, Comparison<T> Comp)
    {
        var cmp = Comparer<T>.Create(Comp);
        var l = -1; //always ng
        var r = Array.Count(); //always ok
        while (r - l > 1)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(Array[mid], Target);
            if (res >= 0) r = mid;
            else l = mid;
        }
        return r;
    }
    public static int Upper_Bound<T>(IList<T> Array, T Target)
    {
        return Upper_Bound<T>(Array, Target, Comparer<T>.Default.Compare);
    }
    public static int Upper_Bound<T>(IList<T> Array, T Target, Comparison<T> Comp)
    {
        var cmp = Comparer<T>.Create(Comp);
        var l = -1;
        var r = Array.Count;
        while (r - l > 1)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(Array[mid], Target);
            if (res > 0) r = mid;
            else l = mid;
        }
        return r;
    }
    public static bool Contains<T>(IList<T> Arr, T Target)
    {
        return Contains<T>(Arr, Target, Comparer<T>.Default.Compare);
    }
    public static bool Contains<T>(IList<T> Arr, T Target, Comparison<T> Comp)
    {
        return (Upper_Bound(Arr, Target, Comp) - Lower_Bound(Arr, Target, Comp) > 0);
    }
}
public static class Math2
{
    public const int INF = 1 << 29;
    public const long INFL = 1L << 62;
    public const long MOD = 1000000007;
    public const long MOD2 = 998244353;

    public static long Power(long a, long b, long MOD = 1000000007) //i^N
    {
        long res = 1;
        while (b > 0)
        {
            if ((b & 1) != 0) res = res * a % MOD;
            a = a * a % MOD;
            b >>= 1;
        }
        return (res + 2 * MOD) % MOD;
    }
    public static long Power2(long a, long b) //i^N
    {
        long res = 1;
        while (b > 0)
        {
            if ((b & 1) != 0) res = res * a;
            a = a * a;
            b >>= 1;
        }
        return res;
    }
    public static BigInteger Power2BI(BigInteger a, BigInteger b) //i^N
    {
        BigInteger res = 1;
        while (b > 0)
        {
            if ((b & 1) != 0) res = res * a;
            a = a * a;
            b >>= 1;
        }
        return res;
    }
    public static long GCD(long a, long b)
    {
        if (a == 0) return b;
        while (b > 0)
        {
            var r = a % b;
            a = b;
            b = r;
        }
        return a;
    }
    public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
    public static long Comb(long n, long r, int MOD = 1000000007)
    {
        if (r > n - r) r = n - r;
        long Nume = 1;
        long Deno = 1;

        if (r > n - r) r = n - r;
        for (long i = 1; i <= r; ++i)
        {
            Deno = (Deno * i) % MOD;
            Nume = Nume * (n - i + 1) % MOD;
        }
        return (Nume * inv(Deno)) % MOD;
    }
    public static long Comb2(long n, long r)
    {
        long Nume = 1;
        long Deno = 1;

        if (r > n - r) r = n - r;
        for (long i = 1; i <= r; ++i)
        {
            Deno *= i;
            Nume *= n - i + 1;
        }
        return Nume / Deno;
    }
    public static long inv(long x, int MOD = 1000000007)
    {
        return Power(x, MOD - 2, MOD);
    }
}
public static class Utils
{
    public static T[] sort<T>(this T[] a)
    {
        Array.Sort(a);
        return a;
    }
    public static long popcnt(long n)
    {
        n = (n & 0x55555555) + (n >> 1 & 0x55555555);
        n = (n & 0x33333333) + (n >> 2 & 0x33333333);
        n = (n & 0x0f0f0f0f) + (n >> 4 & 0x0f0f0f0f);
        n = (n & 0x00ff00ff) + (n >> 8 & 0x00ff00ff);
        n = (n & 0x0000ffff) + (n >> 16 & 0x0000ffff);
        return n;
    }
    public static int popcnt(BigInteger a)
    {
        int cnt = 0;
        while (a > 0)
        {
            if ((a & 1) == 1) ++cnt;
            a >>= 1;
        }
        return cnt;
    }
    public static void Swap<T>(ref T A, ref T B)
    {
        T x = A;
        A = B;
        B = x;
    }
    public static int DigitSum(string N)
    {

        int ret = 0;
        for (int i = 0; i < N.Length; ++i) ret += N[i] - '0';
        return ret;
    }
    public static string ConvertBase(char[] Num, int from, int to)
    {
        if (new string(Num) == "0") return "0";
        char[] sample = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".ToCharArray();
        BigInteger ten = 0;
        int power = 0;
        for (int i = Num.Length - 1; i >= 0; --i)
        {
            ten += (BigInteger)(Array.IndexOf(sample, Num[i])) * Power2BI(from, power);
            ++power;
        }
        if (to == 10)
        {
            return ten.ToString();
        }
        var ret = new List<char>();
        while (ten > 0)
        {
            ret.Add(sample[(int)ten % to]);
            ten /= to;
        }
        ret.Reverse();
        return new string(ret.ToArray());
    }
    public static bool NextPermutation<T>(IList<T> lis, Comparison<T> cmp)
    {
        int n = lis.Count;
        int i = n - 1;
        while (i - 1 >= 0)
        {
            if (cmp(lis[i - 1], lis[i]) < 0) break;
            --i;
        }
        if (i == 0) return false;
        int j = i;
        while (j + 1 < n)
        {
            if (cmp(lis[i - 1], lis[j + 1]) > 0) break;
            ++j;
        }
        var _q = lis[j];
        lis[j] = lis[i - 1];
        lis[i - 1] = _q;
        int k = i;
        int l = n - 1;
        while (k < l)
        {
            var _p = lis[k];
            lis[k] = lis[l];
            lis[l] = _p;

            ++k;
            --l;
        }
        return true;
    }
    public static bool NextPermutation<T>(IList<T> lis) => NextPermutation(lis, Comparer<T>.Default.Compare);
}
class Program
{
    static void Main(string[] args)
    {
        var CP = new CP();
        CP.Solve();
    }
}
public static class Output
{

    public static void Put(string a) => Console.WriteLine(a);
    public static void Put(params object[] i) => Put(string.Join(" ", i));
    public static void Put<T>(IEnumerable<T> a) => Put(string.Join(" ", a));
    public static void PutV<T>(IEnumerable<T> a) { foreach (var z in a) Put(z); }
    public static void YN(bool i)
    {
        if (i) Put("Yes");
        else Put("No");
    }
}
public class Input
{
    public static string Str => Console.ReadLine();
    public static bool IsTypeEqual<T, U>() => typeof(T).Equals(typeof(U));
    public static T ConvertType<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    public static T Cast<T>(string s)
    {
        if (IsTypeEqual<T, int>()) return ConvertType<T, int>(int.Parse(s));
        else if (IsTypeEqual<T, long>()) return ConvertType<T, long>(long.Parse(s));
        else if (IsTypeEqual<T, double>()) return ConvertType<T, double>(double.Parse(s));
        else if (IsTypeEqual<T, char>()) return ConvertType<T, char>(char.Parse(s));
        else if (IsTypeEqual<T, BigInteger>()) return ConvertType<T, BigInteger>(BigInteger.Parse(s));
        else if (IsTypeEqual<T, decimal>()) return ConvertType<T, decimal>(decimal.Parse(s));
        else return ConvertType<T, string>(s);
    }
    public static T[] Castarr<T>(string[] s)
    {

        var ret = new T[s.Length];
        int i = 0;
        if (IsTypeEqual<T, char>())
        {
            var list = new List<T>();
            foreach (var t in s)
            {
                foreach (var u in t)
                {
                    list.Add(ConvertType<T, char>(char.Parse(u.ToString())));
                }
            }
            return list.ToArray();
        }
        foreach (var t in s)
        {
            if (IsTypeEqual<T, int>()) ret[i++] = ConvertType<T, int>(int.Parse(t));
            else if (IsTypeEqual<T, long>()) ret[i++] = ConvertType<T, long>(long.Parse(t));
            else if (IsTypeEqual<T, double>()) ret[i++] = ConvertType<T, double>(double.Parse(t));
            else if (IsTypeEqual<T, BigInteger>()) ret[i++] = ConvertType<T, BigInteger>(BigInteger.Parse(t));
            else ret[i++] = ConvertType<T, string>(t);
        }
        return ret;
    }
    Queue<string> q = new Queue<string>();
    void next() { var ss = Str.Split(' '); foreach (var item in ss) q.Enqueue(item); }
    public T cin<T>() { if (!q.Any()) next(); return Cast<T>(q.Dequeue()); }
    public T[] cinarr<T>() { return Castarr<T>(Str.Split(' ')); }
    public T[] cinarr<T>(int n) { var ret = new T[n]; for (int i = 0; i < n; ++i) ret[i] = cin<T>(); return ret; }
    public int Int => cin<int>();
    public long Long => cin<long>();
    public double Double => cin<double>();
    public char Char => cin<char>();
    public string String => cin<string>();
    public BigInteger BI => cin<BigInteger>();
    public int[] Intarr => cinarr<int>();
    public long[] Longarr => cinarr<long>();
    public double[] Doublearr => cinarr<double>();
    public char[] Chararr => cinarr<char>();
    public string[] Stringarr => cinarr<string>();
    public BigInteger[] BIarr => cinarr<BigInteger>();
    public void cin<T>(out T t) { t = cin<T>(); }
    public void mul<T, U>(out T t, out U u) { t = cin<T>(); u = cin<U>(); }
    public void mul<T, U, V>(out T t, out U u, out V v) { t = cin<T>(); u = cin<U>(); v = cin<V>(); }
    public void mul<T, U, V, W>(out T t, out U u, out V v, out W w) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); }
    public void mul<T, U, V, W, X>(out T t, out U u, out V v, out W w, out X x) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); }
    public void mul<T, U, V, W, X, Y>(out T t, out U u, out V v, out W w, out X x, out Y y) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); y = cin<Y>(); }
    public void mul<T, U, V, W, X, Y, Z>(out T t, out U u, out V v, out W w, out X x, out Y y, out Z z) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); y = cin<Y>(); z = cin<Z>(); }
}