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.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class D { public static void Main() => (new Solver()).Solve(); }

public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		long K = GetLong();
		var P = Range(0, N).Select(_ => GetLong() - 1).ToArray();
		var C = GetLongs(N);

		var uf = new UnionFind(N);
		var sum = new long[N];
		for(long i = 0; i < N; i++)
		{
			if(!uf.IsSame(i, P[i]))
			{
				var rx = uf.Root(i);
				var ry = uf.Root(P[i]);
				uf.Unite(i, P[i]);
				sum[uf.Root(i)] = sum[rx] + sum[ry];
			}
			sum[uf.Root(i)] += C[P[i]];
		}

		long sim(long v, long k)
		{
			if(k == 0)
				return 0;
				
			long max = long.MinValue;
			long res = 0;
			for(long i = 0; i < k; i++)
			{
				v = P[v];
				res += C[v];
				chmax(ref max, res);
			}
			return max;
		}

		long ans = long.MinValue;
		for(long i = 0; i < N; i++)
		{
			long r = uf.Root(i);
			long s = uf.Size(i);
			if(sum[r] >= 0)
			{
				if(K > s)
					chmax(ref ans, ((K - s)/ s) * sum[r] + sim(i, s + (K - s) % s));
				else
					chmax(ref ans, sim(i, K));
			}
			else
				chmax(ref ans, sim(i, Min(K, s)));
		}

		WriteLine(ans);
	}
}

public class UnionFind
{
	private long[] par = null;
	private long[] rank = null;
	private long[] size = null;
	
	public long Size(long x) => size[Root(x)];
	public bool IsSame(long x, long y) => (Root(x) == Root(y));

	public UnionFind(long n)
	{
		par = new long[n];
		rank = new long[n];
		size = new long[n];
		for(long i = 0; i < n; i++)
		{
			par[i] = i;
			rank[i] = 0;
			size[i] = 1;
		}
	}

	public long Root(long x)
	{
		if(par[x] == x)
			return x;

		long r = Root(par[x]);
		par[x] = r;
		return r;
	}
	
	public bool Unite(long x, long y)
	{
		long rx = Root(x);
		long ry = Root(y);
		if(rx == ry)
			return false;
		
		if(rank[rx] < rank[ry])
		{
			long tmp = rx;
			rx = ry;
			ry = tmp;
		}
		else if(rank[rx] == rank[ry])
			rank[rx]++;

		par[ry] = rx;
		size[rx] = size[rx] + size[ry];
		return true;
	}
}

public static class MyIO
{
	private static string[] args = new string[0];
	private static int cnt = 0;
	private static IEnumerable<string> getArgs(long N) => Range(0, N).Select(_ => getArg());
	private static string getArg()
	{
		if(cnt == args.Length) { args = Console.ReadLine().Split(); cnt = 0; }
		return args[cnt++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => getArgs(N).Select(int.Parse).ToArray();
	public static long[] GetLongs(long N) => getArgs(N).Select(long.Parse).ToArray();
	public static double[] GetDoubles(long N) => getArgs(N).Select(double.Parse).ToArray();
	public static decimal[] GetDecimals(long N) => getArgs(N).Select(decimal.Parse).ToArray();
	public static string[] GetStrings(long N) => getArgs(N).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) < 0) x = y; }
	public static void chmin<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) > 0)	x = y; }
	public static void swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }
	public static long rightShift(long x, long y) => (x >> (int)y);
	public static long leftShift(long x, long y) => (x << (int)y);
	public static bool contains(long s, long x) => (rightShift(s, x) & 1L) == 1L;
	public static long gcd(long x, long y) => (y == 0) ? x : gcd(y, x % y);
	public static long lcm(long x, long y) => (x / gcd(x,y)) * y;	
	public static IEnumerable<int> Range(long start, long count) => Enumerable.Range((int)start, (int)count);
	public static void Sort(this List<string> source) => source.Sort(StringComparer.Ordinal);
}