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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
	static final long MOD=1000000007;//998244353;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		long K=sc.nextLong();
		int[] P=sc.nextIntArray(N);
		long[] C=sc.nextLongArray(N);
		UnionFindTree unionFindTree=new UnionFindTree(N);
		for (int i = 0; i < P.length; i++) {
			unionFindTree.union(i, P[i]-1, 0);
		}
		if (K<=N*2) {
			long max=Long.MIN_VALUE;
			for (int i = 0; i < C.length; i++) {
				int now=i;
				long sum=0;
				for (int j = 0; j < K; j++) {
					now=P[now]-1;
					sum+=C[now];
					max=Math.max(max, sum);
				}
			}
			System.out.println(max);
		}else {
			long max=Long.MIN_VALUE;
			long[] cycleweight=new long[N];
			for (int i = 0; i < C.length; i++) {
				int now=i;
				long sum=0;
				for (int j = 0; j < unionFindTree.size(i); j++) {
					now=P[now]-1;
					sum+=C[now];
				}
				cycleweight[i]=sum;
			}
			for (int i = 0; i < C.length; i++) {
				int now=i;
				long sum=0;
				if (cycleweight[i]>=0) {
					sum=(K/(long)unionFindTree.size(i)-1)*cycleweight[i];
				}else {
					sum=0;
				}
				if (sum>0) {
					max=Math.max(max, sum);
					for (int j = 0; j < unionFindTree.size(i)+K%(long)unionFindTree.size(i); j++) {
						now=P[now]-1;
						sum+=C[now];
						max=Math.max(max, sum);
					}
				}else {
					for (int j = 0; j < unionFindTree.size(i); j++) {
						now=P[now]-1;
						sum+=C[now];
						max=Math.max(max, sum);
					}
				}
			}
			System.out.println(max);
		}
 	}
	static class UnionFindTree{
    	int[] par;
    	int[] rank;
    	int[] size;
    	int[] diff_weight;
    	int arraysize;
    	public UnionFindTree(int n) {
    		this.par=new int[n];
    		this.rank=new int[n];
    		this.size=new int[n];
    		this.diff_weight=new int[n];
    		arraysize=n;
    		for (int i = 0; i < arraysize; i++) {
				set(i);
			}
    	}
    	public void set(int i) {
    		par[i]=i;
    		rank[i]=0;
    		size[i]=1;
    		diff_weight[i]=0;
    	}
    	public void union(int x,int y,int w) {
    		w += weight(x); 
    		w -= weight(y);
    		int rootx=find(x);
    		int rooty=find(y);
    		if (rootx==rooty) {
				return;
			}
    		if (rank[rootx]>rank[rooty]) {
				par[rooty]=rootx;
				diff_weight[rooty] = w;
				size[rootx]+=size[rooty];
			}
    		else if (rank[rootx]<rank[rooty]) {
				par[rootx]=rooty;
				w=-w;
				diff_weight[rootx] = w;
				size[rooty]+=size[rootx];
			}
    		else {
    			par[rooty]=rootx;
    			diff_weight[rooty] = w;
    			rank[rootx]++;
				size[rootx]+=size[rooty];
			}
    	}
    	public int find(int x) {
    		if(par[x] == x) return x;
    		int r = find(par[x]);
    		diff_weight[x] += diff_weight[par[x]];
    		return par[x] = r;
    	}
    	public int weight(int x) {
    		find(x);
    		return diff_weight[x];
    	}
    	public int size(int i) {
            return size[find(i)];
        }
    	public int diff(int x, int y) {
    		return weight(y) - weight(x);
    	}
    	public boolean same(int x, int y) {
            return find(x) == find(y);
        }
    }
	static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}