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 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main{
	static long inf=(long)1e16;
	static long maxSubstringSum(ArrayList<Integer>cycle,int maxSubLen) {
		int cycleLen=cycle.size();
		long ans=-inf;
		long curSum=0;
		int i=0,j=0;
		while(j<cycleLen) {
			if(j<i) {
				j++;
				continue;
			}
			if(curSum<0 || j-i>=maxSubLen) {
				curSum-=cycle.get(i);
				i++;
				continue;
			}
			curSum+=cycle.get(j++);
			ans=Math.max(ans, curSum);
		}
		
		return ans;
	}
	static long solve(int i,boolean[]v,int[]c,int[]p,int k) {
		long ans=-inf;
		LinkedList<Integer>all=new LinkedList<Integer>();
		
		long sumCycle=0;
		int cur=i;
		while(!v[cur]) {
			v[cur]=true;
			all.add(cur);
			cur=p[cur];
		}
		LinkedList<Integer>nonCycle=new LinkedList<Integer>();
		while(all.peek()!=cur) {
			nonCycle.add(all.poll());
		}
		
		
		ArrayList<Integer>cycle=new ArrayList<Integer>();
		while(!all.isEmpty()) {
			int o=c[all.poll()];
			sumCycle+=o;
			cycle.add(o);
		}
		int cycleLen=cycle.size();
		long[]bestPref=new long[cycleLen+1];
		long curSum=0;
		for(int j=0;j<cycleLen;j++) {
			cycle.add(cycle.get(j));
			curSum+=cycle.get(j);
			bestPref[j+1]=Math.max(bestPref[j], curSum);
		}
		
		//no cycles
		ans=Math.max(ans, maxSubstringSum(cycle, Math.min(k, cycleLen)));
		
		//take cycles
		ans=Math.max(ans, sumCycle*(k/cycleLen)+maxSubstringSum(cycle, k%cycleLen));
		
		int suff=0;long sum=0;
		
		while(!nonCycle.isEmpty() && k>=suff+1) {
			suff++;
			sum+=nonCycle.pollLast();
			
			//no cycles
			ans=Math.max(ans, sum+bestPref[Math.min(k-suff, cycleLen)]);
			
			//take cycles
			ans=Math.max(ans, sum+sumCycle*((k-suff)/cycleLen)+bestPref[(k-suff)%cycleLen]);
		}
		return ans;
	}
	static void main() throws Exception{
		int n=sc.nextInt(),k=sc.nextInt();
		int[]p=sc.intArr(n),c=sc.intArr(n);
		for(int i=0;i<n;i++)p[i]--;
		int[]inDeg=new int[n];
		for(int i=0;i<n;i++) {
			inDeg[p[i]]++;
		}
		LinkedList<Integer>l=new LinkedList<Integer>();
		for(int i=0;i<n;i++) {
			if(inDeg[i]==0) {
				l.add(i);
			}
		}
		long ans=-inf;
		boolean[]v=new boolean[n];
		while(!l.isEmpty()) {
			int i=l.poll();
			ans=Math.max(ans, solve(i, v, c, p, k));
		}
		
		for(int i=0;i<n;i++) {
			if(v[i])continue;
			ans=Math.max(ans, solve(i, v, c, p, k));
		}
		
		pw.println(ans);
	}
	public static void main(String[] args) throws Exception{
		sc=new MScanner(System.in);
		pw = new PrintWriter(System.out);
		int tc=1;
//		tc=sc.nextInt();
		while(tc-->0)
			main();
		pw.flush();
	}
	static PrintWriter pw;
	static MScanner  sc;
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] longArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	static void shuffle(int[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			int tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
	static void shuffle(long[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			long tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
}