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.*;import java.math.*;
public class Main
{
	static long mod=1000000007l;
    static int max=Integer.MAX_VALUE,min=Integer.MIN_VALUE;
    static long maxl=Long.MAX_VALUE,minl=Long.MIN_VALUE;
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static StringBuilder sb;
    
    static public void main(String[] args)throws Exception
    {
    	st=new StringTokenizer(br.readLine());
    	int n=i();
    	int k=i();
    	int p[]=ari(n);
    	int c[]=ari(n);
    	long m=minl;
    	for(int x=1;x<=n;x++)
    	{
    		int y=x;
    		long cc=0l;
    		boolean b[]=new boolean[n+1];
    		int pp=k;
    		long kk=minl;
    		long ll=0l;
    		//pl(x);
    		LinkedList<Integer> l=new LinkedList<>();
    		while(!b[y])
    		{
    			b[y]=true;
    			y=p[y-1];
    			cc+=c[y-1];
    			//pl(cc+ " "+(y-1));
    			ll+=c[y-1];
    			kk=max(kk,ll);
    			l.add(c[y-1]);
    			pp--;
    			if(pp==0)break;
    			//pl(cc);
    		}
    		if(pp==0)m=max(cc,max(m,kk));
    		else
    		{
    			int mo=k%l.size();
    			long q=cc;
    			cc*=(k/l.size());
    			int i=0;
    			long aa=cc;
    			long bb=cc;
    			if(mo!=0)
    			{
	    			for(int e:l)
	    			{
	    				i++;
	    				bb+=e;
	    				
	    				aa=max(aa,bb);
	    				if(i==mo)break;
	    			}
	    			pl(x+" "+aa);
    			}
    			else
    			{
    				aa-=q;
    				bb-=q;
    				mo=n;
    				for(int e:l)
	    			{
	    				i++;
	    				bb+=e;
	    				
	    				aa=max(aa,bb);
	    				if(i==mo)break;
	    			}
	    	//		pl(x+" "+aa);
    			}
    			m=max(aa,max(m,kk));
    		}
    	}
    	pl(m);
    }
    
    static void s(String s){sb.append(s);}
    static void s(int s){sb.append(s);}
    static void s(long s){sb.append(s);}
    static void s(char s){sb.append(s);}
    static void s(double s){sb.append(s);}
    static void ss(){sb.append(' ');}
    static void sl(String s){sb.append(s);sb.append("\n");}
    static void sl(int s){sb.append(s);sb.append("\n");}
    static void sl(long s){sb.append(s);sb.append("\n");}
    static void sl(char s){sb.append(s);sb.append("\n");}
    static void sl(double s){sb.append(s);sb.append("\n");}
    static void sl(){sb.append("\n");}
    static int max(int a,int b){return a>b?a:b;}
    static int min(int a,int b){return a<b?a:b;}
    static int abs(int a){return Math.abs(a);}
    static long max(long a,long b){return a>b?a:b;}
    static long min(long a,long b){return a<b?a:b;}
    static long abs(long a){return Math.abs(a);}
    static int sq(int a){return (int)Math.sqrt(a);}
    static long sq(long a){return (long)Math.sqrt(a);}
    static int gcd(int a,int b){return b==0?a:gcd(b,a%b);}
    static boolean pa(String s,int i,int j)
    {
    	while(i<j)if(s.charAt(i++)!=s.charAt(j--))return false;
    	return true;
    }
    static int ncr(int n,int c,long m)
    {
        long a=1l;
        for(int x=n-c+1;x<=n;x++)a=((a*x)%m);
        long b=1l;
        for(int x=2;x<=c;x++)b=((b*x)%m);
        return (int)((a*(mul((int)b,m-2,m)%m))%m);
    }
    static boolean[] sieve(int n)
    {
        boolean bo[]=new boolean[n+1];
        bo[0]=true;bo[1]=true;
        for(int x=4;x<=n;x+=2)bo[x]=true;
        for(int x=3;x*x<=n;x+=2)if(!bo[x])for(int y=x*x;y<=n;y+=x)bo[y]=true;
        return bo;
    }
    static int[] fac(int n)
    {
        int bo[]=new int[n+1];
        for(int x=1;x<=n;x++)for(int y=x;y<=n;y+=x)bo[y]++;
        return bo;
    }
    static long mul(long a,long b,long m) 
    {
        long r=1l;
        a%=m;  
        while(b>0)
        {
            if((b&1)==1)r=(r*a)%m; 
            b>>=1;
            a=(a*a)%m;  
        } 
        return r; 
    }
    static int i()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    static long l()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    static String s()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    static double d()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Double.parseDouble(st.nextToken());
    }
    static void p(Object p){System.out.print(p);}
    static void p(String p){System.out.print(p);}
    static void p(int p){System.out.print(p);}
    static void p(double p){System.out.print(p);}
    static void p(long p){System.out.print(p);}
    static void p(char p){System.out.print(p);}
    static void p(boolean p){System.out.print(p);}
    static void pl(Object p){System.out.println(p);}
    static void pl(String p){System.out.println(p);}
    static void pl(int p){System.out.println(p);}
    static void pl(char p){System.out.println(p);}
    static void pl(double p){System.out.println(p);}
    static void pl(long p){System.out.println(p);}
    static void pl(boolean p){System.out.println(p);}
    static void pl(){System.out.println();}
    static int[] ari(int n)throws IOException
    {
        int ar[]=new int[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Integer.parseInt(st.nextToken());
        return ar;
    }
    static int[][] ari(int n,int m)throws IOException
    {
        int ar[][]=new int[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Integer.parseInt(st.nextToken());
        }
        return ar;
    }
    static long[] arl(int n)throws IOException
    {
        long ar[]=new long[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=Long.parseLong(st.nextToken());
        return ar;
    }
    static long[][] arl(int n,int m)throws IOException
    {
        long ar[][]=new long[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Long.parseLong(st.nextToken());
        }
        return ar;
    }
    static String[] ars(int n)throws IOException
    {
        String ar[]=new String[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=st.nextToken();
        return ar;
    }
    static double[] ard(int n)throws IOException
    {
        double ar[]=new double[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Double.parseDouble(st.nextToken());
        return ar;
    }
    static double[][] ard(int n,int m)throws IOException
    {
        double ar[][]=new double[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Double.parseDouble(st.nextToken());
        }
        return ar;
    }
    static char[] arc(int n)throws IOException
    {
        char ar[]=new char[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=st.nextToken().charAt(0);
        return ar;
    }
    static char[][] arc(int n,int m)throws IOException
    {
        char ar[][]=new char[n][m];
        for(int x=0;x<n;x++)
        {
            String s=br.readLine();
            for(int y=0;y<m;y++)ar[x][y]=s.charAt(y);
        }
        return ar;
    }
    static void p(int ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(int a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(int ar[][])
    {
    	StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(int a[]:ar)
        {
            for(int aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(long ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(long a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(long ar[][])
    {
    	StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(long a[]:ar)
        {
            for(long aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(String ar[])
    {
    	int c=0;
    	for(String s:ar)c+=s.length()+1;
        StringBuilder sb=new StringBuilder(c);
        for(String a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(double ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(double a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(double ar[][])
    {
    	StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(double a[]:ar)
        {
            for(double aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(char ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(char aa:ar)
        {
        	sb.append(aa);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(char ar[][])
    {
        StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(char a[]:ar)
        {
            for(char aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
}