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: Wrong Answer)

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {

    static class Task {

        private static final int MOD = 998244353;

        private long gcd(long m, long n) {
            if (n == 0) {
                return m;
            }
            return gcd(n, m % n);
        }

        // 快速幂
        public int pow(long x, long n, int mod) {
            long res = 1;
            x %= mod;
            while (n > 0) {
                if ((n & 1) == 1) {
                    res = res * x % mod;
                }

                x = x * x % mod;
                n >>>= 1;
            }
            return (int) res % mod;
        }


        int[] h,to,next,wt,fa;int ct = 0;
        void init(int n ,int m){
            h = new int[n]; Arrays.fill(h,-1);
            to = new int[m*2+2];
            wt = new int[m*2+2];
            next = new int[m*2+2];
            fa = new int[n];Arrays.fill(fa,-1);
            ct = 0;
        }

        void add(int u,int v,int w){
            to[++ct] = v;
            next[ct] = h[u];
            wt[ct] = w;
            h[u] = ct;
        }


        long[][] mult(long a[][],long b[][], long mod){
            int l1 = a.length;
            int l2 = b.length;
            int l3 = b[0].length;
            long r[][] = new long[l1][l3];
            for(int i=0;i<l1;++i){
                for(int j=0;j<l2;++j){
                    for(int k=0;k<l3;++k){
                        r[i][k] = (r[i][k] + a[i][j] * b[j][k])%mod;
                    }
                }
            }
            return r;
        }

        long[][] ones(int len){
            long r[][] = new long[len][len];
            for(int i=0;i<len;++i){
                r[i][i] = 1L;
            }
            return r;
        }

        long[][] quick(long a[][], int times,long mod){
            int len = a.length;
            long ans[][] = ones(len);

            while(times>0){
                if((times&1)==1) {
                    ans = mult(ans, a, mod);
                }
                a = mult(a, a, mod);
                times >>= 1;
            }

            return ans;
        }


        public void solve(int testNumber, InputReader in, PrintWriter out) {

            int n  =in.nextInt();
            int k  =in.nextInt();
            int p[] = in.nextArray(n);
            long c[] = new long[n];
            for(int i=0;i<n;++i){
                c[i] = in.nextLong();
            }
            long r = Long.MIN_VALUE;
            for(int j=0;j<n;++j){
                int vis[] = new int[n];
                long sum[] = new long[n+1];

                long s = 0;
                int go  = 0;
                int pos = j;
                while(go<k){
                    int to = p[pos]-1;
                    if(vis[to]!=0){

                        int z = go-vis[to]+1;
                        long tot = s-sum[vis[to]]+c[to];

                        if(tot>=0) {
                            int d = (k - go) / z;

                            s += (long) d * tot;
                            go += z * d;

                            int sy = k - go;
                            pos = to;
                            r = Math.max(r, s);
                            for (int jj = 0; jj < sy; ++jj) {
                                s += c[pos];
                                r = Math.max(r, s);
                                pos = p[pos] - 1;

                            }


                            break;
                        }else{

                            long ss = s;
                            pos = to;
                            for (int jj = 0; jj < Math.min(k-go,z); ++jj) {
                                ss += c[pos];
                                r = Math.max(r, ss);
                                pos = p[pos] - 1;
                            }

                           
                            break;



                        }
                    }else{
                        s += c[to];
                        vis[to] = ++go;
                        sum[go] = s;
                        r = Math.max(r, s);
                        pos = to;
                    }
                }

            }
            out.println(r);



        }
    }

    private static void sort(double[] arr) {
        Double[] objArr = Arrays.stream(arr).boxed().toArray(Double[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(int[] arr) {
        Integer[] objArr = Arrays.stream(arr).boxed().toArray(Integer[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(long[] arr) {
        Long[] objArr = Arrays.stream(arr).boxed().toArray(Long[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task task = new Task();
        task.solve(1, in, out);
        out.close();
    }

    public static void main(String[] args) {
        new Thread(null, () -> solve(), "1", 1 << 26).start();
    }

    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public int[] nextArray(int n){
            int res[]  = new int[n];
            for(int i=0;i<n;++i){
                res[i] = nextInt();
            }
            return res;
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }

}