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 static java.lang.Math.max;

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;

public class Main {
    void solve(MyScanner in, MyWriter out) {
        int n = in.nextInt();
        long k = in.nextLong();
        int[] p = decrement(in.nextIntArray(n));
        long[] c = in.nextLongArray(n);
        long ans = Long.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            List<Integer> path = new ArrayList<>();
            boolean[] visited = new boolean[n];
            for (int j = p[i]; !visited[j]; j = p[j]) {
                visited[j] = true;
                path.add(j);
            }
            long s = 0;
            for (int j = 0; j < k && j < path.size(); j++) {
                s += c[path.get(j)];
                ans = max(ans, s);
            }
            if (s > 0 && k > path.size()) {
                long cycles = (k - path.size()) / path.size();
                if (cycles > 0)
                    cycles--;
                s += s * cycles;
                ans = max(ans, s);

                for (long j = path.size() + cycles * path.size(); j < k; j++) {
                    s += c[path.get((int)(j % path.size()))];
                    ans = max(ans, s);
                }
            }
        }
        out.println(ans);
    }
    private static int[] decrement(int[] a) {
        for (int i = 0; i < a.length; i++) {
            a[i]--;
        }
        return a;
    }
    public static void main(String[] args) {
        MyWriter w = new MyWriter(System.out);
        new Main().solve(new MyScanner(System.in), w);
        w.flush();
    }
    static final class MyScanner {
        static final int BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer = new byte[BUFFER_SIZE];
        private int point;
        private int readLength;

        MyScanner(InputStream in) {
            this.in = in;
        }
        private int readByte() {
            if (point < readLength) {
                int result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1) {
                return -1;
            }
            point = 1;
            return buffer[0];
        }
        private static boolean isVisibleChar(int c) {
            return 33 <= c && c <= 126;
        }
        char nextChar() {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            return (char)c;
        }
        String next() {
            return next(16);
        }
        String next(int n) {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            StringBuilder b = new StringBuilder(n);
            do {
                b.append((char)c);
                c = readByte();
            } while (c != -1 && isVisibleChar(c));
            return b.toString();
        }
        long nextLong() {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            boolean minus = false;
            long limit = -Long.MAX_VALUE;
            if (c == '-') {
                minus = true;
                limit = Long.MIN_VALUE;
                c = readByte();
            }
            long n = 0L;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                if (n < limit / 10L) {
                    throw new InputMismatchException();
                }
                n *= 10L;
                int digit = c - '0';
                if (n < limit + digit) {
                    throw new InputMismatchException();
                }
                n -= digit;
                c = readByte();
            } while (c != -1 && isVisibleChar(c));
            return minus ? n : -n;
        }
        int nextInt() {
            long n = nextLong();
            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE) {
                throw new InputMismatchException();
            }
            return (int)n;
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt();
            }
            return result;
        }
        long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong();
            }
            return result;
        }
        char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextChar();
            }
            return result;
        }
        char[][] next2dCharArray(int h, int w) {
            char[][] result = new char[h][w];
            for (int i = 0; i < h; i++) {
                for (int j = 0; j < w; j++) {
                    result[i][j] = nextChar();
                }
            }
            return result;
        }
        int[][] nextVerticalIntArrays(int arrayCount, int arrayLength) {
            int[][] result = new int[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextInt();
                }
            }
            return result;
        }
        long[][] nextVerticalLongArrays(int arrayCount, int arrayLength) {
            long[][] result = new long[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextLong();
                }
            }
            return result;
        }
        char[][] nextVerticalCharArrays(int arrayCount, int arrayLength) {
            char[][] result = new char[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextChar();
                }
            }
            return result;
        }
        List<String> nextStringList(int n) {
            var result = new ArrayList<String>(n);
            for (int i = 0; i < n; i++) {
                result.add(next());
            }
            return result;
        }
        List<Integer> nextIntList(int n) {
            var result = new ArrayList<Integer>(n);
            for (int i = 0; i < n; i++) {
                result.add(nextInt());
            }
            return result;
        }
        List<Long> nextLongList(int n) {
            var result = new ArrayList<Long>(n);
            for (int i = 0; i < n; i++) {
                result.add(nextLong());
            }
            return result;
        }
    }
    static final class MyWriter extends PrintWriter {
        MyWriter(OutputStream out) {
            super(out);
        }
        void println(int[] x) {
            println(x, " ");
        }
        void println(int[] x, String delimiter) {
            if (x.length > 0) {
                print(x[0]);
                for (int i = 1; i < x.length; i++) {
                    print(delimiter);
                    print(x[i]);
                }
            }
            println();
        }
        void println(long[] x) {
            println(x, " ");
        }
        void println(long[] x, String delimiter) {
            if (x.length > 0) {
                print(x[0]);
                for (int i = 1; i < x.length; i++) {
                    print(delimiter);
                    print(x[i]);
                }
            }
            println();
        }
        void println(Iterable<?> iterable) {
            println(iterable, " ");
        }
        void println(Iterable<?> iterable, String delimiter) {
            Iterator<?> i = iterable.iterator();
            if (i.hasNext()) {
                print(i.next());
                while (i.hasNext()) {
                    print(delimiter);
                    print(i.next());
                }
            }
            println();
        }
        void printLines(int[] x) {
            println(x, System.lineSeparator());
        }
        void printLines(long[] x) {
            println(x, System.lineSeparator());
        }
        void printLines(Iterable<?> iterable) {
            println(iterable, System.lineSeparator());
        }
    }
}