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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.util.stream.LongStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedOutputStream;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        DMovingPiece solver = new DMovingPiece();
        solver.solve(1, in, out);
        out.close();
    }

    static class DMovingPiece {
        static int n;
        static int[][] p;
        static long[][] c;

        public void solve(int testNumber, LightScanner in, LightWriter out) {
            n = in.ints();
            p = new int[n][30];
            c = new long[n][30];
            IntUnionFind uf = new IntUnionFind(n);
            long k = in.longs();
            for (int i = 0; i < n; i++) {
                p[i][0] = in.ints() - 1;
                uf.union(i, p[i][0]);
            }
            long[] c0 = in.longs(n);
            for (int i = 0; i < n; i++) c[i][0] = c0[p[i][0]];
            for (int i = 1; i < 30; i++) {
                for (int j = 0; j < n; j++) {
                    int t = p[j][i - 1];
                    p[j][i] = p[t][i - 1];
                    c[j][i] = c[j][i - 1] + c[t][i - 1];
                }
            }

            long ans = Long.MIN_VALUE;
            for (int i = 0; i < n; i++) {
                ans = Math.max(ans, sum(i, k));
                for (int j = 1; j <= uf.size(i); j++) {
                    ans = Math.max(ans, sum(i, j));
                    ans = Math.max(ans, sum(i, k - j));
                }
            }
            out.ans(ans).ln();
        }

        private static long sum(int now, long k) {
            if (k <= 0) return Long.MIN_VALUE;
            long res = 0;
            for (int j = 29; j >= 0; j--) {
                if (((1L << j) & k) == 0) continue;
                res += c[now][j];
                now = p[now][j];
            }
            return res;
        }

    }

    static final class IntUnionFind {
        private int groups;
        private final int[] nodes;
        private final int[] rank;

        public IntUnionFind(int n) {
            groups = n;
            nodes = new int[n];
            Arrays.fill(nodes, -1);
            rank = new int[n];
        }

        public int find(int i) {
            int ans = nodes[i];
            if (ans < 0) {
                return i;
            } else {
                return nodes[i] = find(ans);
            }
        }

        public int size(int i) {
            return -nodes[find(i)];
        }

        public boolean union(int x, int y) {
            x = find(x);
            y = find(y);
            if (x == y) {
                return false;
            } else if (rank[x] < rank[y]) {
                nodes[y] += nodes[x];
                nodes[x] = y;
            } else if (rank[x] == rank[y]) {
                rank[x]++;
                nodes[x] += nodes[y];
                nodes[y] = x;
            } else {
                nodes[x] += nodes[y];
                nodes[y] = x;
            }
            groups--;
            return true;
        }

    }

    static class LightScanner implements AutoCloseable {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

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

        public int ints() {
            return Integer.parseInt(string());
        }

        public long longs() {
            return Long.parseLong(string());
        }

        public long[] longs(int length) {
            return IntStream.range(0, length).mapToLong(x -> longs()).toArray();
        }

        public void close() {
            try {
                this.reader.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new OutputStreamWriter(new BufferedOutputStream(out), Charset.defaultCharset()));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(long l) {
            return ans(Long.toString(l));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }
}