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.util.*;

class Main{
    final static long INF = Long.MAX_VALUE / 2;
    final static int MOD = 1_000_000_007;
    final static int SIZE = 1_000_000;
    long[] fac = new long[SIZE];
    long[] inv = new long[SIZE];
    long[] finv = new long[SIZE];
    FastScanner sc = new FastScanner();

    public static void main(String[] args) {
        new Main().solve();
    }

    int[] p;
    long[] c;
    int[] g;
    int t;
    List<ArrayList<Integer>> m;
    boolean[] seen;

    void solve(){

        int n = sc.nextInt();
        long k = sc.nextLong();
        p = new int[n];
        c = new long[n];
        g = new int[n];
        Arrays.fill(g, -1);
        t = 0;
        Map<Integer, Long> num = new HashMap<>(); // 各グループの1周個数
        Map<Integer, Long> point = new HashMap<>(); // 各グループの1周ポイント
        m = new ArrayList<>();
        for(int i = 0; i < n; i++) m.add(new ArrayList<>());
        seen = new boolean[n];

        for(int i = 0; i < n; i++){
            p[i] = sc.nextInt() - 1;
            m.get(i).add(p[i]);
        }

        for(int i = 0; i < n; i++){
            c[i] = sc.nextLong();
        }

        for(int i = 0; i < n; i++){
            Arrays.fill(seen, false);
            if(g[i] != -1) continue;
            dfs(i);
            t++;
        }

        for(int i = 0; i < n; i++){
            if(point.get(g[i]) == null) point.put(g[i], c[i]);
            else point.put(g[i], point.get(g[i]) + c[i]);
            if(num.get(g[i]) == null) num.put(g[i], 1L);
            else num.put(g[i], num.get(g[i]) + 1);
        }

        long max = -INF;

        for(int i = 0; i < n; i++){
            long k_ = k;
            long tmp = 0;
            if(k_ > num.get(g[i]) && point.get(g[i]) > 0){
                tmp += (k_ / num.get(g[i]) - 1) * point.get(g[i]);
                k_ %= num.get(g[i]);
                k_ += num.get(g[i]);
            }else{
                k_ = num.get(g[i]);
            }
            // System.out.println("num " + num.get(g[i]) + " point " + point.get(g[i]) + " k " + k_);
            tmp += sum(p[i], k_, 0, -INF);
            // System.out.println(sum(p[i], Math.min(num.get(g[i]), k), 0, -INF));
            max = Math.max(max, tmp);
            // System.out.println(i + " = " + tmp);
        }

        System.out.println(max);

        // for(int i = 0; i < n; i++) System.out.println("g" + g[i]);

    }

    void dfs(int x){
        if(seen[x]) return;
        seen[x] = true;
        g[x] = t;
        for(int next : m.get(x)){
            dfs(next);
        }
    }

    long sum(int x, long a, long ts, long tm){
        // System.out.println("tm " + tm + " c[x] " + c[x]);
        if(a == 0){
            return tm;
        }else{
            ts += c[x];
            tm = Math.max(tm, ts);
            return sum(p[x], a - 1, ts, tm);
        }
    }

    long gcd(long a, long b){ // return aとbの最大公約数
        if(b == 0){
          return a;
        }
        return gcd(b, a % b);
    }

    long lcm(long a, long b){ // return aとbの最小公倍数
        return a * b / gcd(a, b);
    }

    long inv(long a){ // return aの逆元 (mod MOD)
        return pow(a, MOD - 2);
    }

    long pow(long a, long r){ // return a^r (mod MOD)
        long sum = 1;
        while(r > 0){
            if((r & 1) == 1){ // 2進数表記で末尾1の時
                sum *= a;
                sum %= MOD;
            }
            a *= a;
            a %= MOD;
            r >>= 1;
        }
        return sum;
    }

    long modFact(long n){ // retur n! (mod MOD)
        if(n == 0){
            return 1;
        }
        return n * modFact(n - 1) % MOD;
    }

    long fact(long n){ // return n!
        if(n == 0){
            return 1;
        }
        return n * fact(n - 1);
    }

    void initCOMB(){
        fac[0] = fac[1] = 1;
        inv[1] = 1;
        finv[0] = finv[1] = 1;
        for(int i = 2; i < SIZE; i++){
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }

    long modComb(int n, int r){ // return nCr (先にinitCOMB()必要)
        if(n < r || n < 0 || r < 0) return 0;
        return fac[n] * finv[r] % MOD * finv[n - r] % MOD;
    }

    long comb(long n, long r){ // return nCr
        long num = 1;
        for(long i = 1; i <= r; i++){
            num = num * (n - i + 1) / i;
        }
        return num;
    }

    boolean isPrime(long a){ // aの素数判定
        if(a <= 1) return false;
        for(int i = 2; i * i <= a; i++){
            if(a % i == 0) return false;
        }
        return true;
    }

    int lowerBound(long[] a, long v){ // return 配列a内のv以上の要素の内最低の要素のイテレータ
        int r = a.length;
        int l = -1;
        while(r - l > 1){
            int mid = (r + l) / 2;
            if(a[mid] >= v){
                r = mid;
            }else{
                l = mid;
            }
        }
        return r;
    }

    int upperBound(long[] a, long v){ // return 配列a内のvより大きい要素の内最低の要素のイテレータ
        int r = a.length;
        int l = -1;
        while(r - l > 1){
            int mid = (r + l) / 2;
            if(a[mid] > v){
                r = mid;
            }else{
                l = mid;
            }
        }
        return r;
    }

    String nextPermutation(String s){ // return sの次の順列
        ArrayList<Character> list = new ArrayList<>();
        for(int i = 0; i < s.length(); i++) list.add(s.charAt(i));

        int pivotPos = -1;
        char pivot = 0;
        for(int i = list.size() - 2; i >= 0; i--){
            if(list.get(i) < list.get(i+1)){
    			pivotPos = i;
    			pivot = list.get(i);
    			break;
    		}
    	}

        if(pivotPos == -1 && pivot == 0) return null;

        int L = pivotPos + 1;
        int R = list.size() - 1;
    	int minPos = -1;
    	char min = Character.MAX_VALUE;
    	for(int i = R; i >= L; i--){
    		if(pivot < list.get(i)){
    			if(list.get(i) < min){
    				min = list.get(i);
    				minPos = i;
    			}
    		}
    	}

    	Collections.swap(list, pivotPos, minPos);
    	Collections.sort(list.subList(L, R + 1));

    	StringBuilder sb = new StringBuilder();
    	for(int i=0; i<list.size(); i++) sb.append(list.get(i));

    	return sb.toString();
    }

    boolean nextPermutation(long[] a){
        for(int i = a.length - 1; i > 0; i--){
            if(a[i - 1] < a[i]){
                int swapIndex = find(a[i - 1], a, i, a.length - 1);
                long temp = a[swapIndex];
                a[swapIndex] = a[i - 1];
                a[i - 1] = temp;
                Arrays.sort(a, i, a.length);
                return true;
            }
        }
        return false;
    }

    int find(long dest, long[] a, int s, int e){
        if(s == e){
            return s;
        }
        int m = (s + e + 1) / 2;
        return a[m] <= dest ? find(dest, a, s, m - 1) : find(dest, a, m, e);
    }

    void elimination(int[][] a, int[] b) {
        int n = a.length;
        double f;
        for(int k = 0; k < n - 1; k++){
            for(int i = k + 1; i < n; i++){
                f = - a[i][k] / a[k][k];
                for(int j = k + 1; j < n; j++){
                    a[i][j] += f * a[k][j];
                }
                b[i] += f * b[k];
            }
            for(int i = n - 1; i >= 0; i--){
                for(int j = i + 1; j < n; j++){
                    b[i] -= a[i][j] * b[j];
                }
                b[i] = b[i] / a[i][i];
            }
        }
    }



    class SegmentTree{

        //------------------------------------------------------------
        // 2 * n - 1 : 木全体のノード数
        // i + n - 1 : 配列のi番目が対応するノードの番号
        // 2 * i + 1, 2 * i + 2 : i番目のノードの子ノードの番号
        // (i - 1) / 2 : i番目のノードの親ノードの番号
        //
        // int n = sc.nextInt();
        // long[] a = new long[n];
        // for(int i = 0; i < n; i++) a[i] = sc.nextLong();
        // SegmentTree st = new SegmentTree(a);
        // int l = sc.nextInt() - 1;
        // int r = sc.nextInt() - 1;
        // System.out.println(st.query(l, r));
        //------------------------------------------------------------

        final static long INF = Long.MAX_VALUE / 2;

        // long e = INF; // 単位元
        long e = 0;
        long func(long a, long b){ // 処理
            // return Math.min(a, b);
            return a + b;
        }

        int n; // 配列の要素数を超える最小の2のべき乗
        long[] node;

        SegmentTree(long[] a){
            init(a);
        }

        void init(long[] a){ // 配列aで初期化
            n = 1;
            while(n < a.length){
                n *= 2;
            }
            node = new long[2 * n - 1];
            Arrays.fill(node, e);
            for(int i = 0; i < a.length; i++){
                node[i + n - 1] = a[i];
            }
            for(int i = n - 2; i >= 0; i--){
                node[i] = func(node[2 * i + 1], node[2 * i + 2]);
            }
        }

        void update(int p, long v){ // 配列のp番目をvに変更し、木全体を更新
            p = p + n - 1;
            node[p] = v;
            while(p > 0){
                p = (p - 1) / 2;
                node[p] = func(node[2 * p + 1], node[2 * p + 2]);
            }
        }

        long query(int a, int b){ // 区間[a, b)についてクエリを処理
            return query(a, b, 0, 0, n);
        }

        long query(int a, int b, int k, int l, int r){
            if(r <= a || b <= l) return e;
            if(a <= l && r <= b) return node[k];
            return func(query(a, b, 2 * k + 1, l, (l + r) / 2), query(a, b, 2 * k + 2, (l + r) / 2, r));
        }

    }



    class UnionFindTree{

        //------------------------------------------------------------
        // int n = sc.nextInt();
        // int q = sc.nextInt();
        // UnionFindTree uft = new UnionFindTree(n);
        // List<String> ans = new ArrayList<>();
        // for(int i = 0; i < q; i++){
        //     int p = sc.nextInt(); // 0 : union, 1 : same
        //     if(p == 0){
        //         int a = sc.nextInt() - 1;
        //         int b = sc.nextInt() - 1;
        //         uft.union(a, b);
        //     }else if(p == 1){
        //         int a = sc.nextInt() - 1;
        //         int b = sc.nextInt() - 1;
        //         if(uft.same(a, b)) ans.add("Yes");
        //         else ans.add("No");
        //     }
        // }
        // for(String s : ans){
        //     System.out.println(s);
        // }
        //------------------------------------------------------------

        int[] parent; // インデックスにとノードを対応させ、そのルートノードのインデックスを格納
        int[] rank; // parentと同様に、木の高さを格納

        UnionFindTree(int size){
            parent = new int[size];
            rank = new int[size];

            for(int i = 0; i < size; i++){
                makeSet(i);
            }
        }

        void makeSet(int i){
            parent[i] = i;
            rank[i] = 0;
        }

        void union(int x, int y){
            int xRoot = find(x);
            int yRoot = find(y);

            if(rank[xRoot] > rank[yRoot]){ // xが属する木の方が大きい場合
                parent[yRoot] = xRoot;
            }else if(rank[xRoot] < rank[yRoot]){
                parent[xRoot] = yRoot; // yの親をxに更新
            }else{
                parent[yRoot] = xRoot;
                rank[xRoot]++; // 同じ高さの木がルートの子として着くから大きさ++;
            }
        }

        int find(int i){ // iの属するルートを返す
            if(i != parent[i]){
                parent[i] = find(parent[i]);
            }
            return parent[i];
        }

        boolean same(int x, int y){ // xとyが同じ木に属しているかを返す
            return find(x) == find(y);
        }

    }



}



class Pair implements Comparable<Pair>{
    long a, b;
    public Pair(long i, long j){
        a = i;
        b = j;
    }

    @Override
    public int compareTo(Pair p){
        if(this.b < p.b) return -1;
        else if(this.b > p.b) return 1;
        else return 0;
    }

    @Override
    public String toString(){
        return a + " " + b;
    }
}



class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte(){
        if(ptr < buflen){
            return true;
        }else{
            ptr = 0;
            try{
                buflen = in.read(buffer);
            }catch(IOException e){
                e.printStackTrace();
            }
            if(buflen <= 0){
                return false;
            }
        }
        return true;
    }
    private int readByte(){
        if(hasNextByte()) return buffer[ptr++];
        else return -1;
    }
    private static boolean isPrintableChar(int c){
        return 33 <= c && c <= 126;
    }
    public boolean hasNext(){
        while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        return hasNextByte();
    }
    public String next(){
        if(!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong(){
        if(!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        if(b < '0' || '9' < b){
            throw new NumberFormatException();
        }
        while(true){
            if('0' <= b && b <= '9'){
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt(){
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble(){
        return Double.parseDouble(next());
    }
}