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.*;
public class Main {
 
  public static void main(String[] args) { 
        solve();
      out.close();
  }

  private static void solve() {
      int n = sc.nextInt();
      int k = sc.nextInt();
      int[] ps = new int[n+1];
      for(int i = 1; i <= n; i++)
        ps[i] = sc.nextInt();
      int[] cs = new int[n+1];
      for(int i = 1; i <= n; i++)
        cs[i] = sc.nextInt();

      long max = Long.MIN_VALUE;
      for(int i = 1; i <= n; i++) {
        int startIdx = ps[i];
        long sum = 0;
        List<Integer> list = new ArrayList<>();
        int cnt = 1;
        while(startIdx != i && cnt <= k) {
          list.add(cs[startIdx]);
          sum += cs[startIdx];
          startIdx = ps[startIdx];
          cnt++;
        }
        list.add(cs[i]);
        sum += cs[i];


        long res = 0;

        if(k > list.size()) {
          int times = k / list.size();
          int restT = k % list.size();
          if(sum > 0) {
            res = times * (long)sum;
            sum = 0;
            long subMax = Integer.MIN_VALUE;
            for(int j = 0; j < restT; j++) {
              sum += list.get(j);
              subMax = Math.max(subMax, sum);
            }
            res += subMax;
          } else {
            sum = 0;
            long subMax = Integer.MIN_VALUE;
            for(int j = 0; j < restT; j++) {
              sum += list.get(j);
              subMax = Math.max(subMax, sum);
            }
            res = subMax;
          }
        } else {
          sum = 0;
          long subMax = Integer.MIN_VALUE;
          for(int j = 0; j < k; j++) {
            sum += list.get(j);
            subMax = Math.max(subMax, sum);
          }
          res = subMax;
        }
        max = Math.max(max, res);
      }
      out.println(max);
  }

  private static String mkArr(int[] arr) {
    StringBuilder sb = new StringBuilder();
    for(int a : arr) {
      sb.append(a + " ");
    }
    return sb.toString();
  }

  private static String mkList(List<Integer> arr) {
    StringBuilder sb = new StringBuilder();
    for(int a : arr) {
      sb.append(a + " ");
    }
    return sb.toString();
  }
  
  static int mod = 1_000_000_007;

    private static long C(int n, int k) {
    long res1 = factor(n-k+1, n);
    long res2 = factor(1, k);
    long reverse = reverse(res2);
    return (res1 * reverse) % mod;
  }

  private static long reverse(long a) {
    return powMod(a, mod - 2);
  }

  private static long factor(int left, int right){
    long res = 1;
    for(int i = left; i <= right; i++)
      res = (res * i) % mod;
    return res;
  }

  public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
 
  public static FastScanner sc = new FastScanner();

  static class FastScanner {
      BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
      StringTokenizer st=new StringTokenizer("");
      String next() {
        while (!st.hasMoreTokens())
          try {
            st=new StringTokenizer(br.readLine());
          } catch (IOException e) {
            e.printStackTrace();
          }
        return st.nextToken();
      }
      
      int nextInt() {
        return Integer.parseInt(next());
      }
      int[] readArray(int n) {
        int[] a=new int[n];
        for (int i=0; i<n; i++) a[i]=nextInt();
        return a;
      }
      long nextLong() {
        return Long.parseLong(next());
      }
  }

  static long pow(long a, long N) {
    if (N == 0) return 1;
    else if (N == 1) return a;
    else {
      long R = pow(a,N/2);
      if (N % 2 == 0) {
        return R*R;
      }
      else {
        return R*R*a;
      }
    }
  }
   
  static long powMod(long a, long N) {
    if (N == 0) return 1;
    else if (N == 1) return a % mod;
    else {
      long R = powMod(a,N/2) % mod;
      R = (R * R) % mod;
      if (N % 2 == 1) {
        R = (R * a) % mod;
      }
        return R % mod;
    }
  }

  static void mergeSort(int[] A){ // low to hi sort, single array only
    int n = A.length;
    if (n < 2) return;
    int[] l = new int[n/2];
    int[] r = new int[n - n/2];

    for (int i = 0; i < n/2; i++){
      l[i] = A[i];
    }

    for (int j = n/2; j < n; j++){
      r[j-n/2] = A[j];
    }

    mergeSort(l);
    mergeSort(r);
    merge(l, r, A);
  }
 
  static void merge(int[] l, int[] r, int[] a){
    int i = 0, j = 0, k = 0;
    while (i < l.length && j < r.length && k < a.length){
      if (l[i] < r[j]){
        a[k] = l[i];
        i++;
      }
      else{
        a[k] = r[j];
        j++;
      }
      k++;
    }
    while (i < l.length){
      a[k] = l[i];
      i++;
      k++;
    }

    while (j < r.length){
      a[k] = r[j];
      j++;
      k++;
    }
  }

  private static class Edge {
    int src;
    int dest;
    int weight;
    public Edge(int s, int d, int w) {
      this.src = s;
      this.dest = d;
      this.weight = w;
    }
  }
  private static int[] prim(Map<Integer, List<Edge>> graph) {
      int n = graph.size(); // number of the nodes
      Edge[] edges = new Edge[n];
      for(int i = 0; i < n; i++)
        edges[i] = new Edge(-1, i, Integer.MAX_VALUE);
      edges[0].weight = 0;

      int[] parents = new int[n];
      parents[0] = -1;

      TreeSet<Edge> treeSet = new TreeSet<>((a, b) -> a.weight - b.weight);
      treeSet.add(edges[0]);

      boolean[] visited = new boolean[n];
      while(treeSet.size() > 0) {
        Edge e = treeSet.pollFirst();
        visited[e.dest] = true;
        for(Edge child : graph.get(e.dest)) {
          if(visited[child.dest]) continue;
          if(edges[child.dest].weight > child.weight) {
            treeSet.remove(edges[child.dest]);
            edges[child.dest].weight = child.weight;
            treeSet.add(edges[child.dest]);
            parents[child.dest] = e.dest;
          }
        }
      }
      return parents;
  }

  private static void testDijkstr() {
    Map<Integer, List<Edge>> graph = new HashMap<>();
    for(int i = 0; i < 9; i++)
      graph.put(i, new ArrayList<>());
    addEdge(0, 1, 4 , graph);
    addEdge(0, 7, 8 , graph);
    addEdge(1, 2, 8 , graph);
    addEdge(1, 7, 11, graph);
    addEdge(2, 3, 7 , graph);
    addEdge(2, 8, 2 , graph);
    addEdge(2, 5, 4 , graph);
    addEdge(3, 4, 9 , graph);
    addEdge(3, 5, 14, graph);
    addEdge(4, 5, 10, graph);
    addEdge(5, 6, 2 , graph);
    addEdge(6, 7, 1 , graph);
    addEdge(6, 8, 6 , graph);
    addEdge(7, 8, 7 , graph);
    Edge[] es = dijkstra(graph);
    for(int i = 0; i < 9; i++)
    out.println(i + ": " + es[i].weight);
  }

  private static void addEdge(int a, int b, int w, Map<Integer, List<Edge>> graph) {
    graph.get(a).add(new Edge(a, b, w));
    graph.get(b).add(new Edge(b, a, w));
  }

  private static Edge[] dijkstra(Map<Integer, List<Edge>> graph) {
    int n = graph.size();
    Edge[] es =  new Edge[n];
    for(int i = 0; i < n; i++)
      es[i] = new Edge(-1, i, Integer.MAX_VALUE);
    es[0].weight = 0;

    TreeSet<Edge> treeSet = new TreeSet<>((a, b) -> a.weight - b.weight);
    treeSet.add(es[0]);

    boolean[] visited = new boolean[n];

    while(treeSet.size() > 0) {
      Edge e = treeSet.pollFirst();
      visited[e.dest] = true;
      for(Edge ed : graph.get(e.dest)) {
        if(visited[ed.dest] || ed.weight + es[e.dest].weight >= es[ed.dest].weight) 
          continue;
        treeSet.remove(es[ed.dest]);
        es[ed.dest].weight = ed.weight + es[e.dest].weight;
        treeSet.add(es[ed.dest]);
      }
    }
    return es;
  }

  private static Edge[] kruskal(int v, Edge[] edges) {
    Edge[] res = new Edge[v-1];

    int[] p = new int[v];
    for(int i = 0; i < v; i++) 
      p[i] = i;

    int[] rank = new int[v];
    Arrays.fill(rank, 1);

    Arrays.sort(edges, (e1, e2) -> e1.weight - e2.weight);
    for(int i = 0, idx = 0; i < res.length;) {
      Edge e = edges[idx++];
      if(union(p, rank, e.src, e.dest)) {
        res[i++] = e;
      }
    }
    return res;
  }

  private static boolean union(int[] root, int[] rank, int u, int v) {
      int rootA = find(root, u);
      int rootB = find(root, v);
      if(rootA == rootB) return false;

      if(rank[rootA] > rank[rootB]) {
        rank[rootA] += rank[rootB];
        root[rootB] = rootA;
      } else {
        rank[rootB] += rank[rootA];
        root[rootA] = rootB;
      }
      return true;
  }

  private static int find(int[] root, int node) {
    if(root[node] != node) {
      root[node] = find(root, root[node]);
    }
    return root[node];
  }

  static class BIT {
    int n;
    int[] nums;
    int[] bit;

    public BIT(int[] nums) {
      this.nums = nums;
      this.n = nums.length;
      this.bit = new int[n + 1];
      for(int i = 0; i < n; i++)
        init(i, nums[i]);
    }

    void init(int i, int val) {
      i++;
      while(i <= n) {
        bit[i] += val;
        i += (i & -i); // (i & (-i)): get moet least significate digit
      }
    }

    void update(int i, int val) {
      int diff = val - nums[i];
      nums[i] = val;
      init(i, diff);
    }

    int getSum(int i) {
      int sum = 0;
      i++;
      while(i > 0) {
        sum += bit[i];
        i -= (i & -i); // ex: 1100 -> 1000 -> 0000. subtract moet least significate digit
      }
      return sum;
    }

    int sumRange(int i, int j) {
      return getSum(j) - getSum(i - 1);
    }
  }
}