Problem: Polycarp is an organizer of a Berland ICPC regional event. There are n universities in Berland numbered from 1 to n. Polycarp knows all competitive programmers in the region. There are n students: the i-th student is enrolled at a university u_i and has a programming skill s_i.

Polycarp has to decide on the rules now. In particular, the number of members in the team.

Polycarp knows that if he chooses the size of the team to be some integer k, each university will send their k strongest (with the highest programming skill s) students in the first team, the next k strongest students in the second team and so on. If there are fewer than k students left, then the team can't be formed. Note that there might be universities that send zero teams.

The strength of the region is the total skill of the members of all present teams. If there are no teams present, then the strength is 0.

Help Polycarp to find the strength of the region for each choice of k from 1 to n.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

The first line of each testcase contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of universities and the number of students.

The second line of each testcase contains n integers u_1, u_2, ..., u_n (1 ≤ u_i ≤ n) — the university the i-th student is enrolled at.

The third line of each testcase contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 10^9) — the programming skill of the i-th student.

The sum of n over all testcases doesn't exceed 2 ⋅ 10^5.

Output

For each testcase print n integers: the strength of the region — the total skill of the members of the present teams — for each choice of team size k.

Example

Input


4
7
1 2 1 2 1 2 1
6 8 3 1 5 1 5
10
1 1 1 2 2 2 2 3 3 3
3435 3014 2241 2233 2893 2102 2286 2175 1961 2567
6
3 3 3 3 3 3
5 9 6 7 9 7
1
1
3083


Output


29 28 26 19 0 0 0 
24907 20705 22805 9514 0 0 0 0 0 0 
43 43 43 32 38 43 
3083 

Note

In the first testcase the teams from each university for each k are: 

  * k=1: 
    * university 1: [6], [5], [5], [3]; 
    * university 2: [8], [1], [1]; 
  * k=2: 
    * university 1: [6, 5], [5, 3]; 
    * university 2: [8, 1]; 
  * k=3: 
    * university 1: [6, 5, 5]; 
    * university 2: [8, 1, 1]; 
  * k=4: 
    * university 1: [6, 5, 5, 3]; 

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.*;


public class codeforces2 {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
//        Scanner scan = new Scanner(System.in);
//for (int i = 1; i <= 10; i++) {
//    System.out.println(i + " " + divisors(i).toString());
//}   
        int tc = sc.ni();
        for (int rep = 0; rep < tc; rep++) {
            int N = sc.ni();
            long[] id = sc.longArray(N);
            long[] levels = sc.longArray(N);
            pw.println(solve(id, levels));
        }
        pw.close();
    }
    public static String solve(long[] id, long[] levels) {
        
        Map<Long, List<Long>> map = new HashMap();
        for (int i = 0; i < id.length; i++) {
            map.putIfAbsent(id[i], new ArrayList());
            map.get(id[i]).add(levels[i]);
        }
        Map<Integer, Long> ret = new HashMap();
        for (List<Long> list : map.values()) {
            Collections.sort(list, Comparator.reverseOrder());
            for (int i = 1; i < list.size(); i++) {
                list.set(i, list.get(i-1) + list.get(i));
            }
//            ret.put(1, ret.getOrDefault(1, 0L) + list.get(list.size() - 1));
//            if (1 != list.size()) ret.put(list.size(), ret.getOrDefault(list.size(), 0L) + list.get(list.size() - 1));
            for (int i = 0; i < list.size(); i++) {
                Set<Integer> PF = divisors(i+1);
                for (int divisor : PF) {
                    //will work for this K value
                    if (i + divisor >= list.size()) {
                        ret.put(divisor, ret.getOrDefault(divisor, 0L)+list.get(i));
                    }
                }
            }
            
        }
//        System.out.println(map.toString());
        StringBuilder sb = new StringBuilder();
        for (int K = 1; K <= id.length; K++) {
            long val = ret.getOrDefault(K, 0L);
            sb.append(val + " ");
        }
        return sb.toString();
    }
    static Set<Integer> divisors(int n) {
        Set<Integer> set = new HashSet();
        for (int i=1; i<=Math.sqrt(n); i++)
        {
            if (n%i==0)
            {
                // If divisors are equal, print only one
                if (n/i == i)
                    set.add(i);
      
                else {// Otherwise print both
                    set.add(i);
                    set.add(n / i);
                }
            }
        }
        return set;
    }
    static Map<Integer, Integer> primeFactorization(int x) {
        //first divide by 2
        Map<Integer, Integer> map = new HashMap();
        if (x == 0) return map;
        int count = 0;
        while (x % 2 == 0) {
            x /=2;
            count++;
        }
        //insert 2
        if (count > 0) map.put(2, count);
        for (int divisor = 3; divisor * divisor <= x; divisor += 2) {
            int cnt = 0;
            while (x % divisor == 0) {
                x /= divisor;
                cnt++;
            }
            if (cnt > 0) map.put(divisor, cnt);
        }
        if (x > 1) {
            map.put(x, 1);
        }
        return map;
    }
    static boolean isPrime(int n)
    {
 
        // Check if number is less than
        // equal to 1
        if (n <= 1)
            return false;
 
        // Check if number is 2
        else if (n == 2)
            return true;
 
        // Check if n is a multiple of 2
        else if (n % 2 == 0)
            return false;
 
        // If not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2) 
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b; 
        return gcd(b % a, a); 
    }
     
    // method to return LCM of two numbers
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }
    public static void sort(int[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            int temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
 
    public static void sort(long[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            long temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
    /* */
    //printing methods
    /* */
    //WOW!
    /* */
    public static void printArr(PrintWriter pw, int[] arr) {
        StringBuilder sb = new StringBuilder();
        for (int x : arr) {
            sb.append(x + "");
        }
        sb.setLength(sb.length() - 1);
        pw.println(sb.toString());
    }
    public static void printArr2d(PrintWriter pw, int[][] arr) {
        StringBuilder sb = new StringBuilder();
        for (int[] row : arr) {
            for (int x : row) {
                sb.append(x + " ");
            }
            sb.setLength(sb.length() - 1);
            sb.append("\n");
        }
        sb.setLength(sb.length() - 1);
        pw.println(sb.toString());
    }
}
class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    public FastScanner() {
        br = new BufferedReader(new InputStreamReader(System.in), 32768);
        st = null;
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int ni() {
        return Integer.parseInt(next());
    }

    int[] intArray(int N) {
        int[] ret = new int[N];
        for (int i = 0; i < N; i++)
            ret[i] = ni();
        return ret;
    }

    long nl() {
        return Long.parseLong(next());
    }

    long[] longArray(int N) {
        long[] ret = new long[N];
        for (int i = 0; i < N; i++)
            ret[i] = nl();
        return ret;
    }

    double nd() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
class UnionFind {
    int size;
    private int[] id;
    public UnionFind(int size) {
        this.size = size;
        id = new int[size];
        for (int i = 0; i < id.length; i++) {
            id[i] = i;
        }
    }
    public int find(int a) {
        if (id[a] != a) {
            id[a] = find(id[a]);
        }
        return id[a];
    }
    public void union(int a, int b) {
        int r1 = find(a);
        int r2 = find(b);
        if (r1 == r2) return;
        size--;
        id[r1] = r2;
    }
    @Override
    public String toString() {
        return Arrays.toString(id);
    }
}