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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
	
	static int mod = 1000000007;
	
	// ------------------------------------------------------- Scanner -------------------------------------------------------------------------------------------
	
	public static class Scanner {
	    BufferedReader br;
	    StringTokenizer st;
	    public Scanner() {
	       br = new BufferedReader(new InputStreamReader(System.in));
	    }
	    String next() {
	        while (st == null || !st.hasMoreElements()) {
	            try {
	                st = new StringTokenizer(br.readLine());
	            } catch (IOException e) {
	                e.printStackTrace();
	            }
	        }
	        return st.nextToken();
	    }
	    int nextInt() {
	        return Integer.parseInt(next());
	    }
	    long nextLong() {
	        return Long.parseLong(next());
	    }
	    double nextDouble() {
	        return Double.parseDouble(next());
	    }
	    String nextLine(){
	        String str = "";
	    try {
	       str = br.readLine();
	    } catch (IOException e) {
	       e.printStackTrace();
	    }
	    return str;
	    }

	}
	
	// ------------------------------------------------------------ Print and Flush -----------------------------------------------------------------------------------
	
	public static void print(int[] arr) {
		for(int i=0 ; i<arr.length ; i++) System.out.print(arr[i]+" ");
		System.out.println();
	}
	
	public static void print(int[][] arr) {
		for(int i=0 ; i<arr.length ; i++) {
			for(int j=0 ; j<arr[0].length ; j++) System.out.print(arr[i][j]+" ");
			System.out.println();
		}
	}
	
	public static void print(int res) {
		System.out.println(res);
	}
	
	public static void print(String res) {
		System.out.println(res);
	}
	
	public static void print(int a , int b) {
		System.out.println(a + " " + b);
	}
	
	public static void print(char[] res) {
		for (int i = 0 ; i < res.length ; i++) 
			System.out.print(res[i]);
		System.out.println();
	}
	
	public static void flush() {
		System.out.flush();
	}
	
	// ---------------------------------------------------------- Is Palindrome --------------------------------------------------------------------------------------
	
	public static boolean isPalindrome(String str) {
		for (int i = 0 ; i < str.length() ; i++) { 
			if (str.charAt(i) != str.charAt(str.length() - i - 1))
				return false;
		}
		return true;
	}
	
	//----------------------------------------------------- Pair ----------------------------------------------------------------------------------------------------
	
	public static class Pair {
		int x;
		int y;
		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
		Pair(Pair p) {
			x = p.x;
			y = p.y;
		}
	}
	
	//----------------------------------------------------- Comparator ------------------------------------------------------------------------------------------------
	
	static class cmp implements Comparator<long[]> {
		public int compare(long[] v1 , long[] v2) {
			if (v1[0] > v2[0])
				return 1;
			else if (v1[0] == v2[0] && v1[1] < v2[1]) 
				return 1;
			return -1;
		}
	}
	
	// ------------------------------------------------------- Tries ------------------------------------------------------------------------------------------------
	
	static class Tries {
		char ch = '\u0000';
		int count = 0;
		Tries[] arr = new Tries[26];
		boolean isEnd = false;
		Tries(char ch) {
			this.ch = ch;
		}
		Tries () { }
	}
	static Tries dummy = new Tries(); 
	static int tries_insert(String str) {
		Tries temp = dummy;
		for (int i = 0 ; i < str.length() ; i++) {
			int pos = str.charAt(i) - 'a';
			if (temp.arr[pos] == null) 
				temp.arr[pos] = new Tries(str.charAt(i));
			temp = temp.arr[pos];
		}
		temp.isEnd = true;
		temp.count += 1;
		return temp.count;
	}
	
	// ------------------------------------------------------ Prime Number (seive) -----------------------------------------------------------------------------------
	
	static int len = 10001;
	static int[] prime_number = new int[len];
	static Set<Integer> prime_number_set = new HashSet<>();
	static Set<Long> three_factor_set = new HashSet<>(); 
	static void seive() {
		prime_number[0] = 1;
		prime_number[1] = 1;
		for (int i = 2 ; i < len ; i++) {
			if (prime_number[i] == 0) {
				long val = i;
				prime_number_set.add(i);
				//three_factor_set.add(val * val);
				for (int j = i + i ; j < len ; j+=i) 
					prime_number[j] = 1;
			}
		}
	}
	
	static long[] product = new long[200001];
	static void multiply() {
		product[0] = 1;
		product[1] = 1;
		for (int i = 2 ; i < 200001 ; i++)
			product[i] = (product[i - 1] * i) % mod;
	}
	
	//---------------------------------------------------------perfect square --------------------------------------------------------------
	
	static Set<Integer> perfect_square = new HashSet();
	static void ps(int len) {
		for (int i = 1 ; i <= len ; i++) {
			perfect_square.add(i * i);
		}
	}
	
	
	// ---------------------------------------------------------- Sqrt ---------------------------------------------------------------------------------------------
		
	static long pow(long a , long b) {
		if (b == 0)
			return 1;
		long mid = pow(a , b/2) % mod;
		if (b % 2 == 0) 
			return (mid * mid) % mod;
		return (((mid * mid) % mod) * a) % mod;
	}
	
	static int sumDigit(long num) {
		int res = 0;
		while (num > 0) {
			res += num % 10;
			num = num / 10;
		}
		return res;
	}
	
	
	// ---------------------------------------------------------- Solve --------------------------------------------------------------------------------------------
	
	public static void solve(Scanner s) {
//		PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		int n = s.nextInt();
//		long m = s.nextLong();
//		long k = s.nextLong();
//		int k1 = s.nextInt();
//		int k2 = s.nextInt();
//		int w = s.nextInt();
//		s.nextLine();
//		String s2 = s.nextLine();
//		List<List<Integer>> arr = new ArrayList<>();
//		for (int i = 0 ; i < n ; i++) {
//			arr.add(new ArrayList<>());
//		}
		long[][] arr = new long[n][2];
		for (int i = 0 ; i < n ; i++) 
			arr[i][0] = s.nextLong();
		for (int i = 0 ; i < n ; i++) 
			arr[i][1] = s.nextLong();
		Arrays.sort(arr , new cmp());
		List<List<Long>> arr2 = new ArrayList<>();
		arr2.add(new ArrayList<>());
		int k = 0;
		long[] res = new long[n + 1];
		for (int i = 1 ; i <= n ; i++) {
			arr2.add(new ArrayList<>());
			long prev = 0;
			while (k < n && arr[k][0] == i) {
				prev += arr[k][1];
				arr2.get(i).add(prev);
				k += 1;	
			}
			for (int j = 1 ; j <= arr2.get(i).size() ; j++) {
				int val = arr2.get(i).size() % j;
				val = arr2.get(i).size() - val - 1;
				if (val >= 0)
					res[j] += arr2.get(i).get(val);
			}
		}
		for (int i = 1 ; i <= n ; i++) {	
			if(res[i] != 0)
				System.out.print(res[i] + " ");
			else
				System.out.print(0 + " ");
			
		}
		System.out.println();
//		int[][] dp = new int[m][n];
//		for (int i = 0 ; i < n ; i++) {
//			for (int j = 0 ; j < m ; j++) 
//				arr.add(new Pair(s.nextInt() , i));
//		}
//		int[] arr = new int[n];
//		for (int i = 0 ; i < n ; i++) 
//			arr[i] = s.nextInt();
//		int[][] data=new int[n][2];
//		String[] arr = new String[n];
//		char[][] data = new char[n][n];
//		for (int i = 0 ; i < n ; i++) 
//			arr[i] = s.nextLine();
//		Pair p1 = new Pair(0 , 0);
//		Pair p2 = new Pair(0 , 0);
//		int count = 0;
//		int a = s.nextInt();
//		int b = s.nextInt();
//		String str = s.nextLine();
//		seive();
//		System.out.println(perfect_square);
//		System.out.println();
		
	}
	public static void main(String[] args) {
		Scanner s = new Scanner();
//	    PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
//	    multiply();
//		int[2000001][][] 
//		seive();
//		ps(101);
//		prime_number_set.add(1);
		int t = s.nextInt();
//	    s.nextLine();
	    while(t-->0) 
	    	solve(s);

	    
//		e(s);
//	    int n      = s.nextInt();        // read input as integer
//	    long k     = s.nextLong();       // read input as long
//	    double d   = s.nextDouble();     // read input as double
//	    String str = s.next();           // read input as String
//	    String str2  = s.nextLine();       // read whole line as String
//	    long result = 3*k;
//	    out.println(result);                    // print via PrintWriter	   
//	    out.close();
	
	}
}