Berland Regional

你是一个地区 IPIC 的特派员，这个地区的 IPIC 是组队制，每个队伍有 $k$ 个人。这个地区有 $n$ 所学校和 $n$ 个人，每个人有一个水平和一个学籍。 学校会将该学校水平前 $k$ 的人组为一个队伍。然后再将剩余人中水平前 $k$ 的人组为一个队伍，直到剩下的人不足 $k$ 个。某个地区 IPIC 的精彩程度为所有参赛人的水平之和。 你需要计算分别当 $k=1,2,3...n-1,n$ 时，IPIC 的精彩程度。

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 $ .

The first line contains a single integer $ t $ ( $ 1 \le t \le 1000 $ ) — the number of testcases. The first line of each testcase contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the number of universities and the number of students. The second line of each testcase contains $ n $ integers $ u_1, u_2, \dots, u_n $ ( $ 1 \le u_i \le n $ ) — the university the $ i $ -th student is enrolled at. The third line of each testcase contains $ n $ integers $ s_1, s_2, \dots, s_n $ ( $ 1 \le s_i \le 10^9 $ ) — the programming skill of the $ i $ -th student. The sum of $ n $ over all testcases doesn't exceed $ 2 \cdot 10^5 $ .

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 $ .

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

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

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] $ ;