CF1642B Power Walking

Sam is a kindergartener, and there are $ n $ children in his group. He decided to create a team with some of his children to play "brawl:go 2". Sam has $ n $ power-ups, the $ i $ -th has type $ a_i $ . A child's strength is equal to the number of different types among power-ups he has. For a team of size $ k $ , Sam will distribute all $ n $ power-ups to $ k $ children in such a way that each of the $ k $ children receives at least one power-up, and each power-up is given to someone. For each integer $ k $ from $ 1 $ to $ n $ , find the minimum sum of strengths of a team of $ k $ children Sam can get.

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 3 \cdot 10^5 $ ) — the number of test cases. Description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 3 \cdot 10^5 $ ). The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) — types of Sam's power-ups. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 3 \cdot 10^5 $ .

For every test case print $ n $ integers. The $ k $ -th integer should be equal to the minimum sum of strengths of children in the team of size $ k $ that Sam can get.

One of the ways to give power-ups to minimise the sum of strengths in the first test case: - $ k = 1: \{1, 1, 2\} $ - $ k = 2: \{1, 1\}, \{2\} $ - $ k = 3: \{1\}, \{1\}, \{2\} $ One of the ways to give power-ups to minimise the sum of strengths in the second test case: - $ k = 1: \{1, 2, 2, 2, 4, 5\} $ - $ k = 2: \{2, 2, 2, 4, 5\}, \{1\} $ - $ k = 3: \{2, 2, 2, 5\}, \{1\}, \{4\} $ - $ k = 4: \{2, 2, 2\}, \{1\}, \{4\}, \{5\} $ - $ k = 5: \{2, 2\}, \{1\}, \{2\}, \{4\}, \{5\} $ - $ k = 6: \{1\}, \{2\}, \{2\}, \{2\}, \{4\}, \{5\} $