A14945. 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:

- $k = 1: \{1, 2, 2, 2, 4, 5\}$
- $k = 2: \{2, 2, 2, 4, 5\}, \{1\}$
- $k = 3: \{2, 2, 2, 5\}, \{1\}, \{4\}$
- $k = 4: \{2, 2, 2\}, \{1\}, \{4\}, \{5\}$
- $k = 5: \{2, 2\}, \{1\}, \{2\}, \{4\}, \{5\}$
- $k = 6: \{1\}, \{2\}, \{2\}, \{2\}, \{4\}, \{5\}$