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.

山姆是一名幼儿园小朋友，他所在的小组共有 $n$ 名儿童。他决定从这些儿童中组建一支队伍来玩“大乱斗：围棋2”。

山姆拥有 $n$ 个增益道具，其中第 $i$ 个道具的类型为 $a_i$。一名儿童的力量值等于他所拥有的增益道具中不同种类的数量。

对于一支大小为 $k$ 的队伍，山姆会将全部 $n$ 个增益道具分发给这 $k$ 名儿童，使得每名儿童至少获得一个道具，且每个道具恰好分配给一名儿童。

对每个从 $1$ 到 $n$ 的整数 $k$，求出山姆所能得到的、由 $k$ 名儿童组成的队伍的力量值总和的最小可能值。

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 $3 \cdot 10^5$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 3 \cdot 10^5$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 3 \cdot 10^5$）。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^9$），表示 Sam 的增益道具的类型。

保证所有测试用例的 $n$ 值之和不超过 $3 \cdot 10^5$。

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.

对每个测试用例，输出 $n$ 个整数。

其中第 $k$ 个整数应等于 Sam 能够组成的大小为 $k$ 的队伍中，队员力量值之和的最小值。

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:

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

使第一组测试用例中强度总和最小的一种分配强化道具的方式：

• $k = 1: {1, 1, 2}$
• $k = 2: {1, 1}, {2}$
• $k = 3: {1}, {1}, {2}$

使第二组测试用例中强度总和最小的一种分配强化道具的方式：

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