Phoenix and Distribution
Contest: Codeforces Round 638 (Div. 2)
Difficulty rating: 1600
Tags: constructive algorithms, greedy, sortings, strings

Phoenix has a string $$$s$$$ consisting of lowercase Latin letters. He wants to distribute all the letters of his string into $$$k$$$ non-empty strings $$$a_1, a_2, \dots, a_k$$$ such that every letter of $$$s$$$ goes to exactly one of the strings $$$a_i$$$. The strings $$$a_i$$$ do not need to be substrings of $$$s$$$. Phoenix can distribute letters of $$$s$$$ and rearrange the letters within each string $$$a_i$$$ however he wants.

For example, if $$$s = $$$ baba and $$$k=2$$$, Phoenix may distribute the letters of his string in many ways, such as:

- ba and ba
- a and abb
- ab and ab
- aa and bb

But these ways are invalid:

- baa and ba
- b and ba
- baba and empty string ($$$a_i$$$ should be non-empty)

Phoenix wants to distribute the letters of his string $$$s$$$ into $$$k$$$ strings $$$a_1, a_2, \dots, a_k$$$ to minimize the lexicographically maximum string among them, i. e. minimize $$$max(a_1, a_2, \dots, a_k)$$$. Help him find the optimal distribution and print the minimal possible value of $$$max(a_1, a_2, \dots, a_k)$$$.

String $$$x$$$ is lexicographically less than string $$$y$$$ if either $$$x$$$ is a prefix of $$$y$$$ and $$$x \ne y$$$, or there exists an index $$$i$$$ ($$$1 \le i \le min(|x|, |y|))$$$ such that $$$x_i$$$ < $$$y_i$$$ and for every $$$j$$$ $$$(1 \le j < i)$$$ $$$x_j = y_j$$$. Here $$$|x|$$$ denotes the length of the string $$$x$$$.

Input format:
The input consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. Each test case consists of two lines.

The first line of each test case consists of two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 10^5$$$) — the length of string $$$s$$$ and the number of non-empty strings, into which Phoenix wants to distribute letters of $$$s$$$, respectively.

The second line of each test case contains a string $$$s$$$ of length $$$n$$$ consisting only of lowercase Latin letters.

It is guaranteed that the sum of $$$n$$$ over all test cases is $$$\le 10^5$$$.

Output format:
Print $$$t$$$ answers — one per test case. The $$$i$$$-th answer should be the minimal possible value of $$$max(a_1, a_2, \dots, a_k)$$$ in the $$$i$$$-th test case.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
In the first test case, one optimal solution is to distribute baba into ab and ab.

In the second test case, one optimal solution is to distribute baacb into abbc and a.

In the third test case, one optimal solution is to distribute baacb into ac, ab, and b.

In the fourth test case, one optimal solution is to distribute aaaaa into aa, aa, and a.

In the fifth test case, one optimal solution is to distribute aaxxzz into az, az, x, and x.

In the sixth test case, one optimal solution is to distribute phoenix into ehinopx.

Example input:
6
4 2
baba
5 2
baacb
5 3
baacb
5 3
aaaaa
6 4
aaxxzz
7 1
phoenix

Example output:
ab
abbc
b
aa
x
ehinopx

Editorial:
We first try to assign one letter to each string $$$a_i$$$. Let's denote the smallest letter in $$$s$$$ as $$$c$$$. If there exists at least $$$k$$$ occurrences of $$$c$$$ in $$$s$$$, we will assign $$$c$$$ as the first letter of each string $$$a_i$$$. Otherwise, the minimal solution is the $$$k$$$th smallest letter in $$$s$$$. For example, if $$$s=$$$aabbb and $$$k=3$$$, the $$$3$$$rd smallest letter is $$$b$$$ and that will be the answer.
Otherwise, we consider the letters that are left in $$$s$$$. If they are all the same letter (or there are no letters left because $$$n=k$$$), we split the remaining letters as evenly as possible among $$$a_i$$$. If not, we will show that it is optimal to sort the remaining letters in $$$s$$$ and append them to arbitrary $$$a_i$$$.
For example, let's suppose after assigning a letter to each $$$a_i$$$ that the remaining letters in $$$s$$$ are aaabb. We want to assign the $$$b$$$s as late as possible, so any string $$$a_i$$$ that receives a $$$b$$$ should have some number of $$$a$$$s before. It makes sense in fact that the string that receives a $$$b$$$ should receive all the $$$a$$$s, because if not it will be lexicographically larger. It can then be shown that all remaining larger letters should be sorted and added to the same string $$$a_i$$$ to minimize the answer.
Time complexity for each test case: $$$O(n \log{n})$$$ (for sorting $$$s$$$)