|Codeforces Round #650 (Div. 3)|
The store sells $$$n$$$ beads. The color of each bead is described by a lowercase letter of the English alphabet ("a"–"z"). You want to buy some beads to assemble a necklace from them.
A necklace is a set of beads connected in a circle.
For example, if the store sells beads "a", "b", "c", "a", "c", "c", then you can assemble the following necklaces (these are not all possible options):
And the following necklaces cannot be assembled from beads sold in the store:
We call a necklace $$$k$$$-beautiful if, when it is turned clockwise by $$$k$$$ beads, the necklace remains unchanged. For example, here is a sequence of three turns of a necklace.
In particular, a necklace of length $$$1$$$ is $$$k$$$-beautiful for any integer $$$k$$$. A necklace that consists of beads of the same color is also beautiful for any $$$k$$$.
You are given the integers $$$n$$$ and $$$k$$$, and also the string $$$s$$$ containing $$$n$$$ lowercase letters of the English alphabet — each letter defines a bead in the store. You can buy any subset of beads and connect them in any order. Find the maximum length of a $$$k$$$-beautiful necklace you can assemble.
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases in the test. Then $$$t$$$ test cases follow.
The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n, k \le 2000$$$).
The second line of each test case contains the string $$$s$$$ containing $$$n$$$ lowercase English letters — the beads in the store.
It is guaranteed that the sum of $$$n$$$ for all test cases does not exceed $$$2000$$$.
Output $$$t$$$ answers to the test cases. Each answer is a positive integer — the maximum length of the $$$k$$$-beautiful necklace you can assemble.
6 6 3 abcbac 3 6 aaa 7 1000 abczgyo 5 4 ababa 20 10 aaebdbabdbbddaadaadc 20 5 ecbedececacbcbccbdec
6 3 5 4 15 10
The first test case is explained in the statement.
In the second test case, a $$$6$$$-beautiful necklace can be assembled from all the letters.
In the third test case, a $$$1000$$$-beautiful necklace can be assembled, for example, from beads "abzyo".