A13499 | Necklace Assembly

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:

The first necklace cannot be assembled because it has three beads "a" (of the two available). The second necklace cannot be assembled because it contains a bead "d", which is not 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.

 As you can see, this necklace is, for example, $3$ -beautiful, $6$ -beautiful, $9$ -beautiful, and so on, but it is not $1$ -beautiful or $2$ -beautiful.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.