Reverse and Concatenate

1000ms

262144K

Description:

Real stupidity beats artificial intelligence every time.

— Terry Pratchett, Hogfather, Discworld

You are given a string $$$s$$$ of length $$$n$$$ and a number $$$k$$$. Let's denote by $$$rev(s)$$$ the reversed string $$$s$$$ (i.e. $$$rev(s) = s_n s_{n-1} ... s_1$$$). You can apply one of the two kinds of operations to the string:

replace the string $$$s$$$ with $$$s + rev(s)$$$
replace the string $$$s$$$ with $$$rev(s) + s$$$

How many different strings can you get as a result of performing exactly $$$k$$$ operations (possibly of different kinds) on the original string $$$s$$$?

In this statement we denoted the concatenation of strings $$$s$$$ and $$$t$$$ as $$$s + t$$$. In other words, $$$s + t = s_1 s_2 ... s_n t_1 t_2 ... t_m$$$, where $$$n$$$ and $$$m$$$ are the lengths of strings $$$s$$$ and $$$t$$$ respectively.

Input:

The first line contains one integer $$$t$$$ ($$$1 \le t \le 100$$$) — number of test cases. Next $$$2 \cdot t$$$ lines contain $$$t$$$ test cases:

The first line of a test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 100$$$, $$$0 \le k \le 1000$$$) — the length of the string and the number of operations respectively.

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

Output:

For each test case, print the answer (that is, the number of different strings that you can get after exactly $$$k$$$ operations) on a separate line.

It can be shown that the answer does not exceed $$$10^9$$$ under the given constraints.

Sample Input:

4
3 2
aab
3 3
aab
7 1
abacaba
2 0
ab

Sample Output:

Note:

In the first test case of the example:

After the first operation the string $$$s$$$ can become either aabbaa or baaaab. After the second operation there are 2 possibilities for $$$s$$$: aabbaaaabbaa and baaaabbaaaab.

Informação

Provedor Codeforces

Código CF1634A