You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
You are given a string $$$s$$$ consisting of $$$n$$$ characters. These characters are among the first $$$k$$$ lowercase letters of the Latin alphabet. You have to perform $$$n$$$ operations with the string.

During the $$$i$$$-th operation, you take the character that initially occupied the $$$i$$$-th position, and perform one of the following actions with it:

- swap it with the previous character in the string (if it exists). This operation is represented as L;
- swap it with the next character in the string (if it exists). This operation is represented as R;
- cyclically change it to the previous character in the alphabet (b becomes a, c becomes b, and so on; a becomes the $$$k$$$-th letter of the Latin alphabet). This operation is represented as D;
- cyclically change it to the next character in the alphabet (a becomes b, b becomes c, and so on; the $$$k$$$-th letter of the Latin alphabet becomes a). This operation is represented as U;
- do nothing. This operation is represented as 0.

For example, suppose the initial string is test, $$$k = 20$$$, and the sequence of operations is URLD. Then the string is transformed as follows:

1. the first operation is U, so we change the underlined letter in test to the next one in the first $$$20$$$ Latin letters, which is a. The string is now aest;
2. the second operation is R, so we swap the underlined letter with the next one in the string aest. The string is now aset;
3. the third operation is L, so we swap the underlined letter with the previous one in the string aset (note that this is now the $$$2$$$-nd character of the string, but it was initially the $$$3$$$-rd one, so the $$$3$$$-rd operation is performed to it). The resulting string is saet;
4. the fourth operation is D, so we change the underlined letter in saet to the previous one in the first $$$20$$$ Latin letters, which is s. The string is now saes.

The result of performing the sequence of operations is saes.

Given the string $$$s$$$ and the value of $$$k$$$, find the lexicographically smallest string that can be obtained after applying a sequence of operations to $$$s$$$.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

Each test case consists of two lines. The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 500$$$; $$$2 \le k \le 26$$$).

The second line contains a string $$$s$$$ consisting of $$$n$$$ characters. Each character is one of the $$$k$$$ first letters of the Latin alphabet (in lower case).

## Output Format
For each test case, print one line containing the lexicographically smallest string that can be obtained from $$$s$$$ using one sequence of operations.

## Examples
```input
6
4 2
bbab
7 5
cceddda
6 5
ecdaed
7 4
dcdbdaa
8 3
ccabbaca
5 7
eabba
```
```output
aaaa
baccacd
aabdac
aabacad
aaaaaaaa
abadb
```

Now solve the problem and return the code.