CF1455F.String and Operations

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 $s$.

给你一个由 $n$ 个字符组成的字符串 $s$。这些字符均属于拉丁字母表前 $k$ 个小写字母。你需要对这个字符串执行 $n$ 次操作。

在第 $i$ 次操作中，你选取最初位于第 $i$ 个位置的字符，并对其执行以下操作之一：

• 将其与字符串中前一个字符交换（若存在）。该操作记为 L；
• 将其与字符串中后一个字符交换（若存在）。该操作记为 R；
• 在字母表中将其循环地变为前一个字符（即 b 变为 a，c 变为 b，依此类推；a 变为拉丁字母表中第 $k$ 个字母）。该操作记为 D；
• 在字母表中将其循环地变为后一个字符（即 a 变为 b，b 变为 c，依此类推；拉丁字母表中第 $k$ 个字母变为 a）。该操作记为 U；
• 不进行任何操作。该操作记为 0。

例如，假设初始字符串为 test，$k = 20$，操作序列为 URLD，则字符串按如下方式变换：

1. 第一次操作为 U，因此我们将 test 中带下划线的字母（即第一个字符 t）变为前 $20$ 个拉丁字母中的下一个字母，即 a。字符串变为 aest；
2. 第二次操作为 R，因此我们将 aest 中带下划线的字母（即第二个字符 e）与它后面的字符交换。字符串变为 aset；
3. 第三次操作为 L，因此我们将 aset 中带下划线的字母（即第三个字符 s；注意：此时它是字符串中第 $2$ 个字符，但它最初是第 $3$ 个字符，因此第 $3$ 次操作作用于它）与它前面的字符交换。结果字符串为 saet；
4. 第四次操作为 D，因此我们将 saet 中带下划线的字母（即第四个字符 t）变为前 $20$ 个拉丁字母中的前一个字母，即 s。字符串变为 saes。

执行该操作序列后的结果为 saes。

给定字符串 $s$ 和参数 $k$，求对 $s$ 执行某一操作序列后所能得到的字典序最小的字符串。

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).

第一行包含一个整数 $t$（$1 \le t \le 1000$）—— 测试用例的数量。

每个测试用例由两行组成。第一行包含两个整数 $n$ 和 $k$（$1 \le n \le 500$；$2 \le k \le 26$）。

第二行包含一个长度为 $n$ 的字符串 $s$。字符串中的每个字符均为拉丁字母表前 $k$ 个小写字母之一。

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

对于每个测试用例，输出一行，包含通过一次操作序列能从 $s$ 得到的字典序最小的字符串。