1675E · Replace With the Previous, Minimize

Problem: You are given a string $s$ of lowercase Latin letters.

The following operation can be used:

• select one character (from 'a' to 'z') that occurs at least once in the string. And replace all such characters in the string with the previous one in alphabetical order on the loop. For example, replace all 'c' with 'b' or replace all 'a' with 'z'.

And you are given the integer $k$ — the maximum number of operations that can be performed. Find the minimum lexicographically possible string that can be obtained by performing no more than $k$ operations.

The string $a=a_1a_2 \dots a_n$ is lexicographically smaller than the string $b = b_1b_2 \dots b_n$ if there exists an index $k$ ($1 \le k \le n$) such that $a_1=b_1$, $a_2=b_2$, ..., $a_{k-1}=b_{k-1}$, but $a_k < b_k$.

Input Format: The first line contains a single integer $t$ ($1 \le t \le 10^4$) —the number of test cases in the test.

This is followed by descriptions of the test cases.

The first line of each test case contains two integers $n$ and $k$ ($1 \le n \le 2 \cdot 10^5$, $1 \le k \le 10^9$) — the size of the string $s$ and the maximum number of operations that can be performed on the string $s$.

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

It is guaranteed that the sum $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output Format: For each test case, output the lexicographically minimal string that can be obtained from the string $s$ by performing no more than $k$ operations.