Left or Right Shift
Description
You're given a string $s$ of $n$ lowercase characters and an integer $k$.
In one operation, you can shift a character left, or shift a character right.
Shift a character left means shift $a$ to $z$,$b$ to $a$,...,or $z$ to $y$.
Shift a character right means shift $a$ to $b$,$b$ to $c$,...,or $z$ to $a$.
What is the lexographically smallest string you can obtain after exactly $k$ moves?
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). The description of the test cases follows.
The first line of each test case contains two integers $n,k$ ($1\le n \le 4 \cdot 10^5,1\le k \le 10^9$).
The second line contains a string $s$ of length $n$ composed of lowercase letters.
The sum of $n$ over all test cases will not exceed $4 \cdot 10^5$.
For each test case, output on a new line — the lexographically smallest string you can obtain.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). The description of the test cases follows.
The first line of each test case contains two integers $n,k$ ($1\le n \le 4 \cdot 10^5,1\le k \le 10^9$).
The second line contains a string $s$ of length $n$ composed of lowercase letters.
The sum of $n$ over all test cases will not exceed $4 \cdot 10^5$.
Output
For each test case, output on a new line — the lexographically smallest string you can obtain.
3
1 3
a
3 10
zkb
4 12
ycew
b
abb
aaaa