B. Omkar and Infinity Clock
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Being stuck at home, Ray became extremely bored. To pass time, he asks Lord Omkar to use his time bending power: Infinity Clock! However, Lord Omkar will only listen to mortals who can solve the following problem:

You are given an array $a$ of $n$ integers. You are also given an integer $k$. Lord Omkar wants you to do $k$ operations with this array.

Define one operation as the following:

1. Set $d$ to be the maximum value of your array.
2. For every $i$ from $1$ to $n$, replace $a_{i}$ with $d-a_{i}$.

The goal is to predict the contents in the array after $k$ operations. Please help Ray determine what the final sequence will look like!

Input

Each test contains multiple test cases. The first line contains the number of cases $t$ ($1 \le t \le 100$). Description of the test cases follows.

The first line of each test case contains two integers $n$ and $k$ ($1 \leq n \leq 2 \cdot 10^5, 1 \leq k \leq 10^{18}$) – the length of your array and the number of operations to perform.

The second line of each test case contains $n$ integers $a_{1},a_{2},...,a_{n}$ $(-10^9 \leq a_{i} \leq 10^9)$ – the initial contents of your array.

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

Output

For each case, print the final version of array $a$ after $k$ operations described above.

Example
Input
3
2 1
-199 192
5 19
5 -1 4 2 0
1 2
69

Output
391 0
0 6 1 3 5
0

Note

In the first test case the array changes as follows:

• Initially, the array is $[-199, 192]$. $d = 192$.

• After the operation, the array becomes $[d-(-199), d-192] = [391, 0]$.