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.

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 $[d-(-199), d-192] = [391, 0]$.

Samples

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

391 0
0 6 1 3 5
0