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:

Set $$$d$$$ to be the maximum value of your array.
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 $$$[d-(-199), d-192] = [391, 0]$$$.

Omkar and Infinity Clock

Examples