Omkar and Infinity Clock

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 ≤ t ≤ 100). Description of the test cases follows.

The first line of each test case contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 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 ≤ a_{i} ≤ 10^9) – the initial contents of your array.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 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].

inputFormat

Input

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

The first line of each test case contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 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 ≤ a_{i} ≤ 10^9) – the initial contents of your array.

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

outputFormat

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].

样例

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

391 0  
0 6 1 3 5

0

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