Problem: 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].

Solution (in JAVA):

Solution:

import java.util.*;

public class InfinityClock {

	public static void main(String[] args) {

		Scanner scan = new Scanner(System.in);
		int t = Integer.parseInt(scan.nextLine());

		StringBuilder sb = new StringBuilder();
		int[] array;
		String[] txt,split;
		while (t-- > 0) {
			String str1 = scan.nextLine();
			split = str1.split(" ");
			int n = Integer.parseInt(split[0]);
			long k =  (Long.parseLong(split[1])%2);
			if(k == 0)  k = 2;
			array = new int[n];
			String str2 = scan.nextLine();
			txt=str2.split(" ");
			for (int i = 0; i < n; i++) {
				array[i] = Integer.parseInt(txt[i]);
			}
			for (int j = 0; j < k ; j++) {
				int max = array[0];
				for (int i:array) {
					if (i > max)
						max = i;
				}
				for (int h = 0; h < n; h++) {

					array[h] = max - array[h];
				}
			}
			for (int j = 0; j < n; j++) {
				sb.append(array[j]);
				if (j + 1 < n)
					sb.append(" ");
			}
			sb.append("\n");
			System.gc();
		}
		System.out.print(sb);

        
	}

}