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.*;
import java.io.*;
 
public class omkarandclock {
	public static long conv(String s) {
		return Long.parseLong(s);
	}
 
	public static void main(String[] args) throws IOException {
		// BufferedReader in = new BufferedReader(new FileReader("omkarandclock.in"));
		// PrintWriter out = new PrintWriter(new BufferedWriter(new
		// FileWriter("omkarandclock.out")));
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		long cases = conv(in.readLine());
		for (long c = 0; c < cases; c++) {
			StringTokenizer st = new StringTokenizer(in.readLine());
			int len = Integer.parseInt(st.nextToken());
			long ops = conv(st.nextToken());
 
			long[] nums = new long[len];
			StringTokenizer st1 = new StringTokenizer(in.readLine());
			long mas = Long.MIN_VALUE;
			for (int i = 0; i < len; i++) {
				nums[i] = conv(st1.nextToken());
				mas = Math.max(mas, nums[i]);
			}
			if(ops%2==0) {
				ops=2;
			}
			else {
				ops=1;
			}
			if (len == 1) {
				System.out.println(0);
			} else {
 
				while (ops > 0) {
					long max1 = Long.MIN_VALUE;
					for (int i = 0; i < len; i++) {
						nums[i] = mas - nums[i];
						max1 = Math.max(max1, nums[i]);
					}
					mas = max1;
				
					ops--;
				}
				for ( int m = 0; m < len; m++) {
					if (m == 0) {
						System.out.print(nums[m]);
					} else {
						System.out.print(" " + nums[m]);
					}
				}
				System.out.println();
			}
		}
 
		in.close();
		out.close();
	}
 
}