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.io.*;
import java.awt.Rectangle;
import java.util.*;



public class problemA 
{
   public static void main (String[] args) throws IOException
   {
      BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
      //BufferedReader input = new BufferedReader(new FileReader("diamond.in"));
      //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("diamond.out")));
      StringTokenizer token = new StringTokenizer(input.readLine());
      int maxCount = Integer.parseInt(token.nextToken());
      for(int b = 0; b < maxCount; b++)
      {
         token = new StringTokenizer(input.readLine());
         int arrayLength = Integer.parseInt(token.nextToken());
         long operations = Long.parseLong(token.nextToken());
         int [] array = new int[arrayLength];
         token = new StringTokenizer(input.readLine());
         int max = Integer.MIN_VALUE;
         for(int x = 0; x < arrayLength; x++)
         {
            array[x] = Integer.parseInt(token.nextToken());
            if(array[x] > max)
               max = array[x];
         }
        
         operations--;
         int max2 = Integer.MIN_VALUE;
         for(int x = 0; x < arrayLength; x++)
         {
            array[x] = max - array[x];
            if(array[x] > max2)
               max2 = array[x];
         }
         operations = operations % 2;
         if(operations == 0)
         {
            for(int x = 0; x < arrayLength; x++)
               System.out.print(array[x] + " "); 
            System.out.println();
         }
         else
         {
            for(int x = 0; x < arrayLength; x++)
            {
               array[x] = max2 - array[x];
               System.out.print(array[x] + " "); 
            }
            System.out.println();
         }  
         
      }
   }
}