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:
/*==============================================
Name        : Shadman Shariar                 ||
Email       : shadman.shariar@northsouth.edu  ||
University  : North South University (NSU)    ||
Facebook    : shadman.shahriar.007            ||
==============================================*/
import java.util.Scanner;

public class Main {
	
	public static int binarysearch(int arr[], int l, int r, int x) 
    { 
        if (r >= l) { 
            int mid = l + (r - l) / 2; 
            if (arr[mid] == x) 
                return mid; 
            if (arr[mid] > x) 
                return binarysearch(arr, l, mid - 1, x); 
            return binarysearch(arr, mid + 1, r, x); 
        }  
        return -1; 
    }
	
	public static int sumofarray(int arr[])  
	{  
	    int sum = 0;
	    for (int i = 0; i < arr.length; i++)  
	    sum += arr[i];  
	    return sum;  
	}
	
	public static int gcd(int a, int b)
	    {
	        if (a == 0)
	            return b; 
	        return gcd(b % a, a); 
	    }
	    static int lcm(int a, int b)
	    {
	        return (a / gcd(a, b)) * b;
	    }
	    
	  public static void rangeofprimenumber(int a, int b) 
	    {  
	    	int i, j, flag;
	    	for (i = a; i <= b; i++) {
	            if (i == 1 || i == 0)
	                continue;
	            flag = 1;
	            for (j = 2; j <= i / 2; ++j) {
	                if (i % j == 0) {
	                    flag = 0;
	                    break;
	                }
	            }
	            if (flag == 1)
	                System.out.println(i);
	        }
	    } 
	  
	   public static boolean isprime(int n)
	    {
	        if (n <= 1)
	            return false;
	        else if (n == 2)
	            return true;
	        else if (n % 2 == 0)
	            return false;
	        for (int i = 3; i <= Math.sqrt(n); i += 2) 
	        {
	            if (n % i == 0)
	                return false;
	        }
	        return true;
	    }
	    
	   public static int factorial(int n) 
	    { 
	      return (n == 1 || n == 0) ? 1 : n * factorial(n - 1); 
	    } 
	   
	   public static int[] reveresearray(int arr[],int start, int end)
             {
               int temp;
     
               while (start < end)
              {
                temp = arr[start]; 
                arr[start] = arr[end];
                arr[end] = temp;
                start++;
                end--;
   } 
               return arr;
} 
	
	   public static int totaldivisor(int n){ 
		   int c = 0;
	        for (int i=1;i<=n;i++) 
	            if (n%i==0)c++;
	        
	        return c;
	    } 
	   
	  public static long findmax(long[]arr) 
	     { 
	         int i; 
	         long max = arr[0];   
	         for (i = 1; i < arr.length; i++) { 
	             if (arr[i] > max) {
	                 max = arr[i]; 
	             }
	         }
	         return max; 
	     } 
	   
	public static void main(String[] args) {
		
		Scanner input = new Scanner (System.in);


		
		int t = input.nextInt();
		
		for (int i = 0; i < t; i++) {
			
			int a = input.nextInt();
			long b = input.nextLong();
			long [] arr = new long[a];
			long max = Long.MIN_VALUE;
			for (int j = 0; j < arr.length; j++) {
				arr[j] = input.nextLong();
				if (arr[j]>=max) {
					max = arr[j];
				}
			}
			if (b%2==0) {
				b=2;
			}
			else {
				b=1;
			}
			for (int j = 0; j < b; j++) {
				for (int j2 = 0; j2 < arr.length; j2++) {
					arr[j2] = max-arr[j2];
				}
				max = findmax(arr);
			}
			 for (int j = 0; j < arr.length; j++) {
				System.out.print(arr[j]+" ");
			}
			System.out.println();
		}
		
		
		

		input.close();
	}

}