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.Scanner;
import java.util.Arrays;

public class Main
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t--!=0)
		{
		    int n = sc.nextInt();
		    long k = sc.nextLong();
		    long arr[] = new long[n];
		    for(int i=0;i<n;i++)
		    {
		        arr[i] = sc.nextInt();
		        
		    }
		    long m = arr[0];
		    for(int i=1;i<n;i++)
		    {
		        if(m<arr[i])
		        {
		            m = arr[i];
		        }
		    }
		   if(k%2!=0)
		   {
		       for(int i=0;i<n;i++)
		       {
		           arr[i] = m-arr[i];
		           System.out.print(arr[i]+" ");
		       }
		   }else
		   {
		       for(int i=0;i<n;i++)
		       {
		           arr[i] = m-arr[i];
		       }
		       m=arr[0];
		       for(int i=1;i<n;i++)
		       {
		           if(m<arr[i])
		           {
		               m=arr[i];
		           }
		       }
		       for(int i=0;i<n;i++)
		       {
		           arr[i] = m-arr[i];
		           System.out.print(arr[i]+" ");
		       }
		   }
		   System.out.println();
		}
	}

}