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.lang.*;
import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class q2
{
	public static void main (String[] args) throws java.lang.Exception
	{
        // your code goes here
        Scanner sc = new Scanner(System.in);
        int t= Integer.parseInt(sc.next());
        while(t-->0)
        { 
            int n = Integer.parseInt(sc.next());
            long k = Long.parseLong(sc.next());
            long[] arr = new long[n];
            long max= Long.MIN_VALUE;
            for(int i=0;i<n;i++)
            {
                arr[i]=Long.parseLong(sc.next());
                if(arr[i]>max)
                {
                    max= arr[i];
                }
            }
            long[] a1= new long[n];
            long[] a2 = new long[n];
            long m2 = Long.MIN_VALUE;
            for(int i=0;i<n;i++)
            {
                a1[i]=max-arr[i];
                m2 = Math.max(m2, a1[i]);
            }
            for(int i=0;i<n;i++)
            {
                a2[i]= m2-a1[i];
            }
            if(k%2==0)
            {
                for(int i=0;i<n;i++)
                {
                    System.out.print(a2[i]+" ");
                }
                System.out.println("");
            }
            else
            {
                for(int i=0;i<n;i++)
                {
                    System.out.print(a1[i]+" ");
                }
                System.out.println("");
            }
 
 
            
        }
    }
}