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:
/* package codechef; // don't place package name! */

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 Codechef
{
    public static void func(long arr[], long k){
        int n = arr.length;
        long min = arr[0];
        long max = arr[0];
        for (int i = 0; i < n; i++){
            min = Math.min(min, arr[i]);
            max = Math.max(max, arr[i]);
        }
        for (int i = 0; i < n; i++){
            arr[i] = max - arr[i];
        }
        if ((k & 1) == 1){
            for (int i = 0; i < n; i++){
                System.out.print(arr[i] + " ");
            }
            System.out.println();
        }else{
            min = arr[0];
            max = arr[0];
            for (int i = 0; i < n; i++){
                min = Math.min(min, arr[i]);
                max = Math.max(max, arr[i]);
            }
            for (int i = 0; i < n; i++){
                arr[i] = max - arr[i];
            }
            for (int i = 0; i < n; i++){
                System.out.print(arr[i] + " ");
            }
            System.out.println();
            
        }
            
        }
       
    
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		while (t--!=0){
		    int n = s.nextInt();
		    long k = s.nextLong();
		    long arr[] = new long[n];
		    for (int i = 0; i < n; i++){
		        arr[i] = s.nextLong();
		    }
		    func(arr, k);
		}
	}
}