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:
//I AM THE CREED
/* //I AM THE CREED
/* package codechef; // don't place package name! */
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;
import java.awt.Point;
public class Main{
    public static void main(String[] args) throws IOException 
    { 
  
        Scanner input = new Scanner(System.in);
        input.nextInt();
        while(input.hasNext()){
            int n=input.nextInt();
            long k=input.nextLong();
            Long[] l=new Long[n];
            long max=Long.MIN_VALUE;
            long min=Long.MAX_VALUE;
            for(int i=0;i<n;i++){
                l[i]=input.nextLong();
                min=Math.min(min, l[i]);
                max=Math.max(max, l[i]);
            }
            if(k%2==1){
                StringBuilder sb=new StringBuilder();
                for(int i=0;i<n;i++){
                    sb.append((max-l[i]));
                    sb.append(" ");
                }
                System.out.println(sb.toString());
                continue;
            }
            StringBuilder sb=new StringBuilder();
            for(int i=0;i<n;i++){
                sb.append((l[i]-min));
                sb.append(" ");
            }
            System.out.println(sb.toString());
        }
        
    }
    


}