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 main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		while(t-- >0){
		    String ss[]=br.readLine().split(" ");
		    long k=Long.parseLong(ss[1]);
		    int n=Integer.parseInt(ss[0]);
		    String s[]=br.readLine().split(" ");
		    int a[]=new int[n];
		    int max=Integer.MIN_VALUE;
		    int min=Integer.MAX_VALUE;
		    for(int i=0;i<n;++i){
		        a[i]=Integer.parseInt(s[i]);
		        if(a[i]>max){
		            max=a[i];
		        }
		        if(a[i]<min){
		            min=a[i];
		        }
		    }
		    if(k%2==1){
    		    for(int i=0;i<n;++i){
    		        a[i]=max-a[i];
    		        System.out.print(a[i]+ " ");
    		    }
		    }
		    else{
		        for(int i=0;i<n;++i){
    		        a[i]=a[i]-min;
    		        System.out.print(a[i]+ " ");
    		    }
		    }
		    System.out.println();
		}
		   
	}
}