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.awt.Desktop;
import java.io.BufferedReader;


import java.io.IOException;
import java.io.InputStreamReader;
import java.net.URI;
import java.net.URISyntaxException;
import java.sql.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedHashMap;
import java.util.LinkedHashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
import java.util.Vector;


public  class codechef3 {
static class comp implements Comparator<Integer>
{

	@Override
	public int compare(Integer o1, Integer o2) {
		if(Math.abs(o1)>Math.abs(o2))
			return -1;
		else return 1;
	
	}

	
	}
	   
		 static class FastReader
		    {BufferedReader br; 
		        StringTokenizer st; 
		 public FastReader() 
		        {  br = new BufferedReader(new
		                     InputStreamReader(System.in)); 
		        } 
		  
		       String next() 
		        { 
		            while (st == null || !st.hasMoreElements()) 
		            { 
		                try
		                { 
		                    st = new StringTokenizer(br.readLine()); 
		                } 
		                catch (IOException  e) 
		                { 
		                    e.printStackTrace(); 
		                } 
		            } 
		            return st.nextToken(); 
		        } 
		  
		        int nextInt() 
		        { 
		            return Integer.parseInt(next()); 
		        } 
		  
		        long nextLong() 
		        { 
		            return Long.parseLong(next()); 
		        } 
		  
		        double nextDouble() 
		        { 
		            return Double.parseDouble(next()); 
		        } 
		  
		        String nextLine() 
		        { 
		            String str = ""; 
		            try
		            { 
		                str = br.readLine(); 
		            } 
		            catch (IOException e) 
		            { 
		                e.printStackTrace(); 
		            } 
		            return str; 
		        } 
		    } 
public static int[] fill(int[] b,int[] a)
{
	int n=a.length;
	for(int i=0;i<n;i++)
		b[i]=a[i];
	
	return b;
	
	
}
		
		 
		    public static void main(String[] args) 
		    {
		    	FastReader s=new FastReader();
		    int t=s.nextInt();
		    while(t-->0)
		    {
		  
		    int n=s.nextInt();
		   long[] a=new long[n];
		   long k=s.nextLong();
		   long[] b=new long[n];
		   long max=Long.MIN_VALUE;
		   long min=Long.MAX_VALUE;
		    for(int i=0;i<n;i++) {
		    	a[i]=s.nextLong();
		    	max=Long.max(max, a[i]);
		          min=Long.min(min, a[i]);
		    }
		   long max1=Long.MIN_VALUE;
		    for(int i=0;i<n;i++)
		    	{a[i]=max-a[i];
                max1=Math.max(max1, a[i]);		    	
		    	}
		    if(k%2==0)
		    {
		    	for(int i=0;i<n;i++)
		    	{
		    		a[i]=max1-a[i];
		    	}
		    }
		    
		    for(int i=0;i<n;i++)
		    	System.out.print(a[i]+" ");
		    System.out.println();
		    
		    
		    
		  
		    
		    
		    
		    
		    
		    
		    
		    	
		    	
		    
		    }
		    	
		       
		    }
		}