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.List;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedHashSet;
import java.util.LinkedList;
import java.util.Map;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Vector;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	//	Template For Fast i/o copied From Gfg
	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 void main(String[] args)throws java.lang.Exception
	{
		try {
				FastReader obj=new FastReader();
				int t=obj.nextInt();
				while(t-->0)
				{
					
					int n=obj.nextInt();
					long k=obj.nextLong();
					
					long []a=new long[n];
					for(int i=0;i<n;i++)
					{
						a[i]=obj.nextLong();
					}
					long max=a[0];
					for(int i=1;i<n;i++)
					{
						if(a[i]>max)
						{
							max=a[i];
						}
					}
					for(int i=0;i<n;i++)
					{
						a[i]=max-a[i];
					}
					if(k%2==1)
					{
						for(int i=0;i<n;i++)
						{
							System.out.print(a[i]+" ");
						}
						System.out.println();
					}
					else
					{
						long max2=a[0];
						for(int i=1;i<n;i++)
						{
							if(a[i]>max2)
							{
								max2=a[i];
							}
						}
						for(int i=0;i<n;i++)
						{
							a[i]=max2-a[i];
						}
						for(int i=0;i<n;i++)
						{
							System.out.println(a[i]+" ");
						}
						System.out.println();
					}
				}
		}
		catch(Exception e)
		{
			return;
		}
	}
}
//Code- aditya7409