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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
//package codechefc;

import java.io.BufferedReader;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;


public class Codechefc {

   
    public static void main(String[] args) throws IOException {
                   FastScanner fs=new FastScanner();
                   int t=fs.nextInt();
                   while(t-->0)
                   {
                     int n=fs.nextInt();
                     long k=fs.nextLong();
                     int a[]=fs.readArray(n);
                   
                     int max=Integer.MIN_VALUE;
                    
                     for(int i=0;i<n;i++)
                     {
                        
                         if(a[i]>max)
                         {
                             max=a[i];
                         }
                     }
                      // System.out.println("first"+max);
                     int a1[]=new int[n];
                     int a2[]=new int[n];
                     for(int i=0;i<n;i++)
                     {
                         a1[i]=max-a[i];
                         //System.out.print(a1[i]+" ");
                     }
                     max=Integer.MIN_VALUE;
                     for(int i=0;i<n;i++)
                     {
                         if(a1[i]>max)
                         {
                             max=a1[i];
                         }
                     }
                       //System.out.println("second"+max);
                     for(int i=0;i<n;i++)
                     {
                         a2[i]=max-a1[i];
                     }
                     if(k%2==0)
                     {
                         for(int i=0;i<n;i++)
                         {
                             System.out.print(a2[i]+" ");
                         }
                         System.out.println("");
                     }
                     else
                     {
                         for(int i=0;i<n;i++)
                         {
                             System.out.print(a1[i]+" ");
                         }
                         System.out.println("");
                     }

                   }
          
                      
                      
                   
    }
    static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
                
		public String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
			
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public long[] readLongArray(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
	}
    
}