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.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.time.LocalTime;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;


public class B {


    public static void main(String[] args) {
    
    	FastScanner scan = new FastScanner();
    	
    	int t = scan.nextInt();
   	for(int tt=0; tt<t; tt++) {
    		long n = scan.nextLong(), k = scan.nextLong();
    		long [] arr = new long[(int) n];
    		for(int i=0; i<n; i++) arr[i] = scan.nextLong();
    		long max = arr[0];
    		for(int i=1; i<n; i++) max = Math.max(arr[i], max);
    		for(int i=0; i<n; i++) arr[i] = max - arr[i];
    		if(k % 2 == 0) {
    			max = arr[0];
    			for(int j=1; j<n; j++) max = Math.max(arr[j], max);
        		for(int j=0; j<n; j++) arr[j] = max - arr[j];
    		}
    		for(int i=0; i<n; i++) System.out.print(arr[i] + " ");
    		System.out.println();
    	}
    	
    }
    
    public static void sort(int [] a) {
    	ArrayList<Integer> b = new ArrayList<>();
    	for(int i: a) b.add(i);
    	Collections.sort(b);
    	for(int i=0; i<a.length; i++) a[i]= b.get(i);
    }
     
    static class FastScanner{
    	
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    	StringTokenizer st = new StringTokenizer("");
    	String next() {
    		while(!st.hasMoreTokens())
    			try {
    				st = new StringTokenizer(br.readLine());
    			} catch (IOException e){
    				e.printStackTrace();
    			}
    		return st.nextToken();
    	}
    	
    	int nextInt() {
    		return Integer.parseInt(next());
    	}
    	
    	int [] readArray(int n) {
    		int [] a = new int[n];
    		for(int i=0; i<n ; i++) a[i] = nextInt();
    		return a;
    	}
    	
    	long nextLong() {
    		return Long.parseLong(next());
    	}
    	
    	
    }
    
   
}