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.*;
import java.io.*;
 
public class Solution{
	static PrintWriter out=new PrintWriter(System.out);
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		String[] input=br.readLine().trim().split(" ");
		
		int numTestCases=Integer.parseInt(input[0]);
		while(numTestCases-->0){
		    input=br.readLine().trim().split(" ");
		    int n=Integer.parseInt(input[0]);
		    long k=Long.parseLong(input[1]);
    		int[] arr=new int[n];
    		input=br.readLine().trim().split(" ");
    		for(int i=0;i<n;i++){
    		    arr[i]=Integer.parseInt(input[i]);
    		}
    		modifyArray(arr,k);
    		for(int i=0;i<n;i++) {
    			out.print(arr[i]+" ");
    		}
    		out.println();
		}
		
		out.flush();
		out.close();
	}
	public static void modifyArray(int[] arr,long k)
	{
		int n=arr.length;
		int max=Integer.MIN_VALUE;
		int min=Integer.MAX_VALUE;
		for(int i=0;i<n;i++) {
			max=Math.max(max, arr[i]);
			min=Math.min(min, arr[i]);
		}
		if(k%2!=0) {
			for(int i=0;i<n;i++) {
				arr[i]=max-arr[i];
			}
		}
		else {
			for(int i=0;i<n;i++) {
				arr[i]=arr[i]-min;
			}
		}
	}
}