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 Omkar_and_Infinity_Clock {

	public static void main(String[] args) throws java.lang.Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t =Integer.parseInt(br.readLine());
		while(t-->0){
			StringTokenizer s = new StringTokenizer(br.readLine());
			StringTokenizer st = new StringTokenizer(br.readLine());
			int n=Integer.parseInt(s.nextToken());long k=Long.parseLong(s.nextToken());
			long a[]=new long[n];
			long max=Long.MIN_VALUE,max1=Long.MIN_VALUE;
			for(int i=0; i<n; i++) {
				a[i]=Long.parseLong(st.nextToken());
				max=Math.max(max, a[i]);
			}
			long A1[]=new long[n],A2[]=new long[n];
			for(int i=0; i<n; i++) {
				A1[i]=max-a[i];
				max1=Math.max(max1, A1[i]);
			}
			for(int i=0; i<n; i++) A2[i]=max1-A1[i];
			if((k&1)==1) {
				for(long e: A1) System.out.print(e+" ");
				System.out.println();
			}else {
				for(long e: A2) System.out.print(e+" ");
				System.out.println();
			}
			
		}
	}

}