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 EdC {

	public static void main(String[] args) throws Exception{
		int num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int t = Integer.parseInt(bf.readLine());
 		for(int i = 0;i<t;i++){
//	 		String input1 = bf.readLine().trim();
//	 		String input2 = bf.readLine().trim();
	 		StringTokenizer st = new StringTokenizer(bf.readLine());
	 		int n = Integer.parseInt(st.nextToken());
	 		long m = Long.parseLong(st.nextToken());
	 		ArrayList<Integer> array = new ArrayList<Integer>();
	 		StringTokenizer st2 = new StringTokenizer(bf.readLine());
	 		int max = Integer.MIN_VALUE;
	 		for(int j=0;j<n;j++){
	 			array.add(Integer.parseInt(st2.nextToken()));
	 			max = Math.max(array.get(j),  max);
	 		}
	 		ArrayList<Integer> array1 = new ArrayList<Integer>();
	 		int max2 = Integer.MIN_VALUE;
	 		for(int j = 0;j<n;j++){
	 			array1.add(max-array.get(j));
	 			max2 = Math.max(array1.get(j),  max2);
	 		}
	 		ArrayList<Integer> array2 = new ArrayList<Integer>();
	 		for(int j = 0;j<n;j++){
	 			array2.add(max2-array1.get(j));
	 		}
	 		
	 		if (m%2 == 1){
	 			for(int j = 0;j<n;j++){
	 				out.print(array1.get(j) + " ");
	 			}
	 			out.println();
	 		}
	 		else{
	 			for(int j = 0;j<n;j++){
	 				out.print(array2.get(j) + " ");
	 			}
	 			out.println();
	 		}

 		}
 		
 		
 		out.println();
	 		
 		out.close();
 		
 		
 		
 	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is