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 A {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t-->0) {
			int n = sc.nextInt();
			long k= sc.nextLong();
			long[] a = new long[n];
			for(int i = 0; i < n; i++) {
				a[i] = sc.nextLong();
			}
			long max=Long.MIN_VALUE;
			long[] first= new long[n];
			long[] second= new long[n];
			for(int i=0;i<n;i++){
			    max=Math.max(max,a[i]);
			}
			
			for(int i=0;i<n;i++){
			   first[i]=max-a[i];
			}
			long max1=Long.MIN_VALUE;
				for(int i=0;i<n;i++){
			    max1=Math.max(max1,first[i]);
			}
		    for(int i=0;i<n;i++){
			   second[i]=max1-first[i];
			}
			if(k%2==1)
			{
			 for(int i=0;i<n;i++){
			  System.out.print(first[i]+" ");
			}   
			}
			else{
			    for(int i=0;i<n;i++){
			  System.out.print(second[i]+" ");
			}
			}
			System.out.println();
		}
	}
}