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.math.BigInteger;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;

public class Main
{

	public static void main(String args[])
	{
		Scanner sc = new Scanner(System.in);
		while (sc.hasNext())
		{
			int sb = sc.nextInt();
			while (sb-- > 0)
			{
				int a = sc.nextInt();
				String g = sc.next();
				long x[] = new long[a];
				long y[] = new long[a];
				long max = Long.MIN_VALUE;
				for (int i = 0; i < x.length; i++)
				{
					long cnm = sc.nextLong();
					x[i] = cnm;
					max = Math.max(max, x[i]);
				}
				long maxx = Long.MIN_VALUE;
				for (int i = 0; i < x.length; i++)
				{
					x[i] = max - x[i];
					maxx = Math.max(maxx, x[i]);
				}

				for (int i = 0; i < y.length; i++)
				{
					y[i] = maxx - x[i];
				}

				int w = g.charAt(g.length() - 1) - '0';
				w++;
				w %= 2;
				if (w == 0)
				{
					for (int i = 0; i < y.length; i++)
					{
						if (i == 0)
						{
							System.out.print(x[i]);
						} else
						{
							System.out.print(" " + x[i]);
						}
					}
					System.out.println();
				} else
				{
					for (int i = 0; i < y.length; i++)
					{
						if (i == 0)
						{
							System.out.print(y[i]);
						} else
						{
							System.out.print(" " + y[i]);
						}
					}
					System.out.println();
				}

			}
		}

	}

}