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.io.*;
import java.util.*;

public class Main{
	static Scanner scan = new Scanner(System.in);
	public static void print_list(ArrayList<Object> a)
	{
		for(int i=0;i<a.size();i++)
		{
			System.out.print(a.get(i)+" ");
		}
		System.out.println();
	}
	static void print_array(Object[] nums)
	{
		for(int i=0;i<nums.length;i++)
		{
			System.out.print(nums[i]+" ");
		}
		System.out.println();
	}

	public static long gcd(long a, long b)
	{
		if(b==0)
			return a;
		return gcd(b,a%b);
	}

	public static long sum_of_digits(long n)
	{
		long sum=0;
		while(n>0)
		{
			sum+=n%10;
			n/=10;
		}
		return sum;
	}

	public static void solve()
	{
		int n = scan.nextInt();
		int[] nums = new int[n];
		long k = scan.nextLong();
		for(int i=0;i<n;i++)
		{
			nums[i]=scan.nextInt();
		}
		int[] first = new int[n];
		int[] second = new int[n];
		int max = nums[0];
		for(int i=0;i<n;i++)
		{
			if(max<nums[i])
				max = nums[i];
		}
		for(int i=0;i<n;i++)
		{
			first[i]=max-nums[i];
		}
		max = first[0];
		for(int i=0;i<n;i++)
		{
			if(first[i]>max)
				max = first[i];
		}
		for(int i=0;i<n;i++)
			second[i]=max-first[i];
		if(k%2==0)
		{
			for(int i=0;i<n;i++)
			{
				System.out.print(second[i]+" ");
			}
			System.out.println();
		}
		else
		{
			for(int i=0;i<n;i++)
			{
				System.out.print(first[i]+ " ");
			}
			System.out.println();
		}
	}
	public static void main(String[] args)
	{
		
		int t = scan.nextInt();
		//int t = 1;
		while(t-->0)
		{
			solve();
		}
	}
}