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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;



public class experiments
{
	public static void main(String args[]) throws IOException
	{
		
		FastScanner fs = new FastScanner();
		int T = fs.nextInt();
		while(T-->0)
		{
			int n = fs.nextInt();long k = fs.nextLong();
			int arr[] = fs.arrayIn(n);
			int min=Integer.MAX_VALUE,max=Integer.MIN_VALUE;
			for(int i:arr) if(max<i) max = i;
			for(int i:arr) if(min>i) min = i;
			k--;
			for(int i=0; i<n; i++)
			{
				arr[i] = max-arr[i];
			}
			if(k%2==0)
			{
				for(int i=0; i<n; i++)
				{
					System.out.print(arr[i]+" ");
				}
			}
			else
			{
				for(int i=0; i<n; i++)
				{
					System.out.print((max-min)-arr[i]+" ");
				}
			}
				
			System.out.println();
		}
		
	}
	
	

	static final Random random = new Random();
	
	static void ruffleSort(int arr[])
	{
		int n = arr.length;
		for(int i=0; i<n; i++)
		{
			int j = random.nextInt(n),temp = arr[j];
			arr[j] = arr[i];
			arr[i] = temp;
			
		}
		Arrays.sort(arr);
	}
	

	static class Pairs implements Comparable<Pairs>
	{
		int value,index;
		Pairs(int value, int index)
		{
			this.value = value;
			this.index = index;
		}
		public int compareTo(Pairs p)
		{
			return Integer.compare(value,p.value);
		}
	}
}
class FastScanner
{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer str = new StringTokenizer("");
	
	String next() throws IOException
	{
		while(!str.hasMoreTokens())
			str = new StringTokenizer(br.readLine());
		
		return str.nextToken();
	}
	
	char nextChar() throws IOException {
		return next().charAt(0);
	}

	int nextInt() throws IOException
	{
		return Integer.parseInt(next());
	}
	
	float nextfloat() throws IOException
	{
		return Float.parseFloat(next());
	}
	
	double nextDouble() throws IOException
	{
		return Double.parseDouble(next());
	}
	long nextLong() throws IOException
	{
		return Long.parseLong(next());
	}
	byte nextByte() throws IOException 
	{
		return Byte.parseByte(next());
	}
	int [] arrayIn(int n) throws IOException
	{
		int  arr[] = new int[n];
		for(int i=0; i<n; i++)
		{
			arr[i] = nextInt();
		}
		return arr;
	}
}