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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int T = in.nextInt();
            while (T-- > 0)
            {
                solveOne(in, out);
            }
        }

        private void solveOne(Scanner in, PrintWriter out)
        {
            int N = in.nextInt();
            long K = in.nextLong();
            int nums[] = CPUtils.readIntArray(N, in);
            int max = CPUtils.maxArray(nums);

            for (int idx = 0; idx < N; idx++)
            {
                nums[idx] = max - nums[idx];
            }

            if (K % 2 == 1)
            {
                CPUtils.printIntArrayNoLastSpace(nums, out);
            } else
            {
                max = CPUtils.maxArray(nums);
                for (int idx = 0; idx < N; idx++)
                {
                    nums[idx] = max - nums[idx];
                }
                CPUtils.printIntArrayNoLastSpace(nums, out);
            }
            out.println();
        }

    }

    static class CPUtils
    {
        public static int[] readIntArray(int size, Scanner in)
        {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
            {
                array[i] = in.nextInt();
            }
            return array;
        }

        public static void printIntArrayNoLastSpace(int[] array, PrintWriter out)
        {
            StringBuilder stringBuilder = new StringBuilder();
            for (int i = 0; i < array.length; i++)
            {
                if (i == array.length - 1)
                    stringBuilder.append(array[i]);
                else
                    stringBuilder.append(array[i] + " ");
            }
            out.print(stringBuilder.toString());
        }

        public static int maxArray(int[] array)
        {
            int max = Integer.MIN_VALUE;
            for (int i = 0; i < array.length; i++)
            {
                max = Math.max(max, array[i]);
            }
            return max;
        }

    }
}