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 B {
    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader() throws FileNotFoundException {
            // reader = new BufferedReader(new FileReader("count.in"));
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        String next() { // reads in the next String
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() { // reads in the next int
            return Integer.parseInt(next());
        }

        public long nextLong() { // reads in the next long
            return Long.parseLong(next());
        }

        public double nextDouble() { // reads in the next double
            return Double.parseDouble(next());
        }

        public int[] nextIntArr(int size) {
            int[] arr = new int[size];
            for (int i = 0; i < size; i++) arr[i] = nextInt();
            return arr;
        }

        public long[] nextLongArr(int size) {
            long[] arr = new long[size];
            for (int i = 0; i < size; i++) arr[i] = nextLong();
            return arr;
        }

        public double[] nextDoubleArr(int size) {
            double[] arr = new double[size];
            for (int i = 0; i < size; i++) arr[i] = nextDouble();
            return arr;
        }
    }

    public static void main(String[] args) throws IOException, FileNotFoundException {
        InputReader in = new InputReader();
        PrintWriter pw = new PrintWriter(System.out);
        int cc = in.nextInt();
        for (int cases = 1; cases <= cc; cases++) {
            long n = in.nextLong();
            long k = in.nextLong();

            boolean hasNeg = false;
            long[] arr = new long[(int) n];
            long max = (long) Integer.MIN_VALUE;
            for (int i = 0; i < n; i++) {
                arr[i] = in.nextLong();
                if (arr[i] <= 0) hasNeg = true;
                max = Math.max(max, arr[i]);
            }
            if (n == 1) {
                pw.println(0);
                continue;
            }
            long nm = (long) Integer.MIN_VALUE;

            k--;
            for (int i = 0; i < n; i++) {
                arr[i] = max - arr[i];
                nm = Math.max(arr[i], nm);
            }

            if ((k & 1) == 0) {
                for (int i = 0; i < n; i++) {
                    pw.print(arr[i] + " ");
                }
            } else {
                for (int i = 0; i < n; i++) {
                    pw.print((nm - arr[i]) + " ");
                }
            }
            pw.println();
        }

        pw.close();
    }
}