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.io.PrintStream;
import java.util.List;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * 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);
        BOmkarAndInfinityClock solver = new BOmkarAndInfinityClock();
        solver.solve(1, in, out);
        out.close();
    }

    static class BOmkarAndInfinityClock {
        public void solve(int testNumber, Scanner sc, PrintWriter out) {
            int t = sc.nextInt();
            //sc.nextLine();
            for (int a = 0; a < t; a++) {
                int n = sc.nextInt();
                long k = sc.nextLong();
                //sc.nextLine();
                int max = Integer.MIN_VALUE;
                List<Integer> list = new ArrayList<>();
                for (int i = 0; i < n; i++) {
                    int temp = sc.nextInt();
                    list.add(temp);
                    max = Math.max(max, temp);
                }
                k--;
                for (int i = 0; i < n; i++) {
                    list.set(i, max - list.get(i));
                }

                long i = k & 1;
                if (i == 1) {
                    int newMax = findMax(list);
                    for (int q = 0; q < n; q++) {
                        list.set(q, newMax - list.get(q));
                    }
                }

                for (int j : list) {
                    System.out.print(j + " ");
                }
                System.out.println();
            }
        }

        public static int findMax(List<Integer> list) {
            int max = Integer.MIN_VALUE;
            for (int i : list) {
                max = Math.max(max, i);
            }

            return max;
        }

    }
}