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.Scanner;

public class Main {

    public static void main(String args[]) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        while (t-- > 0) {
            int n = scanner.nextInt();
            long k = scanner.nextLong();
            long[] a = new long[n];
            long largest = Integer.MIN_VALUE;
            long smallest = Integer.MAX_VALUE;

            for (int i=0; i<n;i++) {
                a[i] = scanner.nextInt();
                smallest = Math.min(smallest, a[i]);
                largest = Math.max(largest, a[i]);
            }
            if (k%2 == 1) {
                doOpn(a, n, largest);
            } else if (k%2 == 0) {
                doOpn(a, n, largest);
                doOpn(a, n, largest-smallest);
            }

            for (int i=0; i<n; i++) {
                System.out.print(a[i] + " ");
            }
            System.out.println();
        }
    }

    private static void doOpn(long[] a, int n, long d) {
        for (int i=0; i<n; i++) {
            a[i] = d-a[i];
        }
    }

}