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.*;

public class B {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        StringBuilder sb = new StringBuilder();
        int t = Integer.parseInt(br.readLine());
        for (int i = 0; i < t; i++) {
            String[] nk = br.readLine().split(" ");
            int n = Integer.parseInt(nk[0]);
            long k = Long.parseLong(nk[1]);
            int max = Integer.MIN_VALUE;
            int min = Integer.MAX_VALUE;
            String[] strArr = br.readLine().split(" ");
            int[] nums = new int[n];
            for (int j = 0; j < n; j++) {
                nums[j] = Integer.parseInt(strArr[j]);
                max = Math.max(nums[j], max);
                min = Math.min(nums[j], min);
            }

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

            if(k % 2 == 1){
                for (int j = 0; j < n; j++) {
                    sb.append(nums[j]).append(" ");
                }
            }else{
                for (int j = 0; j < n; j++) {
                    sb.append((max - min) - nums[j]).append(" ");
                }
            }
            sb.append("\n");
        }
        bw.write(sb.toString());
        bw.flush();
        bw.close();
        br.close();
    }
}