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.BufferedReader;
import java.io.InputStreamReader;

public class B {
    public static void main(String[] args) {
        try {
            BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
            int t = Integer.parseInt(in.readLine());
            for (int i = 0; i < t; i++) {
                String[] s = in.readLine().split(" ");
                int n = Integer.parseInt(s[0]);
                long k = Long.parseLong(s[1]);
                s = in.readLine().split(" ");
                long[] v = new long[n];
                for (int j = 0; j < s.length; j++) {
                    v[j] = Integer.parseInt(s[j]);
                }
                k = (k % 2) + 2;
                for (int j = 0; j < k; j++) {
                    long d = Long.MIN_VALUE;
                    for (long l : v) {
                        if (l > d) d = l;
                    }
                    for (int l = 0; l < n; l++) {
                        v[l] = d - v[l];
                    }
                }
                StringBuilder sb = new StringBuilder();
                for (int j = 0; j < n; j++) {
                    if (j > 0) sb.append(" ");
                    sb.append(v[j]);
                }
                System.out.println(sb.toString());
            }
            in.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}