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.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;

public class B1 {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
     new B1();
	} 
	B1() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(new OutputStreamWriter(System.out));
		int t = Integer.parseInt(in.readLine());
    	for(int i = 0;i<t;i++) solve();
    	out.close();
	}
	void solve() throws IOException {
		String[ ] s = in.readLine().trim().split("\\s+");
		int n = Integer.parseInt(s[0]), max = Integer.MIN_VALUE, min = Integer.MAX_VALUE;
		long k = Long.parseLong(s[1]);
		int[] a = new int[n];
		s = in.readLine().trim().split("\\s+");
		for(int i = 0;i<n;i++) {
			 a[i] = Integer.parseInt(s[i]);
			 max = Math.max(max, a[i]);
			 min = Math.min(min, a[i]);
		}
		int[] a1 = new int[n], a2 = new int[n];
		int max1 = max-min;
		for(int i = 0;i<n;i++) {
			a1[i] = max-a[i];
			a2[i] = max1-a1[i];
		}
		if(k%2==0) {
			for(int i:a2) {
				out.print(i);
                out.print(' ');
			}
		} else {
			for(int i:a1) {
				out.print(i);
                out.print(' ');
			}
		}
		out.print('\n');
	}
	BufferedReader in;
	 PrintWriter out;
}