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.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Random;
import java.util.Scanner;

public class TaskB {

	static Scanner in = new Scanner(System.in);
	static PrintWriter w = new PrintWriter(System.out);

	public static void main(String[] args) {
		int t = Integer.parseInt(in.nextLine());
		outer: while (t-- > 0) {
			int n = in.nextInt();
			long k = in.nextLong();
			long[] arr = new long[n];
			long max = Long.MIN_VALUE;
			for (int i = 0; i < n; i++) {
				arr[i] = in.nextLong();
				max = Math.max(max, arr[i]);
			}
			long newMax = Long.MIN_VALUE;
			for (int i = 0; i < n; i++) {
				arr[i] = max - arr[i];
				newMax = Math.max(newMax, arr[i]);
			}
			k--;
			max = newMax;
			if (newMax == 0) {
				solve(arr);
			} else if (k % 2 == 0) {

				solve(arr);
			} else {
				for (int i = 0; i < n; i++) {
					arr[i] = max - arr[i];
				}
				solve(arr);
			}
		}
		w.flush();
		w.close();
	}

	private static void solve(long[] arr) {
		for (int i = 0; i < arr.length; i++) {
			w.print(arr[i] + " ");
		}
		w.println();
	}

	private static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	private static void shuffleArray(long[] arr) {
		int n = arr.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			long tmp = arr[i];
			int randomPos = i + rnd.nextInt(n - i);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}
}