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.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;

public class B {

	public static void main(String[] srgs) throws NumberFormatException, IOException {

		Scanner nik = new Scanner(System.in);

		int t = nik.nextInt();

		StringBuilder st = new StringBuilder();
		while (t-- > 0) {

			int n = nik.nextInt();
			long k = nik.nextLong() % 2;

			long[] a = new long[n];

			for (int i = 0; i < n; i++) {
				a[i] = nik.nextLong();
			}

			if (k == 0) {
				find(a);
				find(a);

			} else {
				find(a);
			}

			for (long val : a) {
				st.append(val + " ");
			}
			st.append("\n");

		}
		System.out.println(st);
	}

	private static void find(long[] a) {

		long max = a[0];

		for (long val : a) {
			max = Math.max(max, val);
		}

		for (int i = 0; i < a.length; i++) {
			a[i] = max - a[i];
		}

	}
}