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.util.Arrays;
import java.util.Scanner;
import java.util.stream.Collectors;

public class Main {

  /**
   * Omkar and Infinity Clock
   * https://codeforces.com/problemset/problem/1392/B
   */
  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    final int testCases = s.nextInt();
    s.nextLine();
    for (int i = 0; i < testCases; i++) {
      s.nextInt(); // length of the array
      final long numOfOperations = s.nextLong();
      s.nextLine();
      final int[] arr = Arrays.stream(s.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
      process(numOfOperations, arr);
    }
  }

  private static void process(long numOfOperations, int[] arr) {
    int max = Arrays.stream(arr).max().orElse(Integer.MIN_VALUE);
    int nextMax = Integer.MIN_VALUE;
    if (numOfOperations % 2 == 0) {
      numOfOperations = 2;
    } else {
      numOfOperations = 1;
    }
    for (int i = 0; i < numOfOperations; i++) {
      for (int j = 0; j < arr.length; j++) {
        arr[j] = max - arr[j];
        if (numOfOperations > 1) {
          if (arr[j] > nextMax) {
            nextMax = arr[j];
          }
        }
      }
      max = nextMax;
    }
    System.out.println(Arrays.stream(arr).mapToObj(String::valueOf).collect(Collectors.joining(" ")));
  }
}