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.*;
import java.lang.*;
import java.io.*;

public class Solution{
  public static void main(String[] args) throws IOException{
    StringBuilder print = new StringBuilder();
    BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
    long t = Long.parseLong(input.readLine());
    while(t-- > 0){
      StringTokenizer st = new StringTokenizer(input.readLine());
      int n = Integer.parseInt(st.nextToken());
      long k = Long.parseLong(st.nextToken());
      st = new StringTokenizer(input.readLine());
      long maxNum = -1000000007;
      long minNum = 1000000007;
      long[] array = new long[n];
      for(int i = 0; i < n; i++){
        long a = Long.parseLong(st.nextToken());
        array[i] = a;
        if(a > maxNum){
          maxNum = a;
        }
        if(a < minNum){
          minNum = a;
        }
      }
      long addition = 0;
      if(n == 1){
        print.append("0 ");
      }else{
        if(k%2 == 0){
          // normal + negsSum
          addition = 0 - minNum;


          for(int i = 0; i < n; i++){
            //System.out.printf("i: %d, array[i]: %d, addition: %d%n", i, array[i], addition);
            long newArrayNum = addition + array[i];
            print.append(newArrayNum + " ");
          }

        }else{
          // max + negsSum - normal
          addition = maxNum;

          for(int i = 0; i < n; i++){
            //System.out.printf("i: %d, array[i]: %d, addition: %d, maxNeg: %d, maxNum: %d%n", i, array[i], addition, maxNeg, maxNum);
            long newArrayNum = addition - array[i];
            print.append(newArrayNum + " ");
          }
        }
      }
      print.append("\n");
    }
    System.out.println(print.toString());
  }
}