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.*;

public class OmkarAndInfinityClock{
  public static void main(String[] args){
    Scanner gd = new Scanner(System.in);
    int tt = IO.ri();
    int n;
    String k;
    long[] arr;
    long max;
    long min;
    while(tt>0){
      n = IO.ri();
      k = IO.rs();
      int k_last = Integer.parseInt(Character.toString(k.charAt(k.length()-1)));
      arr = IO.ral(n);
      if(k_last%2==0){
        max = UT.max_arr(arr);
        min = UT.min_arr(arr);
        for(int i=0;i<n-1;i++){
          arr[i] = (max-arr[i]);
          arr[i] = ((max-min) - arr[i]);
          IO.pf("%d ",arr[i]);
        }
        arr[arr.length-1] = (max - arr[arr.length-1]);
        arr[arr.length-1] = ((max-min) - arr[arr.length-1]);
        IO.pf("%d",arr[arr.length-1]);
        IO.pf("\n");
      }
      else{
        max = UT.max_arr(arr);
        for(int i=0;i<n-1;i++){
          arr[i] = (max-arr[i]);
          IO.pf("%d ",arr[i]);
        }
        arr[arr.length-1] = (max - arr[arr.length-1]);
        IO.pf("%d",arr[arr.length-1]);
        IO.pf("\n");
      }
      tt--;
    }
  }
}

// Template
class IO{
  static Scanner gd = new Scanner(System.in);
  public static long rl(){
    return gd.nextLong();
  }
  public static int ri(){
    return gd.nextInt();
  }
  public static String rs(){
    return gd.next();
  }
  public static int[] rai(int len){
    int[] temp = new int[len];
    for(int i=0;i<len;i++){
      temp[i] = gd.nextInt();
    }
    return temp;
  }
  public static long[] ral(int len){
    long[] temp = new long[len];
    for(int i=0;i<len;i++){
      temp[i] = gd.nextLong();
    }
    return temp;
  }
  public static String[] ras(int len){
    String[] temp = new String[len];
    for(int i=0;i<len;i++){
      temp[i] = gd.next();
    }
    return temp;
  }
  public static void pf(String format,Object... args){
    System.out.printf(format,args);
  }
  public static void pl(Object data){
    System.out.println(data);
  }
  public static void pai(int arr[]){
    for(int i=0;i<arr.length;i++){
      System.out.printf("%d ",arr[i]);
    }
    System.out.println();
  }
  public static void pal(long arr[]){
    for(int i=0;i<arr.length;i++){
      System.out.printf("%d ",arr[i]);
    }
    System.out.println();
  }
  public static void pas(String arr[]){
    for(int i=0;i<arr.length;i++){
      System.out.printf("%s ",arr[i]);
    }
    System.out.println();
  }
}

class UT{
  public static long fact(long k){
    if(k==1){
      return 1;
    }
    else{
      return k*fact(k-1);
    }
  }
  public static long arr_sum(long[] arr){
    long sum = 0;
    for(int i=0;i<arr.length;i++){
      sum+=arr[i];
    }
    return sum;
  }
  public static long min_arr(long[] arr){
    long min = arr[0];
    for(int i=0;i<arr.length;i++){
      if(arr[i]<min){
        min = arr[i];
      }
    }
    return min;
  }
  public static long max_arr(long[] arr){
    long max = arr[0];
    for(int i=0;i<arr.length;i++){
      if(arr[i]>max){
        max = arr[i];
      }
    }
    return max;
  }
}