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.*;
import java.util.*;

public class Main{
    public static void main(String[] args){
        InputReader in = new InputReader(System.in);
        int t = in.nextInt();
        while(t-- > 0){
            int n = in.nextInt();
            int[] a = new int[n];
            long k = in.nextLong();
            int max = 0, min = 0;
            for(int i = 0; i < n; i++){
                a[i] = in.nextInt();
                if(a[max] < a[i]){
                    max = i;
                }
                if(a[min] > a[i]){
                    min = i;
                }
            }
            solve(a, k, min, max);
            for(int v : a){
                System.out.print(v + " ");
            }
            System.out.println();
        }
    }
    static void solve(int[] a, long k, int min, int max){
        int m = a[max];
        for(int i = 0; i < a.length; i++){
            a[i] = m - a[i];
        }
        if((k&1) == 0){
            m = a[min];
            for(int i = 0; i < a.length; i++){
                a[i] = m - a[i];
            }
        }
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
 
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }
 
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
 
    public int nextInt() {
        return Integer.parseInt(next());
    }
    
    long nextLong() 
    { 
        return Long.parseLong(next()); 
    } 
  
    double nextDouble() 
    { 
        return Double.parseDouble(next()); 
    } 
  
    String nextLine() 
    { 
        String str = ""; 
        try
        { 
            str = reader.readLine(); 
        } 
        catch (IOException e) 
        { 
            e.printStackTrace(); 
        } 
        return str; 
    } 
 
}