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 B {
    public static void main(String[] args){
        FastReader in = new FastReader();
        int t = in.nextInt();
        while(t-- > 0){
            long n = in.nextLong();
            long k = in.nextLong();
            int[] a = in.readArray(n);
            long max = maxi(a);
                for(int i = 0; i < n; i++){
                   a[i] = (int)max - a[i];
                }
                if(k % 2 != 0){
                    for(int i = 0; i < n; i++){
                        System.out.print(a[i] +" ");
                    }
                    System.out.println();
                } else{
                    long max2 = maxi(a);
                    for(int i = 0; i < n; i++){
                        a[i] = (int)max2 - a[i];
                    }
                    for(int i = 0; i < n; i++){
                        System.out.print(a[i] + " ");
                    }
                    System.out.println();
                }
        }

    }
    static long maxi(int[] a){
        long max = Integer.MIN_VALUE;
        for(int i = 0; i < a.length; i++){
            if(a[i] > max){
                max = a[i];
            }
        }
        return max;
    }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        int[] readArray(long n){
            int[] a = new int[(int)n];
            for(int i = 0; i < n; i++){
                a[i] = nextInt();
            }
            return a;
        }
    }
}