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 All_Girls_Are_Bitches{
	
	public static void main(String[] args) {
		FastScanner in=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		int t=in.nextInt();
		while(t-->0)
		solve(in,out);
		out.close();
	}

    static void solve(FastScanner in,PrintWriter out){
       int n=in.nextInt();
       long k=in.nextLong();
       int a[]=new int[n];
       int max=Integer.MIN_VALUE;
       for(int i=0;i<n;i++){
           a[i]=in.nextInt(); max=Math.max(max,a[i]);
       }
       int a1[]=new int[n];
       int a2[]=new int[n];
       int max1=Integer.MIN_VALUE;
       for(int i=0;i<n;i++) { a1[i]=max-a[i]; max1=Math.max(max1,a1[i]); }
       for(int i=0;i<n;i++) { a2[i]=max1-a1[i];  }
       if(k%2==1){
           for(int i=0;i<n;i++) out.print(a1[i]+" "); out.println();
       }
       else{
            for(int i=0;i<n;i++) out.print(a2[i]+" "); out.println();
       }
       
    }    

	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

	
}