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 { 

	static void println(Object o){
		System.out.println(o);
	}

	public static void main(String[] args){
		
		FastScanner sc = new FastScanner();
		int t = sc.nextInt();
		while(t-- > 0){
			int n = sc.nextInt(), max = Integer.MIN_VALUE;
			int a[] = new int[n];
			long k = sc.nextLong();
			for(int i = 0; i<n; i+=1){
				a[i] = sc.nextInt();
				if(a[i] > max){
					max = a[i];
				}
			}
			for(int i = 0; i<n; i+=1){
				a[i] = max - a[i];
			}
			if(k>1 && (k-1)%2 == 1){
				max = Integer.MIN_VALUE;
				for(int i = 0; i<n; i+=1){
					if(a[i] > max){
						max = a[i];
					}
				}
				for(int i = 0; i<n; i+=1){
					a[i] = max - a[i];
				}
			}
			StringBuilder res = new StringBuilder();
			for(int i = 0; i<n; i+=1){
				res.append(a[i]);
				res.append(' ');
			}
			println(res);

		}
		
	}
}

class FastScanner {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = null;

		String nextLine(){
			String s = "";
			try{
				s = br.readLine();
			}
			catch(IOException e){
				e.printStackTrace();
			}
			return s;
		}

		String next(){
			while(st == null || !st.hasMoreTokens()){
				try{
					st = new StringTokenizer(br.readLine());
				}
				catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		int nextInt(){
		    return Integer.parseInt(this.next());
		}
		
		long nextLong(){
		    return Long.parseLong(this.next());
		}

}