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 A {
    public static void main(String args[]) throws IOException{
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t=sc.nextInt();
        while(t--!=0){
            int n = sc.nextInt();
            long k = sc.nextLong();
            int[] arr = new int[n];
            int max = Integer.MIN_VALUE;
            for(int i=0;i<n;i++){
                arr[i]=sc.nextInt();
                if(arr[i]>max)
                    max=arr[i];
            }
            if(k%2==0){
                for(int i=0;i<2;i++){
                    int temp=Integer.MIN_VALUE;
                    for(int j = 0;j<n;j++){
                        arr[j]=max-arr[j];
                        if(i==1){
                        pw.print(arr[j]+" ");
                        }
                        if(arr[j]>temp)
                            temp=arr[j];
                    }
                    
                    max = temp;
                }
                pw.println();
            }else{
                   for(int j = 0;j<n;j++){
                    arr[j]=max-arr[j];
                    pw.print(arr[j]+" ");   
                }
                   pw.println();
                
            }
        }
        pw.close();
    }
    public static int gcd(int a,int b){
        int ans=1;
        for(int i = 1; i <= a && i <= a; i++)
        {
            if(a%i==0 && b%i==0)
                ans = i;
        }
        return ans;
    }
    static class Scanner {
	StringTokenizer st;
	BufferedReader br;
        
	public Scanner(InputStream s) {
		br = new BufferedReader(new InputStreamReader(s));
	}
        
	public Scanner(String file) throws FileNotFoundException {
		br = new BufferedReader(new FileReader(file));
        }
	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

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

	public String nextLine() throws IOException {
		return br.readLine();
	}

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

	public boolean ready() throws IOException {
		return br.ready();
	}

    }
}