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.*;
import java.math.*;
public final class codeForces
{
    static long gcd(long a,long b)
    {
        if(b==0)return a;
        else return gcd(b,a%b);
    }

    public static void main(String args[])throws IOException
    {
        // Scanner in=new Scanner(System.in);
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        //Integer.parseInt(in.readLine());
        //Integer.parseInt(st.nextToken());
        //Long.parseLong(in.readLine());
        //Long.parseLong(st.nextToken());
        /* StringTokenizer st;
        st=new StringTokenizer(in.readLine()); */
        int t=Integer.parseInt(in.readLine());
        while(t-->0)
        {
            StringTokenizer st;
            st=new StringTokenizer(in.readLine()); 
            int N=Integer.parseInt(st.nextToken());
            long K=Long.parseLong(st.nextToken());
            long A[]=new long[N];
            st=new StringTokenizer(in.readLine()); 
            long max=-1000000000;
            for(int i=0; i<N; i++)
            {
                A[i]=Long.parseLong(st.nextToken());
                if(A[i]>max)max=A[i];
            }
            long mx=-1000000000;
            for(int i=0; i<N;  i++)
            {
                A[i]=max-A[i];
                if(A[i]>mx)mx=A[i];

            }
            if(K%2==0)
            {
               for(int i=0; i<N;  i++)
            {
                A[i]=mx-A[i];
                

            } 
            }
            
            for(int i=0; i<N; i++)
            {
              
               System.out.print((A[i])+" ");
            }
            System.out.println();

        }
    }
}