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:
//created by Whiplash99
import java.io.*;
import java.util.*;
public class B
{
    private static StringBuilder sb=new StringBuilder();
    private static void operation(long[] a, long[] b, int N)
    {
        long max=a[0];
        for(int i=0;i<N;i++) if(a[i]>max) max=a[i];
        for(int i=0;i<N;i++) b[i]=max-a[i];
    }
    private static void answer(long[] a, int N)
    {
        for(long tmp:a) sb.append(tmp).append(" ");
        sb.append("\n");
    }
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        int T=Integer.parseInt(br.readLine().trim());

        while (T-->0)
        {
            String[] s=br.readLine().trim().split(" ");
            N=Integer.parseInt(s[0]);
            long K=Long.parseLong(s[1]);

            long[] a=new long[N];
            long[] b=new long[N];
            s=br.readLine().trim().split(" ");
            for(i=0;i<N;i++) a[i]=Integer.parseInt(s[i]);

            operation(a,b,N); K--;
            if(K==0)
            {
                answer(b,N);
                continue;
            }

            operation(b,a,N); K--;
            if(K==0)
            {
                answer(a, N);
                continue;
            }

            operation(a,b,N); K--;
            if(K==0)
            {
                answer(b,N);
                continue;
            }

            operation(b,a,N); K--;
            if(K==0)
            {
                answer(a, N);
                continue;
            }

            operation(a,b,N); K--;
            if(K%2==0) answer(b,N);
            else answer(a,N);
        }
        System.out.println(sb);
    }
}