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.util.*;
import java.io.*;

public class Main {
    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);
    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    //    long mod = 998244353;
    long mod = (long)1e9+7;
    int maxn = 200000+5;
    int[] head = new int[maxn], tail = new int[maxn];
    int[][] interval = new int[maxn][2];
    public static void main(String[] args) throws Exception {
        Main main = new Main();
        int t = sc.nextInt();
//        int t = 1;
        /*
        while(t-->0){
            main.solve();
        }*/
        for(int i=1; i<=t; i++){
            main.solve();
        }
        out.flush();
    }

    void solve() throws Exception {
        int n = neInt();
        long[] arr = new long[n];
        long maxi = Long.MIN_VALUE/2, k = neLong();
        for(int i=0; i<n; i++){
            arr[i] = neLong();
            maxi = Math.max(maxi, arr[i]);
        }
        k --;
        long mx = Long.MIN_VALUE/2;
        for(int i=0; i<n; i++){
            arr[i] = maxi-arr[i];
            mx = Math.max(mx, arr[i]);
        }
        for(int i=0; i<n; i++){
            if(k%2==0) out.print(arr[i]);
            else out.print(mx-arr[i]);
            out.print(" ");
        }
        out.println();
    }
    String neS(){
        return sc.next();
    }
    int neInt(){
        return Integer.parseInt(sc.next());
    }
    long neLong(){
        return Long.parseLong(sc.next());
    }

    int paIn(String s){return Integer.parseInt(s);}

}