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 B{
    final static String alpha = "ABCDEFGHIJKLMNOPQRSTUVWXYZ".toLowerCase();//.toCharArray();
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){br = new BufferedReader(new InputStreamReader(System.in));}
        String next(){while (st == null || !st.hasMoreElements()){try{st = new StringTokenizer(br.readLine());}catch (IOException  e){e.printStackTrace();}}return st.nextToken();}
        int nextInt(){return Integer.parseInt(next());}
        long nextLong(){return Long.parseLong(next());}
        double nextDouble(){return Double.parseDouble(next());}
        int[] readArray(int n){int[] a=new int[n];for (int i=0; i<n; i++) a[i]=nextInt();return a;}
        long[] readLongArray(int n){long[] a=new long[n];for (int i=0; i<n; i++) a[i]=nextLong();return a;}
        String nextLine(){String str = "";try{str = br.readLine();}catch (IOException e){e.printStackTrace();}return str;}
    }
    static int getGcd(int n1,int n2){
        while(n1 != n2){
            if(n1 > n2) n1 -= n2;
            else n2 -= n1;
        }
        return n1;
    }
    static boolean isSorted(int[] arr, int n){
        for(int i=1;i<n;i++){
            if(arr[i]<arr[i-1]) return false;
        }
        return true;
    }
    static boolean isPrime(long n){
        if(n==2) return true;
        else if(n%2==0) return false;
        for(int i=3;i<=n/2;i+=2){
            if(n%i==0) return false;
        }
        return true;
    }
    static boolean isPrime(int n){
        if(n==2) return true;
        else if(n%2==0) return false;
        for(int i=3;i<=n/2;i+=2){
            if(n%i==0) return false;
        }
        return true;
    }
    static void printArray(int[] arr){
        for(int x:arr){
            System.out.print(x+" ");
        }
        System.out.println();
    }
    static long Fact(int n){
        //int p=1000000007;
        long result = 1;
        for (int i = 1; i <= n; i++) result = (result*i);
        //for (int i = 1; i <= n; i++) result = (result*i)%p;
        return result;
    }
    public static void main(String[] args) throws NumberFormatException, IOException {
        FastReader s = new FastReader();
        PrintWriter pw = new PrintWriter(System.out,true);
        int t = s.nextInt();
        int n,max,min,mini,temp;
        long k;
        String str;
        while(t-- > 0){
            n=s.nextInt();k=s.nextLong();
            int[] a = new int[n];
            a[0]=s.nextInt();
            max=a[0];min=a[0];mini=0;
            for(int i=1;i<n;i++){
                a[i]=s.nextInt();
                max=Math.max(a[i],max);
                if(a[i]<min){
                    min=a[i];mini=i;
                }
            }
            for(int i=0;i<n;i++){
                a[i]=max-a[i];
            }
            if(k%2==0) {
                temp=a[mini];
                for(int i=0;i<n;i++){
                    a[i]=temp-a[i];
                }
            }
            printArray(a);
        }
    }
}