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 Main{
    public static void main(String[] args) {
        FastReader fs=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int t=1;
        t=fs.nextInt();
        for(int i=1;i<=t;i++) {
        	Main m=new Main();
            m.solve(i,out,fs);
        }
        out.close();
    }
    public void solve(int t,PrintWriter out,FastReader fs){
    	int n=fs.nextInt();
    	long k=fs.nextLong();
    	long a[]=fs.nextLongArray(n);
    	long max=Long.MIN_VALUE;
    	for(int i=0;i<n;i++) {
    		max=Long.max(max,a[i]);
    	}
    	long od[]=new long[n];
    	long max2=Long.MIN_VALUE;
    	for(int i=0;i<n;i++) {
    		od[i]=max-a[i];
    		max2=Long.max(max2,od[i]);
    	}
    	long ev[]=new long[n];
    	for(int i=0;i<n;i++) {
    		ev[i]=max2-od[i];
    	}
    	if(k%2==1) { 
    		for(long i:od) {
    			out.print(i+" ");
    		}
    	}else {
    		for(long i:ev) {
    			out.print(i+" ");
    		}
    	}
    	out.println();
    }
}
class FastReader{
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st=new StringTokenizer("");
    String next(){
        while(!st.hasMoreTokens()){
            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());
    }
    int[] nextIntArray(int n){
        int a[]=new int[n];
        for(int i=0;i<n;i++)a[i]=nextInt();
        return a;
    }
    long[] nextLongArray(int n){
        long a[]=new long[n];
        for(int i=0;i<n;i++)a[i]=nextInt();
        return a;
    }
    char[] nextCharArray(){
        char a[]=next().toCharArray();
        return a;
    }
}