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[]){
        Solver s=new Solver();
        s.run();
    }
}



class Solver {
    StringBuilder out=new StringBuilder(40000000);
    FastReader in=new FastReader();
    public long pow(long a, long b){
        long ans=1;
        while(b>0){
            if(b%2==1){
                ans*=a;
            }
            a*=a;
            b/=2;
        }
        return ans;
    }
    public int[] getIntArray(int n){
        int arr[]=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=in.nextInt();
        }
        return arr;
    }


    int mod=(int)1e9 +7;

    public void solve(){
        int n=in.nextInt();
        long arr[]=new long[n], K=in.nextLong();
        Long max=Long.MIN_VALUE;
        for(int i=0;i<n;i++){
            arr[i]=in.nextLong();
            max=Math.max(arr[i], max);
        }
        long temp;
        long p=-1,k=0;
        while(true){
            temp=Long.MIN_VALUE;
            for(int i=0;i<n;i++){
                arr[i]=max-arr[i];
                temp=Math.max(temp, arr[i]);
            }
            // System.out.println(k+" "+temp+" ");
            if(++k==K || temp == 0 || (K-k)%2==0){
                break;
            }
            max=temp;
        }
        for(int i=0;i<n;i++){
            out.append(arr[i]).append(' ');
        }
        

    }
    public void run(){
        int t=in.nextInt();
        for(int i=0;i<t;i++){
            solve();
            out.append('\n');
        }
        System.out.println(out);
    }
}
    
    
class FastReader { 
    final private int BUFFER_SIZE = 1 << 16; 
    private DataInputStream din; 
    private byte[] buffer; 
    private int bufferPointer, bytesRead; 
    
    public FastReader() { 
        din = new DataInputStream(System.in); 
        buffer = new byte[BUFFER_SIZE]; 
        bufferPointer = bytesRead = 0; 
    } 
    
    public FastReader(String file_name) throws IOException{ 
        din = new DataInputStream(new FileInputStream(file_name)); 
        buffer = new byte[BUFFER_SIZE]; 
        bufferPointer = bytesRead = 0; 
    } 
    
    public String nextLine() { 
        try{
            byte[] buf = new byte[10000]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        }catch (Exception e){
            System.out.println(e.getMessage());
            return null;
        }
    } 
    
    public int nextInt()  { 
        int ret = 0; 
        try {
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) c = read(); 
            do{ 
                ret = ret * 10 + c - '0'; 
            } while ((c = read()) >= '0' && c <= '9'); 
            if (neg) return -ret; 
            return ret; 
        } catch (Exception e) {
            System.out.println(e.getMessage());
                return -1;
            }
        } 
    
    public long nextLong()   {         
        try {
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret;
        } catch (Exception e) {
            System.out.println(e.getMessage());
            return -1;
        }
    }
    
    public double nextDouble()  {
        try {
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) c = read();     
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (c == '.') { 
                while ((c = read()) >= '0' && c <= '9') { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
            if (neg) return -ret; 
            return ret;
        } catch (Exception e) {
            System.out.println(e.getMessage());
            return -1;
        }
    } 
    
    private void fillBuffer() throws IOException{ 
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
        if (bytesRead == -1) 
            buffer[0] = -1; 
    } 
    
    private byte read() throws IOException  { 
        try{
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
            }catch(Exception e){
                System.out.println(e.getMessage());
                return -1;
            }
        } 
    
    public void close() throws IOException { 
        if (din == null) 
            return; 
        din.close(); 
    } 
} 


    // 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());
    //     }
    
    //     String nextLine() {
    //         String str = "";
    //         try {
    //             str = br.readLine();
    //         } catch (IOException e) {
    //             e.printStackTrace();
    //         }
    //         return str;
    //     }
    // }