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:
/************************************************************************
 AUTH : krishna-3249 
 DATE : 8/17/20
 TIME : 6:13 PM

 Everyone’s a whore, Grace. We just sell different parts of ourselves.
 ************************************************************************/

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

public class B {

    public void solve(Read input, Write output) throws Exception {
        int cases = input.readInt();
        while (cases-- > 0) {
            int N = input.readInt();
            int K = input.readInt();
            int[] arr = new int[N];
            int[] next = new int[N];
            int max = Integer.MIN_VALUE;
            for (int i=0;i<N;i++) {
                arr[i] = input.readInt();
                max = Math.max(max, arr[i]);
            }
            int nextmax = Integer.MIN_VALUE;
            for (int i=0;i<N;i++) {
                next[i] = max-arr[i];
                nextmax = Math.max(nextmax, next[i]);
            }
            for (int i=0;i<N;i++) {
                if (K%2==0) {
                    next[i] = nextmax-next[i];
                }
            }
            for (int i=0;i<N;i++) {
                output.print(next[i]);
                output.print(" ");
            }
            output.printLine("");
        }
    }

    public static void main(String[] args) throws Exception {
        Read input = new Read();
        Write output = new Write();
        B D = new B();
        D.solve(input, output);
        output.flush();
        output.close();
    }

    // java fast io reader and writer
    // taken from various sources and customized

    static class Read {

        private byte[] buffer = new byte[10 * 1024];
        private int index;
        private InputStream input_stream;
        private int total;

        public Read() {
            input_stream = System.in;
        }

        public int read() throws IOException {
            if (total < 0)
                throw new InputMismatchException();
            if (index >= total) {
                index = 0;
                total = input_stream.read(buffer);
                if (total <= 0)
                    return -1;
            }
            return buffer[index++];
        }

        public long readLong() throws IOException {
            long number = 0;
            int n = read();
            while (isWhiteSpace(n))
                n = read();
            long neg = 1l;
            if (n == '-') {
                neg = -1l;
                n = read();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    number *= 10l;
                    number += (long) (n - '0');
                    n = read();
                } else throw new InputMismatchException();
            }
            return neg * number;
        }

        public int readInt() throws IOException {
            int integer = 0;
            int n = read();
            while (isWhiteSpace(n))
                n = read();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = read();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = read();
                } else throw new InputMismatchException();
            }
            return neg * integer;
        }

        public double readDouble() throws IOException {
            double doub = 0;
            int n = read();
            while (isWhiteSpace(n))
                n = read();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = read();
            }
            while (!isWhiteSpace(n) && n != '.') {
                if (n >= '0' && n <= '9') {
                    doub *= 10;
                    doub += n - '0';
                    n = read();
                } else throw new InputMismatchException();
            }

            if (n == '.') {
                n = read();
                double temp = 1;
                while (!isWhiteSpace(n)) {
                    if (n >= '0' && n <= '9') {
                        temp /= 10;
                        doub += (n - '0') * temp;
                        n = read();
                    } else throw new InputMismatchException();
                }
            }
            return doub * neg;
        }

        public String readString() throws IOException {
            StringBuilder sb = new StringBuilder();
            int n = read();
            while (isWhiteSpace(n))
                n = read();
            while (!isWhiteSpace(n)) {
                sb.append((char) n);
                n = read();
            }
            return sb.toString();
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
                return true;
            return false;
        }
    }

    static class Write {

        private final BufferedWriter bw;

        public Write() {
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        public void print(Object str) throws IOException {
            bw.append(str + "");
        }

        public void printLine(Object str) throws IOException {
            print(str);
            bw.append("\n");
        }

        public void close() throws IOException {
            bw.close();
        }

        public void flush() throws IOException {
            bw.flush();
        }
    }
}