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.*;
import java.lang.*;
import java.math.*;

public class B {
	public void run() throws Exception {
		FastScanner sc = new FastScanner();
		
		int test = sc.nextInt();
		for (int loop = 0; loop<test; loop++) {
			int n = sc.nextInt();
			long k = sc.nextLong()%2;
			long[] arr = new long[n];
			long max = Long.MIN_VALUE;
			for (int i  =0; i<n; i++) {
				arr[i] = sc.nextLong();
				max = Math.max(max, arr[i]);
			}
			long max1 = Long.MIN_VALUE;
			for (int i = 0; i<n; i++) {
				arr[i] = max-arr[i];
				max1 = Math.max(arr[i], max1);
			}
			if (k%2 == 0) {
				for (int i = 0; i<n; i++) {
					arr[i] = max1-arr[i];
				}
			}
			for (int i =0; i<n; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
		}
	}
	//SSR <3 2020
	public class Pair implements Comparable<Pair>{
		int num, times;
		public Pair(int a, int b) {
			num = a;
			times = b;
		}
		public int compareTo(Pair a) {
			if (num == a.num) return times-a.times;
			return num-a.num;
		}
		public String toString() {
			return num + " " + times;
		}
	}
	public int[] shuffleArray(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
        	int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
        return arr;
	}
	public boolean isPrime(long n) {
		for (long i = 2; i<=Math.sqrt(n); i++) {
			if (n%i == 0) return false;
		}
		return true;
	}
	public static long gcd(long a, long b)   {
		if (a == b) return a;
		if (a > b) return gcd(a-b, b);
		return gcd(a, b-a);
    }
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
 
		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}
 
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
 
		public int nextInt() {
			return Integer.parseInt(next());
		}
 
		public long nextLong() {
			return Long.parseLong(next());
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
 
	}
	public static void main (String[] args) throws Exception {
		new B().run();
	}
}