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.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Solution {

//	public static void main(String[] args) {
//		Scanner in = new Scanner(System.in);
//		int cases = in.nextInt();
//		for (int i = 0; i < cases; i++) {
//			int n = in.nextInt();
//			ArrayList<Integer> a = new ArrayList<>(n);
//			int curr = -1;
//			int prev = curr;
//			boolean one = false;
//			for (int j = 0; j < n; j++) {
//				prev = curr;
//				curr = in.nextInt();
//				if(prev != curr && prev != -1){
//					one = true;
//				}
//				a.add(j, curr);
//			}
//			if(one){
//				System.out.println(1);
//			} else{
//				System.out.println(a.size());
//			}
//		}
//	}

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int cases = in.nextInt();
		for (int i = 0; i < cases; i++) {
			int n = in.nextInt();
			BigInteger[] a = new BigInteger[n];
			BigInteger k = in.nextBigInteger();
			BigInteger max = in.nextBigInteger();
			a[0] = max;
			for (int j = 1; j < n; j++) {
				BigInteger curr = in.nextBigInteger();
				if (curr.compareTo(max) == 1) {
					max = curr;
				}
				a[j] = curr;
			}
			BigInteger newMax = new BigInteger("0");
			if(k.equals(0)){
			} else if ((k.mod(new BigInteger("2"))).equals(new BigInteger("0"))) {
				for (int j = 0; j < n; j++) {
					a[j] = max.subtract(a[j]);
					if(a[j].compareTo(newMax) == 1){
						newMax = a[j];
					}
				}
				for (int j = 0; j < n; j++) {
					a[j] = newMax.subtract(a[j]);
				}
				} else if ((k.mod(new BigInteger("2"))).equals(new BigInteger("1"))) {
				for (int j = 0; j < n; j++) {
					a[j] = max.subtract(a[j]);
				}
			}
			for(int j = 0; j < n; j++){
				System.out.print(a[j] + " ");
			}
			System.out.println();

		}
	}

}