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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;
public class T {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		
		while(t--!=0) {
			String s[]=br.readLine().split(" ");
			int n=Integer.parseInt(s[0]);
			BigInteger big=new BigInteger(s[1]);
			BigInteger two=new BigInteger("2");
			long max=-1000000001;
			long min=1000000001;
			String sq[]=br.readLine().split(" ");
			long a[]=new long[n];
			for(int i=0;i<n;i++) {
				a[i]=Long.parseLong(sq[i]);
				min=Math.min(min, a[i]);
				max=Math.max(max, a[i]);
			}
			
			long b[]=new long[n];
			long max1=0;
			long min1=1000000001;
			for(int i=0;i<n;i++) {
				b[i]=max-a[i];
				max1=Math.max(max1, b[i]);
				min1=Math.min(min1, b[i]);
			}
			
			long c[]=new long[n];
			for(int i=0;i<n;i++) {
				c[i]=max1-b[i];
			}
			BigInteger z=new BigInteger("0");
			if(n==1) System.out.println("0");
			else {
//				if(max==min) {
//					for(int i=0;i<n;i++) {
//						System.out.print("0"+" ");
//					}
//				}
				if(big.mod(two).equals(z)) {
					for(long v:c) {
						System.out.print(v+" ");
					}
				}
				else {
					for(long v:b) {
						System.out.print(v+" ");
					}
				}
				System.out.println();
			}
		}
	}

}