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:
// package LeetCode;

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

public class Main {

	static class Reader {
		BufferedReader br;
		StringTokenizer st;

		public Reader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public int nextInt() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return Integer.parseInt(st.nextToken());
		}

		public float nextFloat() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return Float.parseFloat(st.nextToken());
		}

		public long nextLong() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return Long.parseLong(st.nextToken());
		}

		public double nextDouble() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return Double.parseDouble(st.nextToken());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public String next() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return st.nextToken();
		}
	}

//	static class Pair implements Comparable<Pair> {
//		long first;
//		long second;
//
//		public Pair(long first, long second) {
//			this.first = first;
//			this.second = second;
//		}
//
//		@Override
//		public int compareTo(Pair o) {
//			if (this.first > o.first) {
//				return -1;
//			} else if (this.first < o.first) {
//				return 1;
//			} else {
//				return 0;
//			}
//		}
//	}

	static class Pair<T1,T2> {
		T1 first;
		T2 second;

		public Pair(T1 first, T2 second) {
			this.first = first;
			this.second = second;
		}
	}


	private static void solve() throws IOException {
		int n = sc.nextInt();
		long k = sc.nextLong();
		long arr[] = new long[n];
		long max = Long.MIN_VALUE;
		for(int i=0;i<n;i++) {
			arr[i] = sc.nextInt();
			if(max<arr[i]) {
				max = arr[i];
			}
		}
		long max2 = Long.MIN_VALUE;
		for(int i=0;i<n;i++) {
			arr[i] = max-arr[i];
			if(max2<arr[i]) {
				max2 = arr[i];
			}
		}
		k--;
		if(k%2==1) {
			for(int i=0;i<n;i++) {
				out.print(max2-arr[i]);
				out.print(' ');
			}
		} else {
			for(int i=0;i<n;i++) {
				out.print(arr[i]);
				out.print(' ');
			}
		}
		out.println();
	}

	private static void readt() throws IOException {
		T = sc.nextInt();
	}

	static int mod = (int) (1e9 + 7);
	static int T;
	static Reader sc;
	static PrintWriter out;
	public static void main(String[] args) throws IOException {
		sc = new Reader();
		out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		try {
			T = 1;
			readt();
			while (T-- > 0) {
				solve();
			}
			out.flush();
		} catch (Exception e) {
			e.printStackTrace();
		}
	}
}