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.lang.reflect.Array;
import java.util.*;

public class file {



    private static final Scanner sc = new Scanner(System.in);
    private static String s;
    private static int[] arr;
    private static HashSet<Long> set;
    private static HashMap<Character, Integer> cmap;
    private static Map<Long, Long> map;
    private static Stack<Integer> stk;
    private static ArrayList<Integer>[] graph;
    private static boolean[] visited;
    private static int[] population;
    private static int[] hap_index;
    private static int[] happy;


    private static int findMax(int[] arr) {
        int max = Integer.MIN_VALUE;
        for (int x : arr) {
            max = Math.max(x, max);
        }
        return max;
    }

    private static void printArray(int[] arr) {
        for (int x : arr) {
            System.out.print(x + " ");
        }
        System.out.println();
    }


    private static void foo(int testCase) {
        int n = sc.nextInt();
        long k = sc.nextLong();
        arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
        }
        int x = findMax(arr);
        int[] odd = new int[n];
        for (int i = 0; i < n; i++) {
            odd[i] = x - arr[i];
        }
        x = findMax(odd);
        int[] even = new int[n];
        for (int i = 0; i < n; i++) {
            even[i] = x - odd[i];
        }
        if (k%2 == 0) {
            printArray(even);
        } else {
            printArray(odd);
        }

    }



    public static void main(String[] args) throws IOException {
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            foo(t);
        }
    }
}