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 PYTHON):

Solution:
import sys
import copy

cases = int(input())
for i in range(cases):
    n_k = sys.stdin.readline().strip().split()
    n, k = int(n_k[0]), int(n_k[1])
    numbers = sys.stdin.readline().strip().split()
    nums = map(int, numbers)
    d = {}
    step = 0
    d[tuple(nums)] = step

    # perform operation
    skip_check = False
    while step < k:
        step += 1
        m = max(nums)
        nums_next = copy.deepcopy(nums)
        nums_next = map(lambda x : m - x, nums_next)
        t = tuple(nums_next)
        if not skip_check:
            if t in d:
                # we have a cycle
                cycle_len = step - d[t]
                remaining = k - step
                offset_from_cur = remaining % cycle_len
                step = 0
                k = offset_from_cur
                skip_check = True
            else:
                d[t] = step
        
        nums = nums_next
        
    print(' '.join(map(str, nums)))