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 PYTHON3):

Solution:
def solve(arr, n, k):
    if k < 5:
        mx = max(arr)
        nm = float("-inf")
        while k:
            for i in range(n):
                arr[i] = mx-arr[i]
                nm = max(nm, arr[i])
            mx = nm
            k -= 1
        return arr
    
    config2 = []
    config2 += arr
    curr_k = 2
    mx = max(arr)
    nm = float("-inf")
    while curr_k:
        for i in range(n):
            arr[i] = mx-arr[i]
            nm = max(nm, arr[i])
        mx = nm
        curr_k -= 1
    
    check_same = True
    for i in range(n):
        if arr[i] != config2[i]:
            check_same = False
            break
    if not check_same:
        k -= 1
        mx = max(config2)
        for i in range(n):
            config2[i] = mx-config2[i]
    
    if k%2 == 0:
        return config2
    
    return arr
   

t = int(input())
for _ in range(t):
    n,k = map(int, input().split())
    arr = list(map(int, input().split()))
    for val in solve(arr, n, k):
        print(val, end=" ")
    print("\n", end="")