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:
from sys import stdin, stdout, setrecursionlimit
#import threading

# tail-recursion optimization
# In case of tail-recusion optimized code, have to use python compiler.
# Otherwise, memory limit may exceed.
# declare the class Tail_Recursion_Optimization
class Tail_Recursion_Optimization:
    def __init__(self, RECURSION_LIMIT, STACK_SIZE):
        setrecursionlimit(RECURSION_LIMIT)
        threading.stack_size(STACK_SIZE)
        return None
        
class SOLVE:
    def solve(self):
        R = stdin.readline
        #f = open('input.txt');R = f.readline
        W = stdout.write
        
        ans = []
        
        for i in range(int(R())):
            n, k = map(int, R().split())
            a    = [int(x) for x in R().split()]
            
            mx   = max(a)
            a    = [mx - a[j] for j in range(n)]
            mx   = max(a)
            
            for j in range(n):
                if k%2:
                    ans.append('{} '.format(a[j]))
                else:
                    ans.append('{} '.format(mx - a[j]))
            ans.append('\n')
        
        W(''.join(ans))
        return 0
        
def main():
    s = SOLVE()
    s.solve()
#Tail_Recursion_Optimization(10**7, 100*1024**2) # recursion-call size, stack-size in byte (MB*1024**2)
#threading.Thread(target=main).start()
main()