human
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].
Using python3 can you solve the prior task?
 ... Can you provide a Python program to determine what the final sequence will look like!?
assistant
#Here is Python program to determine what the final sequence will look like!
.

# import math
# from collections import Counter
#from collections import defaultdict
#from collections import deque
# from bisect import bisect_left as bl, bisect_right as br
# from itertools import accumulate,permutations as perm,combinations as comb
# from heapq import heapify,heappush,heappop,nlargest,nsmallest
# from fractions import Fraction
import sys
# from functools import reduce, lru_cache
"""author-bravotango. FastIO code by pajenegod"""

def main():
    t = Iint()
    for _ in range(t):
        n, k = Imap()
        a = Ilist()
        ma = max(a)
        a = [ma-ai for ai in a]
        if k % 2 == 1:
            Plist(a)
        elif k % 2 == 0:
            ma = max(a)
            a = [ma-ai for ai in a]
            Plist(a)

en = enumerate
# IO region1
FIO = 10

def debug(*args, c=6): pass; print('\033[3{}m'.format(c), *args, '\033[0m', file=sys.stderr)

BUFSIZE = 8*1024

def Istr(): return input()

def Iint(): return int(input())

def Ilist(): return list(map(int, input().split()))   # int list

def Imap(): return map(int, input().split())   # int map

def Plist(li, s=' '): print(s.join(map(str, li)))   # non string iterable

if not FIO:
    if __name__ == '__main__':
        main()
        exit()
else:
    from io import BytesIO, IOBase
    import os
# FastIO

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size,...