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 itertools import accumulate as ac
from collections import Counter as cc
from bisect import bisect_left as bsl
from bisect import bisect as bs
from math import factorial as f
from collections import *
from itertools import *
from string import *
from bisect import *
from queue import *
from heapq import *
from math import *
from sys import *
from re import *
def fast(): return stdin.readline().strip()
def zzz(): return [int(i) for i in fast().split()]


z, zz = input, lambda: list(map(int, z().split()))
szz, graph, mod, szzz = lambda: sorted(
    zz()), {}, 10**9 + 7, lambda: sorted(zzz())


def lcd(xnum1, xnum2): return (xnum1 * xnum2 // gcd(xnum1, xnum2))
def output(answer): stdout.write(str(answer))


###########################---Test-Case---#################################
"""

  If you Know me , Then you probably don't know me !


"""
###########################---START-CODING---##############################

num = int(z())

for _ in range(num):
    n,k=zzz()
    arr=zzz()
    lst=[]
    for i in range(2):
        m=max(arr)
        new=[0]*n
        for j in range(n):
            new[j]=m-arr[j]
        lst.append(new)
        arr = new
    print(*lst[(k+1)%2])