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:
import sys
import math
import bisect
from sys import stdin, stdout
from math import gcd, floor, sqrt, log
from collections import defaultdict as dd
from bisect import bisect_left as bl, bisect_right as br
from collections import Counter

#sys.setrecursionlimit(100000000)

inp = lambda: int(input())
strng = lambda: input().strip()
jn = lambda x, l: x.join(map(str, l))
strl = lambda: list(input().strip())
mul = lambda: map(int, input().strip().split())
mulf = lambda: map(float, input().strip().split())
seq = lambda: list(map(int, input().strip().split()))

ceil = lambda x: int(x) if (x == int(x)) else int(x) + 1
ceildiv = lambda x, d: x // d if (x % d == 0) else x // d + 1

flush = lambda: stdout.flush()
stdstr = lambda: stdin.readline()
stdint = lambda: int(stdin.readline())
stdpr = lambda x: stdout.write(str(x))
stdarr = lambda: map(int, stdstr().split())

mod = 1000000007


for  _ in range(stdint()):
    n, k = stdarr()

    arr = list(stdarr())

    m = max(arr)
    res = []

    if(k%2 == 0):
        mi = min(arr)
        for i in range(n):
            res.append(arr[i]-mi)
    else:
        ma = max(arr)
        for i in range(n):
            res.append(ma - arr[i])

    print(*res)