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:
'''
      ___           ___                         ___                       ___           ___                         ___
     /\__\         /\  \         _____         /\  \                     /\  \         /\  \                       /\__\
    /:/ _/_        \:\  \       /::\  \        \:\  \       ___         /::\  \       |::\  \         ___         /:/ _/_
   /:/ /\  \        \:\  \     /:/\:\  \        \:\  \     /\__\       /:/\:\__\      |:|:\  \       /\__\       /:/ /\  \
  /:/ /::\  \   ___  \:\  \   /:/  \:\__\   ___ /::\  \   /:/__/      /:/ /:/  /    __|:|\:\  \     /:/  /      /:/ /::\  \
 /:/_/:/\:\__\ /\  \  \:\__\ /:/__/ \:|__| /\  /:/\:\__\ /::\  \     /:/_/:/__/___ /::::|_\:\__\   /:/__/      /:/_/:/\:\__\
 \:\/:/ /:/  / \:\  \ /:/  / \:\  \ /:/  / \:\/:/  \/__/ \/\:\  \__  \:\/:::::/  / \:\~~\  \/__/  /::\  \      \:\/:/ /:/  /
  \::/ /:/  /   \:\  /:/  /   \:\  /:/  /   \::/__/       ~~\:\/\__\  \::/~~/~~~~   \:\  \       /:/\:\  \      \::/ /:/  /
   \/_/:/  /     \:\/:/  /     \:\/:/  /     \:\  \          \::/  /   \:\~~\        \:\  \      \/__\:\  \      \/_/:/  /
     /:/  /       \::/  /       \::/  /       \:\__\         /:/  /     \:\__\        \:\__\          \:\__\       /:/  /
     \/__/         \/__/         \/__/         \/__/         \/__/       \/__/         \/__/           \/__/       \/__/

'''
"""
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"""
import sys
import math
import collections
import operator as op
from collections import deque
from math import gcd, inf, sqrt, pi, cos, sin, ceil, log2
from bisect import bisect_right, bisect_left

# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')

from functools import reduce
from sys import stdin, stdout, setrecursionlimit
setrecursionlimit(2**20)


def factorial(n):
    if n == 0:
        return 1
    return (n * factorial(n - 1))


def ncr(n, r):
    r = min(r, n - r)
    numer = reduce(op.mul, range(n, n - r, -1), 1)
    denom = reduce(op.mul, range(1, r + 1), 1)
    return numer // denom  # or / in Python 2


def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return (list(factors))


def sumDigits(no):
    return 0 if no == 0 else int(no % 10) + sumDigits(int(no / 10))

MOD = 1000000007
PMOD = 998244353
N = 10**5
T = 1
T = int(stdin.readline())
for _ in range(T):
    n, k = list(map(int, stdin.readline().rstrip().split()))
    # n = int(stdin.readline())
    a = list(map(int, stdin.readline().rstrip().split()))
    # b = list(map(int, stdin.readline().rstrip().split()))
    # a = list(stdin.readline().strip('\n'))
    # b = list(stdin.readline().strip('\n'))
    # q = list(stdin.readline().strip('\n'))
    # q = int(stdin.readline())
    # s = list(map(int, stdin.readline().rstrip().split()))
    # print(a)

    d1 = max(a)
    for i in range(n):
        a[i] = d1 - a[i]
    f1 = a.copy()

    d2 = max(a)
    for i in range(n):
        a[i] = d2 - a[i]
    f2 = a.copy()
    k -= 1

    if k % 2 == 0:
        print(*f1)
    else:
        print(*f2)