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:
'''input
3
4 2
1 2 3 4
5 19
5 -1 4 2 0
1 2
69
'''

import math
import sys
import itertools
import random
import bisect
import heapq
import collections

def lcm(x, y):
	return (x*y)//math.gcd(x,y)
def hcf(x, y):
	return math.gcd(x, y)
def primes(n):
	prime=[True for _ in range(0, n+1)]
	res=[]
	p=2
	while p*p<=n:
		if prime[p]==True:
			for i in range(p*p,n+1,p):
				prime[p]=False
		p+=1
	for i in range(0, n+1):
		if prime[i]==True:
			res.append(i)
	return res
def primeFactors(n):
	res=[]
	while n%2==0:
		res.append(2)
		n//=2
	for i in range(3, math.sqrt(n)+1, 2):
		while n%i==0:
			res.append(i)
			n//=i
	if n>2:
		res.append(n)
	return res


for _ in range(0, int(input())):
	# n=int(input())                                 # Single Digit Input
	n, k = map(int, input().strip().split())    # Many Digit Input
	l=list(map(int, input().strip().split()))      # List Input
	# s=list(input())                                # Character Array Input

	odd = []
	even = []
	d = max(l)
	for i in l:
		odd.append(d-i)
	d = max(odd)
	for i in odd:
		even.append(d-i)
	# print(odd, even)

	if k%2==0:
		print(*even)
	else:
		print(*odd)