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:

#: <<<<<<<<<<<  :/

######################################################################
# Write your code here
import sys
#import resource
#resource.setrlimit(resource.RLIMIT_STACK, [0x10000000, resource.RLIM_INFINITY])
#sys.setrecursionlimit(0x100000)
# Write your code here
# For getting input from input.txt file 
# sys.stdin = open('input.txt', 'r')  
# Printing the Output to output.txt file 
# sys.stdout = open('output.txt', 'w')
RI =   lambda : [int(x) for x in sys.stdin.readline().strip().split()]
rw =   lambda : sys.stdin.readline().strip().split()
ri =   lambda : int(sys.stdin.readline().strip())
rs =   lambda : sys.stdin.readline().strip()
from collections import defaultdict as df
#import heapq 
#heapq.heapify(li) heappush(li,4) heappop(li)
import random
# random.shuffle(list)
#infinite = float('inf')
#######################################################################
from queue import PriorityQueue as pq
# from math import pow as p
from math import ceil

t = ri()
for _ in range(t):
	n,k = RI()
	l = RI()

	maxo = max(l)
	mini = min(l)
	m3 = maxo - mini

	for i in l:
		if(i==maxo):
			if(k%2==0):
				print(m3,end=" ")
			else:
				print(0,end=" ")
		elif(i==mini):
			if(k%2==0):
				print(0,end=" ")
			else:
				print(m3,end=" ")
		else:
			if(k%2==1):
				print(maxo-i,end=" ")
			else:
				print(m3-(maxo-i),end=" ")
	print()