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:
#!/bin/python3
import math; import os; import random; import re; import sys
from collections import defaultdict, Counter, deque
import heapq
from functools import lru_cache
from itertools import accumulate, chain, combinations, permutations, groupby, zip_longest
from math import floor, ceil, sqrt


def solve(arr, k):
	mx = max(arr)
	arr = [mx-v for v in arr] # thats one operation
	k -= 1
	if k%2==0:
		# we are done
		return arr
	else:
		mx = max(arr)
		return [mx-v for v in arr]





t = int(input())
results = []
for _ in range(t):
	n, k = list(map(int, input().split()))
	arr = list(map(int, input().split()))
	results += solve(arr, k),
for res in results:
	# print(res)
	print(' '.join(map(str, res)))