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:
from fractions import Fraction
import bisect
import os
import io
from collections import Counter
import bisect
from collections import defaultdict
import math
import random
import heapq 
from math import sqrt
import sys
from functools import reduce, cmp_to_key
from collections import deque
import threading
from itertools import combinations
from io import BytesIO, IOBase
from itertools import accumulate
from queue import Queue
 
 
# sys.setrecursionlimit(200000)
# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
 
 
def input():
    return sys.stdin.readline().strip()
 
 
def iinput():
    return int(input())
 
 
def tinput():
    return input().split()
 
 
def rinput():
    return map(int, tinput())
 
 
def rlinput():
    return list(rinput())
 
 
mod = int(1e9)+7
 
 
def factors(n):
    return set(reduce(list.__add__,
                      ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
 
 
# ----------------------------------------------------
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
 
 
 
t = 1
t = iinput()
for _ in range(t):
    n, k = rinput()
    a = rlinput()
    state1 = []
    state2 = []
    mx = max(a)
    for i in range(n):
        state1.append(mx - a[i])
    mx = max(state1)
    for i in range(n):
        state2.append(mx - state1[i])
    if k % 2:
        print(*state1)
    else:
        print(*state2)