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:
import math
import sys
#####sorting a dictionary by the values#####
def dict_sort(ans):
    ans=sorted(ans.items(),reverse=True,key=lambda kv:(kv[1]))
##### naive method for testing prime or not#####
def is_prime(n):
    if n==1:
        return 0
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            return False
    return True
#####greatest common divisor of two numbers#####
def gcd(a,b):
    if b==0:
        return a
    return gcd(b,a%b)
#####least common multiplyer of two numbers#####
def lcm(a,b):
    return (a*b)//gcd(a,b)
#####function that return all the letters#####
def alphbates():
    return "abcdefghijklmnopqrstuvwxyz"
#####binary search#####
def binary_search(ls,n,flag):
    low=0
    hi=n-1
    while(low<=hi):
        mid=(low+hi)//2
        if ls[mid]==flag:
            return mid
        elif ls[mid]>flag:
            hi=mid-1
        else:
            low=mid+1
    return -1
#####taking an array/list as input#####
def inp():
    ls=list(map(int,input().split()))
    return ls
#####taking multiple inputs#####
def mult_inp():
    return map(int,input().split())
#####Main function starts from here#####
t=int(input())
for _i in range(t):
    n,k=mult_inp()
    ls=inp()
    mx=max(ls)
    mn=min(ls)
    ans1=[]
    ans2=[]
    if n==1:
        print(0)
    else:
        for i in ls:
            ans1.append(mx-i)
        j=0
        for i in ls:
            ans2.append(mx-mn-ans1[j])
            j+=1
        if k%2==1:
            for i in ans1:
                print(i,end=" ")
        else:
            for i in ans2:
                print(i,end=" ")
        print()