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 sys import stdin,stdout
from itertools import combinations
from collections import defaultdict,Counter
import math
 
def listIn():
    return list((map(int,stdin.readline().strip().split())))
 
def stringListIn():
    return([x for x in stdin.readline().split()])
    
def intIn():
    return (int(stdin.readline()))
 
def stringIn():
    return (stdin.readline().strip())
    
 
if __name__=="__main__":
    t=intIn()
    while(t>0):
        t-=1
        n,k=listIn()
        a=listIn()
        
        val=2
        li=[]
        while(val>0):
            val-=1
            m=max(a)
            a=[m-i for i in a]
            li.append(a)
        
        #print(li)
        if k%2==0:
            print(*li[1])
        else:
            print(*li[0])