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 sys
from math import sqrt
from collections import OrderedDict
inpt = sys.stdin.readline

def inp():
    return(int(inpt()))

def inlist():
    return(list(map(int,inpt().split())))

def instr():
    s = inpt()
    return(list(s[:len(s)-1]))

def invr():
    return(map(int,inpt().split()))

class node(object):
    def __init__(self,x,p,h):
        self.x, self.p, self.h = x,p,h  
        self.children = []
    
    def add_child(self,obj):
        self.children.append(obj)

def main():
        
        t = inp()

        for l in range(t):

            n,k = invr()
            a = inlist()

            mx = max(a)
            mn = mx-min(a)

            a1 = a.copy()
            for i in range(n):
                a1[i] = mx-a1[i]
            
            a2 = a1.copy()
            for i in range(n):
                a2[i] = mn-a2[i]

            if(k%2==0):
                for i in range(n):
                    print(a2[i],end=' ')
                print()
            else:
                for i in range(n):
                    print(a1[i],end=' ')
                print()



main()