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:
for _ in range(int(input())):
    n,k=map(int,input().split())
    lis=list(map(int,input().split()))
    gr=max(lis)
    while k>0:
        ma=gr
        ini=0
        for i in range(n):
            lis[i]=ma-lis[i]
            if lis[i]>=ini:
                ini=lis[i]
                gr=ini
        k-=1
        if gr==ma:
            break
        elif gr==0:
            break
    if gr==0:
        print("0 "*n)
    else:
        if k%2==0:
            print(*lis)
        else:
            for i in lis:
                if i==gr:
                    print(0,end=" ")
                elif i==0:
                    print(gr,end=" ")
                else:
                    print(gr-i,end=" ")
            print()