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 CPP):

Solution:
#include <bits/stdc++.h>
using ll = long long;
int const inf = 1000000000;
void solve() {
  int n;
  ll k;
  std::cin >> n >> k;
  std::vector<int> v(n);
  for (int i = 0; i < n; i++) std::cin >> v[i];
  if (3 < k) {
    if (k % 2 == 0)
      k = 4;
    else
      k = 5;
  }
  for (int i = 1; i <= k; i++) {
    int smax = -inf;
    for (int j = 0; j < n; j++) smax = std::max(smax, v[j]);
    for (int j = 0; j < n; j++) v[j] = smax - v[j];
  }
  for (int j = 0; j < n; j++) std::cout << v[j] << " ";
  std::cout << '\n';
}
int main() {
  std::ios::sync_with_stdio(0);
  std::cin.tie(0);
  int t;
  std::cin >> t;
  for (int testcase = 1; testcase <= t; testcase++) solve();
  return 0;
}