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 namespace std;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    long long n, k;
    cin >> n >> k;
    vector<long long> v(n);
    for (long long i = 0; i < n; i++) cin >> v[i];
    while (k > 0) {
      k--;
      long long mx = -10000000000, qtd0 = 0, qtdneg = 0;
      for (long long i = 0; i < n; i++) {
        mx = max(mx, v[i]);
        if (v[i] == 0) qtd0++;
        if (v[i] < 0) qtdneg++;
      }
      if (qtd0 >= 1 and qtdneg == 0) {
        k++;
        break;
      } else
        for (long long i = 0; i < n; i++) v[i] = mx - v[i];
    }
    if (k == 0)
      for (long long i = 0; i < n; i++) cout << v[i] << " ";
    else {
      if (k & 1) {
        long long mx = -10000000000, qtd0 = 0, qtdneg = 0;
        for (long long i = 0; i < n; i++) mx = max(mx, v[i]);
        for (long long i = 0; i < n; i++) v[i] = mx - v[i];
      }
      for (long long i = 0; i < n; i++) cout << v[i] << " ";
    }
    cout << "\n";
  }
  return 0;
}