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;
int getFldsFromLine(char *line, std::vector<char *> &res,
                    const char *sep = " \t\n\v\f\r");
int main(int argc, char **argv) {
  FILE *infile = stdin;
  char *line;
  line = (char *)calloc(3000000, sizeof(char));
  if (line == NULL) {
    fprintf(stderr, "Couldn't allocate space for '%s'\nBye!\n", "line");
    exit(-1);
  };
  std::vector<char *> flds;
  int numFlds, numCases, caseNum = 0;
  fgets(line, 3000000, infile);
  numFlds = getFldsFromLine(line, flds);
  numCases = atoi(flds[0]);
  for (caseNum = 1; caseNum <= numCases; ++caseNum) {
    fgets(line, 3000000, infile);
    numFlds = getFldsFromLine(line, flds);
    int n = atoi(flds[0]), k = atoi(flds[1] + strlen(flds[1]) - 1);
    k %= 2;
    fgets(line, 3000000, infile);
    numFlds = getFldsFromLine(line, flds);
    int min0 = 1e9 + 1, max0 = -1e9 - 1;
    vector<int> a;
    for (int i = 0; i < n; ++i) {
      int tval = atoi(flds[i]);
      a.push_back(tval);
      if (tval < min0) min0 = tval;
      if (tval > max0) max0 = tval;
    }
    for (int i = 0; i < n; ++i) {
      if (i > 0) printf(" ");
      int tval;
      if (k == 0)
        tval = a[i] - min0;
      else
        tval = max0 - a[i];
      printf("%d", tval);
    }
    printf("\n");
  }
  return (0);
}
int getFldsFromLine(char *line, std::vector<char *> &res, const char *sep) {
  res.clear();
  char *tok = strtok(line, sep);
  while (tok) {
    res.push_back(tok);
    tok = strtok(0, sep);
  }
  return res.size();
}