#include <bits/stdc++.h>
#define sz(x) (int)x.size()

using ll = long long;
using namespace std;

void solve() {
  int n, x;
  cin >> n >> x;
  vector<pair<ll, ll>> a;
  ll ans = 0;
  for (int i = 0, l; i < n; ++i) {
    cin >> l;
    a.emplace_back(l, 1);
  }
  int i = 0;
  while (1) {
      if (i == a.size()) break;
      if (a[i].first % x) {
        break;
      }
      a.emplace_back(a[i].first / x, a[i].second * x);
      ++i;
  }
  for (int i = 0; i < a.size(); i++) {
    ans += a[i].first * a[i].second;
  }
  cout << ans << '\n';
}
 
int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int t = 1;
  cin >> t;
  while (t--) { 
    solve();
  }
  return 0;
}
### Prompt

In Cpp, your task is to solve the following problem:

You have given an array a of length n and an integer x to a brand new robot. What the robot does is the following: it iterates over the elements of the array, let the current element be q. If q is divisible by x, the robot adds x copies of the integer q/x to the end of the array, and moves on to the next element. Note that the newly added elements could be processed by the robot later. Otherwise, if q is not divisible by x, the robot shuts down.

Please determine the sum of all values of the array at the end of the process.

Input

The first input line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains two integers n and x (1 ≤ n ≤ 10^5, 2 ≤ x ≤ 10^9) — the length of the array and the value which is used by the robot.

The next line contains integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the initial values in the array.

It is guaranteed that the sum of values n over all test cases does not exceed 10^5.

Output

For each test case output one integer — the sum of all elements at the end of the process.

Example

Input


2
1 2
12
4 2
4 6 8 2


Output


36
44

Note

In the first test case the array initially consists of a single element [12], and x=2. After the robot processes the first element, the array becomes [12, 6, 6]. Then the robot processes the second element, and the array becomes [12, 6, 6, 3, 3]. After the robot processes the next element, the array becomes [12, 6, 6, 3, 3, 3, 3], and then the robot shuts down, since it encounters an element that is not divisible by x = 2. The sum of the elements in the resulting array is equal to 36.

In the second test case the array initially contains integers [4, 6, 8, 2], and x=2. The resulting array in this case looks like  [4, 6, 8, 2, 2, 2, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1].

### Response

```cpp
#include <bits/stdc++.h>
#define sz(x) (int)x.size()

using ll = long long;
using namespace std;

void solve() {
  int n, x;
  cin >> n >> x;
  vector<pair<ll, ll>> a;
  ll ans = 0;
  for (int i = 0, l; i < n; ++i) {
    cin >> l;
    a.emplace_back(l, 1);
  }
  int i = 0;
  while (1) {
      if (i == a.size()) break;
      if (a[i].first % x) {
        break;
      }
      a.emplace_back(a[i].first / x, a[i].second * x);
      ++i;
  }
  for (int i = 0; i < a.size(); i++) {
    ans += a[i].first * a[i].second;
  }
  cout << ans << '\n';
}
 
int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int t = 1;
  cin >> t;
  while (t--) { 
    solve();
  }
  return 0;
}
```