#include <bits/stdc++.h>
#define FIO ios::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define FOR(a,b,c) for(int a = (b); a <= (c); a++)
#define RFOR(a,b,c) for(int a = (b); a >= (c); a--)
#define all(x) (x).begin(), (x).end()
#define vi vector <int>
#define vvi vector <vi>
#define ll long long
#define vll vector <ll>
#define vvl vector <vll>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define eb emplace_back
#define ep emplace
#define fs first
#define sd second
#define mod 998244353
#define EPS 1e-9
using namespace std;

int main() {
	FIO;
	int t; cin >> t; while (t--) {
		int n, x;
		cin >> n >> x;

		queue <pair<int, int>> q;
		FOR(i, 1, n) {
			int a; cin >> a;
			q.push({ a,a });
		}

		ll ans = 0;

		while (q.size()) {
			auto a = q.front();
			q.pop();
			ans += a.sd;
			if (a.fs % x) break;
			
			q.push({ a.fs / x, a.sd });
		}
		while (q.size()) {
			ans += q.front().sd;
			q.pop();
		}

		cout << ans << '\n';
	}
	return 0;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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 FIO ios::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define FOR(a,b,c) for(int a = (b); a <= (c); a++)
#define RFOR(a,b,c) for(int a = (b); a >= (c); a--)
#define all(x) (x).begin(), (x).end()
#define vi vector <int>
#define vvi vector <vi>
#define ll long long
#define vll vector <ll>
#define vvl vector <vll>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define eb emplace_back
#define ep emplace
#define fs first
#define sd second
#define mod 998244353
#define EPS 1e-9
using namespace std;

int main() {
	FIO;
	int t; cin >> t; while (t--) {
		int n, x;
		cin >> n >> x;

		queue <pair<int, int>> q;
		FOR(i, 1, n) {
			int a; cin >> a;
			q.push({ a,a });
		}

		ll ans = 0;

		while (q.size()) {
			auto a = q.front();
			q.pop();
			ans += a.sd;
			if (a.fs % x) break;
			
			q.push({ a.fs / x, a.sd });
		}
		while (q.size()) {
			ans += q.front().sd;
			q.pop();
		}

		cout << ans << '\n';
	}
	return 0;
}
```