#include <bits/stdc++.h>
using namespace std;
#define int int64_t
#define um unordered_map
#define float double
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define B begin()
#define E end()
#define all(x) x.begin(), x.end()
#define sortall(x) sort(all(x))
#define rall(x) x.rbegin(), x.rend()
#define revsortall(x) sort(rall(x))
#define clr(x) memset(x, 0, sizeof(x))
#define clr_dp(x) memset(x, -1, sizeof(x))
#define loop(i, n) for(i=0;i<n;i++)
#define Loop(i, k, n) for(i=k;k<n?i<n:i>n;k<n?i+=1:i-=1)
#define outarr(i, a, n) loop(i, n){cout << a[i] << " ";}
#define len length()
#define si size()
#define tr(it, x) for(auto it = x.begin(); it != x.end(); it++)
#define trr(it, x) for(auto it = x.rbegin(); it != x.rend(); it+)
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pii> vpii;
typedef vector<vi> vvi;
const int mod = 1000000007;
const int MAX=INT_MAX;
const int MIN=INT_MIN;
void IO(){
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);cout.setf(ios::fixed);
    srand(chrono::high_resolution_clock::now().time_since_epoch().count());
    #ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
    #endif
}
void resultout(bool ans){
    ans? cout<<"YES":cout<<"NO";cout<<"\n";
}
void run_time_terror(){
    int n,x;
    cin>>n>>x;
    int a[n],b[n],temp,sum=0,mn=INT_MAX,indx;
    for (int i = 0; i < n; ++i)
    {
        cin>>a[i];
        sum+=a[i];
        temp=a[i];
        b[i]=0;
        while(temp%x==0){
            b[i]++;
            temp/=x;
        }
        if(mn>b[i]){
            mn=b[i];
            indx=i;
        }
    }
    for (int i = 0; i < n; ++i)
    {
        sum+=mn*a[i];
    }
    for (int i = 0; i < indx; ++i)
    {
        sum+=a[i];
    }
    cout<<sum<<"\n";
}
int32_t main(){
    // cout << setprecision(0);
    IO();
    int tt=1;
    cin>>tt;
    while(tt--){
        run_time_terror();
    }
    // cerr<<(float)clock()/CLOCKS_PER_SEC*1000<<" ms"<<endl;
    return 0;
}       
### Prompt

Generate a cpp solution to 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>
using namespace std;
#define int int64_t
#define um unordered_map
#define float double
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define B begin()
#define E end()
#define all(x) x.begin(), x.end()
#define sortall(x) sort(all(x))
#define rall(x) x.rbegin(), x.rend()
#define revsortall(x) sort(rall(x))
#define clr(x) memset(x, 0, sizeof(x))
#define clr_dp(x) memset(x, -1, sizeof(x))
#define loop(i, n) for(i=0;i<n;i++)
#define Loop(i, k, n) for(i=k;k<n?i<n:i>n;k<n?i+=1:i-=1)
#define outarr(i, a, n) loop(i, n){cout << a[i] << " ";}
#define len length()
#define si size()
#define tr(it, x) for(auto it = x.begin(); it != x.end(); it++)
#define trr(it, x) for(auto it = x.rbegin(); it != x.rend(); it+)
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pii> vpii;
typedef vector<vi> vvi;
const int mod = 1000000007;
const int MAX=INT_MAX;
const int MIN=INT_MIN;
void IO(){
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);cout.setf(ios::fixed);
    srand(chrono::high_resolution_clock::now().time_since_epoch().count());
    #ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
    #endif
}
void resultout(bool ans){
    ans? cout<<"YES":cout<<"NO";cout<<"\n";
}
void run_time_terror(){
    int n,x;
    cin>>n>>x;
    int a[n],b[n],temp,sum=0,mn=INT_MAX,indx;
    for (int i = 0; i < n; ++i)
    {
        cin>>a[i];
        sum+=a[i];
        temp=a[i];
        b[i]=0;
        while(temp%x==0){
            b[i]++;
            temp/=x;
        }
        if(mn>b[i]){
            mn=b[i];
            indx=i;
        }
    }
    for (int i = 0; i < n; ++i)
    {
        sum+=mn*a[i];
    }
    for (int i = 0; i < indx; ++i)
    {
        sum+=a[i];
    }
    cout<<sum<<"\n";
}
int32_t main(){
    // cout << setprecision(0);
    IO();
    int tt=1;
    cin>>tt;
    while(tt--){
        run_time_terror();
    }
    // cerr<<(float)clock()/CLOCKS_PER_SEC*1000<<" ms"<<endl;
    return 0;
}       
```