#include<iostream>
#include<vector>
#include<algorithm>
#include<string>
using namespace std;

typedef int64_t ll;

#define f first
#define s second

ll process(ll a,ll x){
    ll c=0;
    while(a%x==0){
        c++;
        a/=x;
    }
    return c;
}

void solve(){
    int n;ll x;
    cin>>n>>x;
    vector<ll>v(n,0);
    vector<ll>hmm(1e5+10,0);
    //vector<bool> pros(1e9+10,0);
    ll sum=0,mi=LONG_LONG_MAX,cur;
    bool val=true;
    ll a,h;
    int pos=0;
    for(int i=0;i<n;i++){
        cin>>a;
        cur=mi;
        h=process(a,x);
        mi=min(mi,h);        
        if(cur!=mi)pos=i;
        sum+=a;
        hmm[i]=sum;
    }
    sum*=(mi+1);
    if(pos!=0)sum+=hmm[pos-1];
    cout<<sum<<endl;
    
}


int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int t;
    cin>>t;
    while(t--){
        solve();
    }
    return 0;
}

/*



   _______                       _______ _______
  |       |  |_      | |       |    |       |
  |       |  | |_    | |       |    |       |
  |_______|  |   |_  | |       |    |       |
  |       |  |     |_| |       |    |       |
  |       |  |       | |_______|    |    ___|   




*/
### Prompt

Create a solution in Cpp for 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<iostream>
#include<vector>
#include<algorithm>
#include<string>
using namespace std;

typedef int64_t ll;

#define f first
#define s second

ll process(ll a,ll x){
    ll c=0;
    while(a%x==0){
        c++;
        a/=x;
    }
    return c;
}

void solve(){
    int n;ll x;
    cin>>n>>x;
    vector<ll>v(n,0);
    vector<ll>hmm(1e5+10,0);
    //vector<bool> pros(1e9+10,0);
    ll sum=0,mi=LONG_LONG_MAX,cur;
    bool val=true;
    ll a,h;
    int pos=0;
    for(int i=0;i<n;i++){
        cin>>a;
        cur=mi;
        h=process(a,x);
        mi=min(mi,h);        
        if(cur!=mi)pos=i;
        sum+=a;
        hmm[i]=sum;
    }
    sum*=(mi+1);
    if(pos!=0)sum+=hmm[pos-1];
    cout<<sum<<endl;
    
}


int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int t;
    cin>>t;
    while(t--){
        solve();
    }
    return 0;
}

/*



   _______                       _______ _______
  |       |  |_      | |       |    |       |
  |       |  | |_    | |       |    |       |
  |_______|  |   |_  | |       |    |       |
  |       |  |     |_| |       |    |       |
  |       |  |       | |_______|    |    ___|   




*/
```