#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int findMaxMid(vector<int> arr, int start, int end, int mid)
{
    int maxRight = arr[mid];
    int maxLeft = arr[mid];
    int i = mid+1;
    int sum = arr[mid];
    while(i <= end)
    {
        sum += arr[i];
        if(sum > maxRight)
        {
            maxRight = sum;
        }
        i++;
    }
    i = mid-1;
    sum = arr[mid];
    while(i >= start)
    {
        sum += arr[i];
        while(sum > maxLeft)
        {
            maxLeft = sum;
        }
        i--;
    }
    return maxLeft + maxRight - arr[mid];
}

int findMax(vector<int> arr, int start, int end)
{
    if(start > end)
    {
        return -1000;
    }
    if(start == end)
    {
        return arr[start];
    }
    int mid = (start+end)/2;
    int val1 = findMax(arr,start,mid-1);
    int val2 = findMax(arr, mid+1,end);
    int val3 = findMaxMid(arr,start,end,mid);
    if(val1 > val2 && val1 > val3)
    {
        return val1;
    }
    else if(val2 > val1 && val2 > val3)
    {
        return val2 ;
    } 
    else
    {
        return val3;
    }
}

int simpleMaxMid(vector<int> red, vector<int> blue)
{
    int sumRed = 0;
    int sumBlue = 0;
    int maxRed = -10000;
    int maxBlue = -10000;
    for(int i=0;i<red.size();i++)
    {
        sumRed += red[i];
        if(sumRed > maxRed)
        {
            maxRed = sumRed;
        }
    }
    for(int i=0;i<blue.size();i++)
    {
        sumBlue += blue[i];
        if(sumBlue > maxBlue)
        {
            maxBlue = sumBlue;
        }
    }
    //cout<<maxRed<<" "<<maxBlue;
    if(maxBlue < 0 && maxRed < 0)
    {
        return 0;
    }
    if(maxBlue > 0 && maxRed < 0)
    {
        return maxBlue;
    }
    if(maxRed > 0 && maxBlue < 0)
    {
        return maxRed;
    }
    return maxRed + maxBlue;
}

int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        int n;
        cin>>n;
        long long x;
        cin>>x;
        vector<long long> arr;
        vector<long long> original;
        long long output = 0;
        for(int i=0;i<n;i++)
        {
            int temp;
            cin>>temp;
            arr.push_back(temp);
            original.push_back(temp);
            output += temp;
        }
        int j = 0;
        while(true)
        {
            if(j == n)
            {
                j = 0;
            }
            if(arr[j] % x != 0)
            {
                break;
            }
            else
            {
                output += original[j];
                arr[j] = arr[j]/x;
            }
            j++;
        }
        cout<<output;
        cout<<"\n";
    }
}
### Prompt

Please create a solution in CPP 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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int findMaxMid(vector<int> arr, int start, int end, int mid)
{
    int maxRight = arr[mid];
    int maxLeft = arr[mid];
    int i = mid+1;
    int sum = arr[mid];
    while(i <= end)
    {
        sum += arr[i];
        if(sum > maxRight)
        {
            maxRight = sum;
        }
        i++;
    }
    i = mid-1;
    sum = arr[mid];
    while(i >= start)
    {
        sum += arr[i];
        while(sum > maxLeft)
        {
            maxLeft = sum;
        }
        i--;
    }
    return maxLeft + maxRight - arr[mid];
}

int findMax(vector<int> arr, int start, int end)
{
    if(start > end)
    {
        return -1000;
    }
    if(start == end)
    {
        return arr[start];
    }
    int mid = (start+end)/2;
    int val1 = findMax(arr,start,mid-1);
    int val2 = findMax(arr, mid+1,end);
    int val3 = findMaxMid(arr,start,end,mid);
    if(val1 > val2 && val1 > val3)
    {
        return val1;
    }
    else if(val2 > val1 && val2 > val3)
    {
        return val2 ;
    } 
    else
    {
        return val3;
    }
}

int simpleMaxMid(vector<int> red, vector<int> blue)
{
    int sumRed = 0;
    int sumBlue = 0;
    int maxRed = -10000;
    int maxBlue = -10000;
    for(int i=0;i<red.size();i++)
    {
        sumRed += red[i];
        if(sumRed > maxRed)
        {
            maxRed = sumRed;
        }
    }
    for(int i=0;i<blue.size();i++)
    {
        sumBlue += blue[i];
        if(sumBlue > maxBlue)
        {
            maxBlue = sumBlue;
        }
    }
    //cout<<maxRed<<" "<<maxBlue;
    if(maxBlue < 0 && maxRed < 0)
    {
        return 0;
    }
    if(maxBlue > 0 && maxRed < 0)
    {
        return maxBlue;
    }
    if(maxRed > 0 && maxBlue < 0)
    {
        return maxRed;
    }
    return maxRed + maxBlue;
}

int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        int n;
        cin>>n;
        long long x;
        cin>>x;
        vector<long long> arr;
        vector<long long> original;
        long long output = 0;
        for(int i=0;i<n;i++)
        {
            int temp;
            cin>>temp;
            arr.push_back(temp);
            original.push_back(temp);
            output += temp;
        }
        int j = 0;
        while(true)
        {
            if(j == n)
            {
                j = 0;
            }
            if(arr[j] % x != 0)
            {
                break;
            }
            else
            {
                output += original[j];
                arr[j] = arr[j]/x;
            }
            j++;
        }
        cout<<output;
        cout<<"\n";
    }
}
```