// Problem Link -
#include <bits/stdc++.h>
using namespace std;

#define ll                   long long int
#define pb                   push_back
#define mod                  1000000007
#define M2                   998244353
#define inf                  1e18
#define ff                   first
#define ss                   second
#define w(x)                 ll x=1; cin>>x; while(x--)
#define mid_of(l,r)          (l+(r-l)/2)
#define pii                  pair<ll,ll>
#define vi                   vector<ll>
#define mii                  unordered_map<ll, ll>
#define sii                  unordered_set<ll>
#define ps(x,y)              fixed<<setprecision(y)<<x
#define loop(i,a,b)          for(ll i = (a); i <= (b); i++)
#define looprev(i,b,a)       for(ll i = (b); i >= (a); i--)
#define mem(dp, val)         memset(dp, val, sizeof(dp))
#define setbits(x)           __builtin_popcountll(x)
#define pq_max               priority_queue<ll>
#define pq_min               priority_queue<ll,vector<ll>,greater<ll>>
#define all(v)               v.begin(), v.end()
#define logarr(arr,a,b)      for(ll i=(a);i<=(b);i++) cout<<(arr[i])<<" "; cout<<"\n";
#define fast_io              ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);



void solve() {
    ll n, x;
    cin >> n >> x;

    vector<pii> v;
    ll num, cnt = 1, temp;

    loop(i, 0, n - 1) {
        cin >> num;
        v.push_back({num, cnt});
    }

    ll i = 0, len = n;
    while(true) {
        len = v.size();
        if(i == len) {
            break;
        }

        num = v[i].ff;
        cnt = v[i].ss;

        if((num % x) != 0) {
            break;
        }

        temp = (num / x);
        v.push_back({temp, (x * cnt)});
        i++;
    }

    ll ans = 0;
    i = 0;
    len = v.size();

    while(i < len) {
        num = v[i].ff;
        cnt = v[i].ss;

        ans += (num * cnt);
        i++;
    }

    cout << ans << "\n";
}

int32_t main() {
    fast_io;

    ll ntc = 1;
    cin >> ntc;

    for(ll t = 1; t <= ntc; t++) {
        // cout << "Case #" << t << ": ";
        solve();
    }

    return 0;
}
### Prompt

Your challenge is to write 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
// Problem Link -
#include <bits/stdc++.h>
using namespace std;

#define ll                   long long int
#define pb                   push_back
#define mod                  1000000007
#define M2                   998244353
#define inf                  1e18
#define ff                   first
#define ss                   second
#define w(x)                 ll x=1; cin>>x; while(x--)
#define mid_of(l,r)          (l+(r-l)/2)
#define pii                  pair<ll,ll>
#define vi                   vector<ll>
#define mii                  unordered_map<ll, ll>
#define sii                  unordered_set<ll>
#define ps(x,y)              fixed<<setprecision(y)<<x
#define loop(i,a,b)          for(ll i = (a); i <= (b); i++)
#define looprev(i,b,a)       for(ll i = (b); i >= (a); i--)
#define mem(dp, val)         memset(dp, val, sizeof(dp))
#define setbits(x)           __builtin_popcountll(x)
#define pq_max               priority_queue<ll>
#define pq_min               priority_queue<ll,vector<ll>,greater<ll>>
#define all(v)               v.begin(), v.end()
#define logarr(arr,a,b)      for(ll i=(a);i<=(b);i++) cout<<(arr[i])<<" "; cout<<"\n";
#define fast_io              ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);



void solve() {
    ll n, x;
    cin >> n >> x;

    vector<pii> v;
    ll num, cnt = 1, temp;

    loop(i, 0, n - 1) {
        cin >> num;
        v.push_back({num, cnt});
    }

    ll i = 0, len = n;
    while(true) {
        len = v.size();
        if(i == len) {
            break;
        }

        num = v[i].ff;
        cnt = v[i].ss;

        if((num % x) != 0) {
            break;
        }

        temp = (num / x);
        v.push_back({temp, (x * cnt)});
        i++;
    }

    ll ans = 0;
    i = 0;
    len = v.size();

    while(i < len) {
        num = v[i].ff;
        cnt = v[i].ss;

        ans += (num * cnt);
        i++;
    }

    cout << ans << "\n";
}

int32_t main() {
    fast_io;

    ll ntc = 1;
    cin >> ntc;

    for(ll t = 1; t <= ntc; t++) {
        // cout << "Case #" << t << ": ";
        solve();
    }

    return 0;
}
```