#include <bits/stdc++.h>
using namespace std;
long long int M = 100000000000000;
long long int M1 = 1000000007;
int main() {
  double f1;
  int n, m, a, b, x1, x2, x3, ans, ans1, x4;
  cin >> n >> m >> a >> b;
  f1 = (double)b / m;
  if (f1 >= (double)a) {
    ans = n * a;
    cout << ans << endl;
  } else {
    x1 = n / m + 1;
    if (n % m == 0) x1--;
    x2 = n / m;
    x3 = n - m * x2;
    x4 = x3 * a;
    ans = b * x2 + x4;
    ans1 = min(ans, b * x1);
    cout << ans1 << endl;
  }
}

### Prompt

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

Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?

Input

The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket. 

Output

Print a single integer — the minimum sum in rubles that Ann will need to spend.

Examples

Input

6 2 1 2


Output

6


Input

5 2 2 3


Output

8

Note

In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long int M = 100000000000000;
long long int M1 = 1000000007;
int main() {
  double f1;
  int n, m, a, b, x1, x2, x3, ans, ans1, x4;
  cin >> n >> m >> a >> b;
  f1 = (double)b / m;
  if (f1 >= (double)a) {
    ans = n * a;
    cout << ans << endl;
  } else {
    x1 = n / m + 1;
    if (n % m == 0) x1--;
    x2 = n / m;
    x3 = n - m * x2;
    x4 = x3 * a;
    ans = b * x2 + x4;
    ans1 = min(ans, b * x1);
    cout << ans1 << endl;
  }
}

```