#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, m, a, b, x, y;
  cin >> n >> m >> a >> b;
  long long s[3];
  s[0] = n * a;
  x = n / m;
  y = n % m;
  s[1] = (1 + x) * b;
  s[2] = x * b + y * a;
  sort(s, s + 3);
  cout << s[0];
}

### Prompt

Construct a cpp code solution to the problem outlined:

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;
int main() {
  long long n, m, a, b, x, y;
  cin >> n >> m >> a >> b;
  long long s[3];
  s[0] = n * a;
  x = n / m;
  y = n % m;
  s[1] = (1 + x) * b;
  s[2] = x * b + y * a;
  sort(s, s + 3);
  cout << s[0];
}

```