#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, m, a, b;
  cin >> n >> m >> a >> b;
  int sum1 = 0, sum2 = 0, sum3 = 0, d1, r1;
  sum1 = n * a;
  d1 = (n / m);
  r1 = (n - m * d1) * a;
  sum2 = d1 * b + r1;
  if (n % m != 0)
    sum3 = (d1 + 1) * b;
  else
    sum3 = d1 * b;
  int ar[3];
  ar[0] = sum1;
  ar[1] = sum2;
  ar[2] = sum3;
  sort(ar, ar + 3);
  cout << ar[0] << "\n";
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

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() {
  int n, m, a, b;
  cin >> n >> m >> a >> b;
  int sum1 = 0, sum2 = 0, sum3 = 0, d1, r1;
  sum1 = n * a;
  d1 = (n / m);
  r1 = (n - m * d1) * a;
  sum2 = d1 * b + r1;
  if (n % m != 0)
    sum3 = (d1 + 1) * b;
  else
    sum3 = d1 * b;
  int ar[3];
  ar[0] = sum1;
  ar[1] = sum2;
  ar[2] = sum3;
  sort(ar, ar + 3);
  cout << ar[0] << "\n";
  return 0;
}

```