#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  long long n, m, a, b;
  cin >> n >> m >> a >> b;
  long long rs = 1e6;
  for (long long i = 0; i <= n; i++) {
    for (long long j = 0; j <= n; j++) {
      long long s = i + j * m;
      if (s >= n) {
        long long cost = a * i + b * j;
        rs = min(rs, cost);
      }
    }
  }
  cout << rs;
}

### Prompt

Develop a solution in cpp 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;
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  long long n, m, a, b;
  cin >> n >> m >> a >> b;
  long long rs = 1e6;
  for (long long i = 0; i <= n; i++) {
    for (long long j = 0; j <= n; j++) {
      long long s = i + j * m;
      if (s >= n) {
        long long cost = a * i + b * j;
        rs = min(rs, cost);
      }
    }
  }
  cout << rs;
}

```