#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int rides, mrides, oneride_price, mridesprice;
  cin >> rides >> mrides >> oneride_price >> mridesprice;
  int oneRideTotals = oneride_price * rides;
  if (rides % mrides == 0) {
    if ((rides / mrides) * mridesprice <= oneRideTotals) {
      cout << (rides / mrides) * mridesprice;
    } else {
      cout << oneRideTotals;
    }
  } else {
    if ((rides / mrides) * mridesprice + (rides % mrides) * oneride_price <=
        rides * oneride_price) {
      if ((rides % mrides) * oneride_price <= mridesprice) {
        cout << (rides / mrides) * mridesprice +
                    (rides % mrides) * oneride_price;
      } else {
        cout << (rides / mrides) * mridesprice + mridesprice;
      }
    } else {
      cout << rides * oneride_price;
    }
  }
}

### 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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int rides, mrides, oneride_price, mridesprice;
  cin >> rides >> mrides >> oneride_price >> mridesprice;
  int oneRideTotals = oneride_price * rides;
  if (rides % mrides == 0) {
    if ((rides / mrides) * mridesprice <= oneRideTotals) {
      cout << (rides / mrides) * mridesprice;
    } else {
      cout << oneRideTotals;
    }
  } else {
    if ((rides / mrides) * mridesprice + (rides % mrides) * oneride_price <=
        rides * oneride_price) {
      if ((rides % mrides) * oneride_price <= mridesprice) {
        cout << (rides / mrides) * mridesprice +
                    (rides % mrides) * oneride_price;
      } else {
        cout << (rides / mrides) * mridesprice + mridesprice;
      }
    } else {
      cout << rides * oneride_price;
    }
  }
}

```