#include <bits/stdc++.h>
using namespace std;
inline void use_io_optimizations() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
}
int main() {
  use_io_optimizations();
  unsigned int rides;
  unsigned int m_rides;
  unsigned int one_ride_price;
  unsigned int m_rides_price;
  cin >> rides >> m_rides >> one_ride_price >> m_rides_price;
  if (one_ride_price * m_rides <= m_rides_price) {
    cout << rides * one_ride_price;
  } else {
    cout << (rides / m_rides) * m_rides_price +
                min(m_rides_price, (rides % m_rides) * one_ride_price);
  }
  cout << '\n';
  return 0;
}

### 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;
inline void use_io_optimizations() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
}
int main() {
  use_io_optimizations();
  unsigned int rides;
  unsigned int m_rides;
  unsigned int one_ride_price;
  unsigned int m_rides_price;
  cin >> rides >> m_rides >> one_ride_price >> m_rides_price;
  if (one_ride_price * m_rides <= m_rides_price) {
    cout << rides * one_ride_price;
  } else {
    cout << (rides / m_rides) * m_rides_price +
                min(m_rides_price, (rides % m_rides) * one_ride_price);
  }
  cout << '\n';
  return 0;
}

```