#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int N, M, A, B, X, Y = 0, Z = 0, u, i;
  cin >> N >> M >> A >> B;
  X = N * A;
  Y += M;
  Z += B;
  while ((Y + M) < N) {
    Y += M;
    Z += B;
  }
  if (Y < N) {
    u = Y;
    u = N - u;
    if ((u * A) >= (u * B)) {
      Y += M;
      Z += B;
    } else if ((u * A) < (u * B)) {
      while (Y + 1 <= N) {
        Y++;
        Z += A;
      }
    }
  }
  cout << min(Z, X);
  return 0;
}

### Prompt

In CPP, your task is to solve 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() {
  long long int N, M, A, B, X, Y = 0, Z = 0, u, i;
  cin >> N >> M >> A >> B;
  X = N * A;
  Y += M;
  Z += B;
  while ((Y + M) < N) {
    Y += M;
    Z += B;
  }
  if (Y < N) {
    u = Y;
    u = N - u;
    if ((u * A) >= (u * B)) {
      Y += M;
      Z += B;
    } else if ((u * A) < (u * B)) {
      while (Y + 1 <= N) {
        Y++;
        Z += A;
      }
    }
  }
  cout << min(Z, X);
  return 0;
}

```