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.
#include <bits/stdc++.h>
using namespace std;
int make1(int n, int m, int a, int b) {
  int wk = 0;
  while (n > 0) {
    n--;
    wk += a;
  }
  return wk;
}
int make2(int n, int m, int a, int b) {
  int wk = 0;
  while (n > 0) {
    n -= m;
    wk += b;
  }
  return wk;
}
int make3(int n, int m, int a, int b) {
  int wk = 0;
  while (n >= m) {
    n -= m;
    wk += b;
  }
  while (n > 0) {
    n--;
    wk += a;
  }
  return wk;
}
int main() {
  int n = 0, m = 0, a = 0, b = 0, last = 0;
  scanf("%i%i%i%i", &n, &m, &a, &b);
  if (a * m < b) {
    last = a * n;
    printf("%i\n", last);
  } else {
    int q = make1(n, m, a, b);
    int qq = make2(n, m, a, b);
    int qqq = make3(n, m, a, b);
    int min = q;
    if (qq < min) {
      min = qq;
    }
    if (qqq < min) {
      min = qqq;
    }
    printf("%i\n", min);
  }
  return 0;
}
