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.

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.