466A. Cheap Travel

implementation, 1200, https://codeforces.com/problemset/problem/466/A

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.

n,m,a,b = [int(i) for i in input().split()]
 
min_v = min(n*a, b*(n//m) + (n%m)*a, n*b, b*(n//m) + b )
if m >= n:
        print( min(b, min_v) )
else:
        print( min_v )