Cheap Travel Problem !!!

 PROBLEM 15: Cheap Travel

Problem Reference : Codeforces 

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.

Solution:

1. import math
2. n, m, a, b = input().split()
3. n1 = int(n)
4. m1 = int(m)
5. a1 = int(a)
6. b1 = int(b)
7. n2 = n1
8. sum1 = 0
9. n3 = n1
10. m3 = m1
11. b3 = b1
12. a3 = a1
13.  
14. d = n1 / m1
15. d1 = math.ceil(d)
16. d2 = d1 * b1
17.  
18. d3 = n2 * a1
19.  
20. while n3 >= m1:
21. n3 = n3 - m1
22. sum1 = sum1 + b3
24. while n3 > 0:
25. sum1 = sum1 + a3
26. n3 = n3 - 1
29. print(min(d2,d3,sum1))

This above solution is in python language.

Examples

input

6 2 1 2

output

6

input

5 2 2 3

output

8