Problem Description

The Takahashi family has decided to buy \( K \) oranges for the current season. Oranges are sold for \( A \) yen each, and also in sets of \( L \) oranges for \( B \) yen. Write a program to determine the minimum amount of money needed to buy at least \( K \) oranges by purchasing a combination of individual oranges and sets of \( L \) oranges.

Input Format

The input is given from the standard input in the following format:

\( A \) \( B \) \( K \) \( L \)

Output Format

Output the minimum amount of money required to buy at least \( K \) oranges.

Sample Input and Output

Sample Input #1

3 7 10 3

Sample Output #1

24

Sample Input #2

4 5 11 3

Sample Output #2

20

Sample Input #3

3 8 3 3

Sample Output #3

8

Sample Input #4

3 8 2 3

Sample Output #4

6

Notes/Hints

Constraints

• \( 1 \leq A, B, K \leq 10^9 \)
• \( 2 \leq L \leq 10^9 \)
• \( B \leq A \times L \)

Sample Explanation 1

Buying 3 sets of 3 oranges and 1 individual orange totals 24 yen. There is no cheaper way to buy 10 oranges.

Sample Explanation 2

The optimal solution is to buy 4 sets of 3 oranges.

见题面 Input 部分

见题面 Output 部分