Problem Statement

A fruit store sells apples.
You may perform the following operations as many times as you want in any order:

• Buy one apple for X yen (the currency in Japan).
• Buy three apples for Y yen.

How much yen do you need to pay to obtain exactly N apples?

Input

Input is given from Standard Input in the following format:
X Y N

Output

Print the answer as an integer.

Constraints

• $1 \leq X \leq Y \leq 100$
• $1 \leq N \leq 100$
• All values in input are integers.

Sample Input 1

10 25 10

Sample Output 1

85

Buy three apples for 25 yen three times and one apple for 10 yen, and you will obtain exactly 10 apples for a total of 85 yen.
You cannot obtain exactly 10 apples for a lower cost, so the answer is 85 yen.

Sample Input 2

10 40 10

Sample Output 2

100

It is optimal to buy an apple for 10 yen 10 times.

Sample Input 3

100 100 2

Sample Output 3

200

The only way to obtain exactly 2 apples is to buy an apple for 100 yen twice.

Sample Input 4

100 100 100

Sample Output 4

3400

见题面 Input 部分

见题面 Output 部分