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?
Constraints
- $1 \leq X \leq Y \leq 100$
- $1 \leq N \leq 100$
- All values in input are integers.
Input
Input is given from Standard Input in the following format:
$X$ $Y$ $N$
Output
Print the answer as an integer.
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