Problem Description

A store sells notebooks in two types of packages: the first type is a single notebook for $x$ yuan, and the second type is a ten-pack with a discount, priced at $y$ yuan.

The store has launched a "Double Eleven" promotion where each package is discounted by 1 yuan. After the discount, the single notebook costs $x - 1$ yuan, and the ten-pack costs $y - 1$ yuan.

Xiao Ming wants to buy exactly $n$ notebooks. How much money does he need to spend at least?

Note: "Exactly" means that Xiao Ming cannot buy fewer than $n$ notebooks or more than $n$ notebooks.

Input Format

A single line containing three numbers $x, y, n$, representing the price of a single notebook, the price of a ten-pack, and the number of notebooks Xiao Ming needs, respectively.

Output Format

A single number representing the minimum amount of money Xiao Ming needs to spend to buy $n$ notebooks.

Sample Input and Output

Sample Input #1

10 80 10

Sample Output #1

79

Sample Input #2

10 80 11

Sample Output #2

88

Sample Input #3

10 80 1

Sample Output #3

9

Notes

Sample Explanation:

The original price of a single notebook is $10$ yuan, and the original price of a ten-pack is $80$ yuan.

After the discount, the price of a single notebook is $9$ yuan, and the price of a ten-pack is $79$ yuan.

At this time, if Xiao Ming buys $10$ notebooks, he needs $79$ yuan; if he buys $1$ notebook, he needs $9$ yuan; if he buys $11$ notebooks, he needs $88$ yuan.

Data Range:

For $20\%$ of the data, $n < 10$;

For another $20\%$ of the data, $n$ is a multiple of $10$;

For $80\%$ of the data, $0 \le n, x, y \le 10^4$;

For $100\%$ of the data, $0 \le n, x, y \le 10^9$.

见题面 Input 部分

见题面 Output 部分