102650: [AtCoder]ABC265 A - Apple

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

Sample Output 4

3400

问题描述

一家水果店出售苹果。

你可以按照任何顺序想买多少次就买多少次以下操作：

• 以X日元（日本货币）的价格买一个苹果。
• 以Y日元的价格买三个苹果。

你需要支付多少日元才能获得正好 N 个苹果？

约束

• $1 \leq X \leq Y \leq 100$
• $1 \leq N \leq 100$
• 输入中的所有值都是整数。

输入

输入格式如下，从标准输入中给出：

$X$ $Y$ $N$

输出

以整数形式打印答案。

样例输入 1

10 25 10

样例输出 1

85

以25日元的价格购买3个苹果3次，然后以10日元的价格购买1个苹果，总共用85日元就可以获得正好10个苹果。 你不能以更低的成本获得正好10个苹果，所以答案是85日元。

样例输入 2

10 40 10

样例输出 2

100

购买10次10日元的苹果是最佳选择。

样例输入 3

100 100 2

样例输出 3

200

获得正好 2个苹果的唯一方法是购买两次100日元的苹果。

样例输入 4

100 100 100

样例输出 4

3400