We have had record hot temperatures this summer. To avoid heat stroke, you decided to buy a quantity of drinking water at the nearby supermarket. Two types of bottled water, 1 and 0.5 liter, are on sale at respective prices there. You have a definite quantity in your mind, but are willing to buy a quantity larger than that if: no combination of these bottles meets the quantity, or, the total price becomes lower.
Given the prices for each bottle of water and the total quantity needed, make a program to seek the lowest price to buy greater than or equal to the quantity required.
The input is given in the following format.
$A$ $B$ $X$
The first line provides the prices for a 1-liter bottle $A$ ($1\leq A \leq 1000$), 500-milliliter bottle $B$ ($1 \leq B \leq 1000$), and the total water quantity needed $X$ ($1 \leq X \leq 20000$). All these values are given as integers, and the quantity of water in milliliters.
Output the total price.
180 100 2400
460
200 90 2018
450