URI Online Judge | 3105

Folding Paper

By Giovanna Kobus Conrado, University of São Paulo BR Brazil

Timelimit: 1

You have a huge paper you need to fold. It is N centimeters long, M centimeters wide and 1 millimeter tall. You can fold it perfectly along both axis. For any integers X and Y greater or equal to zero, if you fold it X times vertically and Y times horizontally, it will now be N/(X+1) centimeters long, M/(Y+1) centimeters wide and (X+1)×(Y+1) milimeters tall.

You want to store your paper in a box. For any integer G, you can buy a box that can fit any paper no more than than G centimeters wide, no more than G centimeters long and no more than K milimeters tall, for G dollars. K is a number set by the store that sells the boxes and is the same for all the boxes that they sell.

Now you want to know what is the least you can spend on a box to store your paper.


The input consists of three, integers, N, M (1≤N,M≤1018) and K (1≤K≤105), as described above.


The output must consist of a single integer that represent the price in dollars of the cheapest box your paper can fit in if you fold it optimally.

Input Sample Output Sample

600 400 7