Cake Cutting

You are given a rectangular cake with integer dimensions $w \times h$. Divide the cake into $m$ rectangular pieces, each with integer dimensions, so that the area of the largest piece is as small as possible. Every cut must be a straight line parallel to one of the sides of the cake, and it must split a single existing piece into two pieces, each of positive area. Because each cut splits exactly one piece into two, dividing the cake into $m$ pieces requires exactly $m - 1$ cuts.

The input contains several test cases. Each test case is a line with three integers $w$, $h$, and $m$ separated by single spaces, where $1 \le w, h, m \le 20$ and $m \le wh$. The line $w = h = m = 0$ marks the end of the input and must not be processed.

For each test case, print a single line containing one positive integer: the minimum possible area of the largest piece.

When $w = 4$, $h = 4$, and $m = 4$, the following cuts minimize the area of the largest piece:

When $w = 4$, $h = 4$, and $m = 3$, the following cuts are optimal: