You are given a rectangular cake of integral dimensions w × h. Your goal is to divide this cake into m rectangular pieces of integral dimensions such that the area of the largest piece is minimal. Each cut must be a straight line parallel to one of the sides of the original cake and must divide a piece of cake into two new pieces of positive area. Note that since a cut divides only a single piece, exactly m−1 cuts are needed.
If w = 4, h = 4, and m = 4, then the following cuts minimize the area of the largest piece would be shaped as the first example. However, if w = 4, h = 4, and m = 3, then the second picture would be the optimal.
The input test file will contain multiple test cases, each of which consists of three integers w, h, m separated by a single space, with 1 <= w, h, m <= 20 and m <= wh. The end-of-file is marked by a test case with w = h = m = 0 and should not be processed.
For each test case, write a single line with a positive integer indicating the area of the largest piece.
4 4 4 4 4 3 0 0 0