## Cake Cutting

• 문제 ID
• 시간 제한
• 메모리 제한
• 제출 횟수
• 정답 횟수 (비율)
• 출처
• 분류

#### 문제

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.

#### 입력

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.

#### 출력

For each test case, write a single line with a positive integer indicating the area of the largest piece.

#### 예제 입력

4 4 4
4 4 3
0 0 0

#### 예제 출력

4
6