CF449A.Jzzhu and Chocolate

Jzzhu has a big rectangular chocolate bar that consists of n × m unit squares. He wants to cut this bar exactly k times. Each cut must meet the following requirements:

• each cut should be straight (horizontal or vertical);
• each cut should go along edges of unit squares (it is prohibited to divide any unit chocolate square with cut);
• each cut should go inside the whole chocolate bar, and all cuts must be distinct.

The picture below shows a possible way to cut a 5 × 6 chocolate for 5 times.

Imagine Jzzhu have made k cuts and the big chocolate is splitted into several pieces. Consider the smallest (by area) piece of the chocolate, Jzzhu wants this piece to be as large as possible. What is the maximum possible area of smallest piece he can get with exactly k cuts? The area of a chocolate piece is the number of unit squares in it.

Jzzhu 有一块大小为 $n \times m$ 的矩形巧克力，由 $n \times m$ 个单位小方格组成。他希望恰好切 $k$ 刀。每次切割必须满足以下要求：

• 每刀必须是直线（水平或垂直）；
• 每刀必须沿单位小方格的边进行（禁止将任何一个单位巧克力小方格切开）；
• 每刀必须完全位于整块巧克力内部，且所有切割互不重合。

下图展示了一种对 $5 \times 6$ 巧克力进行 $5$ 次切割的可行方式。

假设 Jzzhu 已完成 $k$ 次切割，整块巧克力被分成了若干块。考虑其中面积最小的一块（面积定义为所含单位小方格的数量），Jzzhu 希望该最小块的面积尽可能大。那么，在恰好进行 $k$ 次切割的前提下，所能得到的最小块的最大可能面积是多少？

A single line contains three integers n, m, k (1 ≤ n, m ≤ 109; 1 ≤ k ≤ 2·109).

一行包含三个整数 $n$、$m$、$k$（$1 \le n, m \le 10^9$；$1 \le k \le 2\cdot10^9$）。

Output a single integer representing the answer. If it is impossible to cut the big chocolate k times, print -1.

输出一个整数表示答案。如果无法将大巧克力切割 $k$ 次，则输出 $-1$。

In the first sample, Jzzhu can cut the chocolate following the picture below:

In the second sample the optimal division looks like this:

In the third sample, it's impossible to cut a 2 × 3 chocolate 4 times.

在第一个样例中，Jzzhu 可以按照下图所示的方式切割巧克力：

在第二个样例中，最优的分割方式如下图所示：

在第三个样例中，无法将一块 $2 \times 3$ 的巧克力切割 $4$ 次。