P6452 [COCI 2008/2009 #4] TREZOR

In the Cartesian coordinate plane, there is a rectangle whose two opposite vertices on a diagonal are $(1,-A)$ and $(L,B)$. Inside this rectangle, there are $L \times (A+1+B)$ points. Now there are two guards at the points $(0,-A)$ and $(0,B)$. They both look toward this rectangle. If a guard’s line of sight (a ray) to a point inside the rectangle is blocked by other points, then he cannot see that point. For each point: - If it can be seen by both guards, then it is considered very safe. - If it can be seen by only one guard, then it is considered safe. - If it cannot be seen by either guard, then it is considered dangerous. Given $A$, $B$, and $L$, you need to find the numbers of very safe points, safe points, and dangerous points.

The first line contains two integers $A$ and $B$. The second line contains one integer $L$.

Output $3$ lines. Each line contains one integer, in order: the number of dangerous points, the number of safe points, and the number of very safe points.

#### Constraints - For $50\%$ of the testdata, $L \le 1000$. - For another $25\%$ of the testdata, $A,B \le 100$. - For $100\%$ of the testdata, $1 \le A,B \le 2000$, $1 \le L \le 10^9$. #### Notes **This problem is translated from [COCI2008-2009](https://hsin.hr/coci/archive/2008_2009/) [CONTEST #4](https://hsin.hr/coci/archive/2008_2009/contest4_tasks.pdf) *T5 TREZOR*.** Translated by ChatGPT 5