Mirko decided to open a new business—bank vaults. A branch of the bank can be visualized in a plane, vaults being points in the plane. Mirko’s branch contains exactly $L\cdot (A+1+B)$ vaults, so that each point with integer coordinates inside the rectangle with corners $(1, -A)$ and $(L, B)$ contains one vault.

The vaults are watched by two guards—one at $(0, -A)$, the other at $(0, B)$. A guard can see a vault if there are no other vaults on the line segment connecting them.

A vault is not secure if neither guard can see it, secure if only one guard can see it and super-secure if both guards can see it. Given $A$, $B$ and $L$, output the number of insecure, secure and super-secure vaults.

-----Input-----
The first line contains integers $A$ and $B$ separated by a space ($1 \leq A \leq 2000, 1 \leq B \leq 2000$). The second line contains the integer $L$ ($1 \leq L \leq 1000000000$).

-----Output-----
Output on three separate lines the numbers of insecure, secure and super-secure vaults.

-----Examples-----
Sample Input 1:
1 1
3
Sample Output 1:
2
2
5

Sample Input 2:
2 3
4
Sample Output 2:
0
16
8

Source: kattis | Difficulty: HARD


Solutions: