OpenKattis
National University of Singapore

Trezor

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 ($1 \leq A \leq 2\, 000, 1 \leq B \leq 2\, 000$). The second line contains the integer $L$ ($1 \leq L \leq 1\, 000\, 000\, 000$).

Output

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

Sample Input 1 Sample Output 1
1 1
3
2
2
5
Sample Input 2 Sample Output 2
2 3
4
0
16
8
Sample Input 3 Sample Output 3
7 11
1000000
6723409
2301730
9974861