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 Specification

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

Output Specification

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

Scoring

In test cases worth $50\mathrm{\%}$ of points, $L$ will be at most $1000$.

In test cases worth another $25\mathrm{\%}$ of points, $A$ and $B$ will be at most $100$ (but $L$ can be as large as one billion).

Sample Input 1

1 1
3

Sample Output 1

2
2
5

Sample Input 2

2 3
4

Sample Output 2

0
16
8

Sample Input 3

7 11
1000000

Sample Output 3

6723409
2301730
9974861