# 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 |