## TREZOR - Trezor

English | Vietnamese |

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·(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 ≤ A ≤ 2000, 1 ≤ B ≤ 2000).

The second line contains the integer L (1 ≤ L ≤ 1 000 000 000).

### Output

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

### Example

Input:1 1 3Output:2 2 5

Input:2 3 4Output:0 16 8

Input:7 11 1000000Output:6723409 2301730 9974861

Added by: | Race with time |

Date: | 2009-01-18 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ERL JS-RHINO NODEJS PERL6 VB.NET |

Resource: | COCI 2008/2009 |