SP3733 TREZOR - Trezor

[English](/problems/TREZOR/en/) [Vietnamese](/problems/TREZOR/vn/)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.

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