TREZOR

문제

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. 

입력

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 ≤ 1000000000).

출력

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

 

1 1
3

2
2
5

2 3
4

0
16
8

7 11
1000000

6723409
2301730
9974861