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

입출력 예

input 

1 1 
3 

output 

2 
2 
5 

input 

2 3 
4 

output 

0 
16 
8 

input 

7 11 
1000000 

output 

6723409 
2301730 
9974861

출처: coci 2008/2009 contest4 5/6