## Task 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 x (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.

### Scoring

In test cases worth 50% of points, L will be at most 1000.
In test worth another 25% of points, A and B will be at most 100 (but L can be as large as one billion).

`1 13`

`225`

`2 34`

`0168`

### Input

`7 111000000`

### Output

`672340923017309974861`

Point Value: 30 (partial)
Time Limit: 2.00s
Memory Limit: 16M
Added: Jan 19, 2009

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

## Comments (Search)

• (0/0)
I'm currently getting this error when I try to submit:

A PHP Error was encountered
Severity: Warning
Message: stream_socket_client(): unable to connect to unix:///var/run/pegjudge/socket (No such file or directory)
Filename: controllers/submissions.php
Line Number: 784
An Error Was Encountered
Could not connect to grader. Your submission was not saved.

Is this just me?

• (0/0)
No, I got the same error.