COCI 2008/2009, Contest #4

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).

Examples

Input 1 1 3 Output 2 2 5

Input 2 3 4 Output 0 16 8

Input 7 11 1000000 Output 6723409 2301730 9974861

All Submissions
Best Solutions

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

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