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.

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.

Example

Input:
1 1
3

Output:
2
2
5

Input:
2 3
4

Output:
0
16
8

Input:
7 11
1000000

Output:
6723409
2301730
9974861