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\cdot (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 Specification

The first line contains integers ~A~ and ~B~ separated by a space ~(1 \le A, B \le 2000)~. The second line contains the integer ~L~ ~(1 \le L \le 1\,000\,000\,000)~.

Output Specification

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

Sample Input 1

1 1
3

Sample Output 1

2
2
5

Sample Input 2

2 3
4

Sample Output 2

0
16
8

Sample Input 3

7 11
1000000

Sample Output 3

6723409
2301730
9974861