Problem Description

In a Cartesian coordinate system, there is a rectangle with diagonally opposite corners at $(1, -A)$ and $(L, B)$. This rectangle contains $L \times (A + 1 + B)$ points.

There are two guards positioned at $(0, -A)$ and $(0, B)$, both facing the rectangle. A guard cannot see a point within the rectangle if there is another point blocking the line of sight to that point.

For each point:

• If it can be seen by both guards, it is considered very safe;
• If it can be seen by only one guard, it is considered safe;
• If it cannot be seen by either guard, it is considered dangerous.

Given $A, B, L$, you need to determine the number of very safe, safe, and dangerous points.

Input Format

The first line contains two integers $A, B$.

The second line contains one integer $L$.

Output Format

Output three lines. Each line contains one integer, representing the number of dangerous, safe, and very safe points respectively.

Sample Input and Output

Input Sample #1

1 1
3

Output Sample #1

2
2
5

Input Sample #2

2 3
4

Output Sample #2

0
16
8

Input Sample #3

7 11
1000000

Output Sample #3

6723409
2301730
9974861

Notes

Data Size and Constraints

• For $50\%$ of the data, $L \le 1000$;
• For another $25\%$ of the data, $A, B \le 100$;
• For $100\%$ of the data, $1 \le A, B \le 2000$, $1 \le L \le 10^9$.

Notes

This problem is translated from COCI2008-2009 CONTEST #4 T5 TREZOR.

见题面 Input 部分

见题面 Output 部分