레이팅 미적용Mirko 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.
The first line contains integers \(A\) and \(B\) separated by a space (\(1 \le A \le 2000\), \(1 \le B \le 2000\)).
The second line contains the integer \(L\) (\(1 \le L \le 1\,000\,000\,000\)).
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 tests worth another \(25\%\) of points, \(A\) and \(B\) will be at most \(100\) (but \(L\) can be as large as one billion).
| 서브태스크 | 점수 | 설명 |
|---|---|---|
Subtask 1 | 60점 | \(L \le 1000\) |
Subtask 2 | 30점 | \(A \le 100\), \(B \le 100\) (\(L\) up to \(10^9\)) |
Subtask 3 | 30점 | No additional constraints. |
1 1
32
2
52 3
40
16
87 11
10000006723409
2301730
9974861