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.

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).

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).

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출처 COCI 2008/2009 Contest 4