There are many Equations. Some are difficult to solve, for example: `a _{n} x^{n} + a_{n-1} x^{n-1} + .. + a_{0} = 0`.

In this problem, you are given a simple equation: `AX + BY = XY`. To simplify the problem, here `A`, `B`, `X`, `Y` are positive integers. Your task is to find the solution `(X, Y)` of this equation where `X` is not less than M. If there are multiple solutions, you should choose the solution with the minimal `X + Y`. If there are still ties, you should choose the solution with the minimal `X`.

There are multiple test cases (about 3000). For each test case:

There is only one line contains three integers `A`, `B` (1 <= `A`, `B` <= 10 ^ 9) and `M` (1 <= `M` <= 10 ^ 18).

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