Meshed Gears

You are given two meshed gears, A and B. Gear A must rotate a times such that gear B rotates exactly b times. In order to satisfy precision requirements, each gear must have at least c teeth.

Formally, assume gear A has T_A teeth and gear B has T_B teeth with the conditions:

• T_A, T_B \(\ge c\)
• \(a \cdot T_A = b \cdot T_B\)

Find the minimum possible value of \(T_A + T_B\).

inputFormat

The input consists of a single line containing three integers a, b, and c.

outputFormat

Output a single integer: the minimum total number of teeth on gears A and B.

sample

2 3 4

10