Problem 2 : Basic Operations

Algebra Level 4

A positive real number is given. In each move, we can either add 33 to it, subtract 33 to it, multiply it by 33 and divide it by 33. The sum of all numbers such that after exactly 33 moves, the original number comes back is ab\frac{a}{b}, where aa and bb are relatively prime positive integers. Find a+ba + b.

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