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Brilliant answers are integers ranging from 0 to 999. Let $$x$$ be the answer to this problem, where $$0 \leq x \leq 999$$. Without any clue to solving this problem, Tom randomly picks an integer $$y$$ as his answer in the same range. The probability that $$1 \leq y < x$$ can be expressed as $$\frac {a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers in the simplest form. Since usual problems that ask for a fraction have their answer as the sum of $$a$$ and $$b$$, find the smallest possible answer $$x=a+b$$.

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