# It isn't 2013!

For $$1\le i\le 10000$$, an integer is chosen uniformly at random between 1 and $$i$$ inclusive. Let $$S$$ be the sum of all numbers chosen in this way. If the probability that $$2014$$ divides $$S$$ but $$2013$$ does not divide $$S$$ can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are relatively prime positive integers, find the remainder when $$a+b$$ is divided by 1000.

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