2013C13

Before you, Brilli the Ant places 2013 urns labelled 1 through 2013. In urn ii, there are i1 i-1 white balls and 2013i 2013 - i black balls. If you randomly choose an urn, and then randomly choose 13 balls without replacement, the probability that all balls are the same color is ab \frac{a}{b} , where aa and bb are positive coprime integers. What is the value of a+ba + b ?

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