Let $a$ and $b$ be nonzero real numbers such that $\frac{1}{3a} + \frac{1}{b} = 2011$ and $\frac{1}{a} + \frac{1}{3b} = 1$. What is the quotient when $a + b$ is divided by $ab$?

Let's think step by step and output the final answer within \boxed{}.
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