Consider the sequence \(a_{1}=3\), \(a_{2}\), \(a_{3} , \ldots\), where \[\dfrac{1}{a_{k+1}}=\dfrac{1}{a_{1}}+\dfrac{1}{a_{2}}+\cdots+\dfrac{1}{a_{k}} \text{ for all integers } k \ge 1.\]

Find \(a_{2016}\).

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