Define the sequence $a_i$ as follows: \(a_1 = 1\), \(a_2 = 2015\), and \(a_n = \frac{n a_{n-1}^2}{a_{n-1} + n a_{n-2}}\) for \(n > 2\). What is the least \(k\) such that \(a_k < a_{k-1}\)?

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