Welcome 2016! Part 32

For each positive integer \(n\), let

\[\large a_{n}=\dfrac{(n+9)!}{(n-1)!}\]

Let \(k\) denote the smallest positive integer for which the rightmost nonzero digit of \(a_{k}\) is odd. What is the rightmost nonzero digit of \(a_{k}\)?

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