3, 2, 1, Go!

\[ \large { {2016 \, 2015 \, 2014 \ldots 4 \, 3 \, 2 \, 1} } \]

The above expression shows the concatenation of the first \(2016\) positive integers written backwards.

Let \(L \) and \(S\) denote the number of digits and the sum of digits, respectively, of this large number. Compute \[ \dfrac1{10} \left[ (S-L) \pmod{2016} \right]. \]

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