Let $a$ be a positive real number and $n$ a non-negative integer. Determine $S-T$, where 
$$ S = \sum_{k=-2n}^{2n+1} \frac{(k-1)^2}{a^{| \lfloor \frac{k}{2} \rfloor |}} $$ 
and  
$$ T = \sum_{k=-2n}^{2n+1} \frac{k^2}{a^{| \lfloor \frac{k}{2} \rfloor |}} $$

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