Combinatorics?

Let \[ S = \displaystyle\sum_{r=1}^{33}\left(r-\dfrac{2}{3} \right)\dbinom{97}{3r-2} \]

Where \( S = k(2^{94}+\frac{1}{2}) \). Find \( \lfloor k \rfloor \).

\[ \] Notation: \( \dbinom MN \) denotes the binomial coefficient, \( \dbinom MN = \dfrac{M!}{N!(M-N)!} \).

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