Worst impact an Earthquake can have!

Mayank and Akul are badly affected by the earthquake.

Mayank is trying a calculus question:-

Calculate $S=\displaystyle\int_{0}^{\frac { \pi }{ 2 }}\sin { ({ x }^{ 2 }) } dx$

Akul asks Mayank to give him an algebra problem to solve. Mayank gives him:-

$\displaystyle\sum_{r=0}^n a_{r} { (x-S+1) }^{ r } = \displaystyle\sum_{r=0}^n b_{r} { (x-S) }^{ r }$ where n=2k for some k $\in\mathbb{N}$

and $a_{t}$ =1 for all t $\ge$ k

If $b_{k} = \frac { (\alpha k+\beta )! }{ (\gamma k+\delta )!(\mu k+\lambda )! }$

Find the remainder when ( $\alpha +\beta +\gamma +\delta +\mu +\lambda$ ) is divided by 97.

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