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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