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You should definitely familiarize with the 'modulus' operator % – calculating the 'un-rotated' (original) position of the item to find is waaay faster than performing a hundred thousand rotations (k is up to \10ドル^5\$) of one hundred thousand-item array (n up to \10ドル^5\$).
It is even faster than a single rotation.

But that is for StackOverflow rather than CodeReview...