Continue cycling from a particular element in collection

[Heime]

I am using 'completing-read' with INITIAL-INPUT to prefill the minibuffer with
the first entry "alpha".  Hew can I then start at index k from collection as 
the 
next entry.

Thus, initially I have the minibuffer prefilled with "alpha", and after that I 
get the 
cycling continue from "gamma".

Thus the cycling would be "alpha" "gamma" "theta" "alpha" "beta" and so on.

  (interactive
    (let ( (csel '("alpha" "beta" "gamma" "theta"))
      (list
        (completing-read "Imprint: " csel nil t "alpha")) ))