You have obtained a job in a thriving candy factory, which has recently acquired a specialized machine for producing chewy candy. Your job's objective is to maximize this machine's output, producing unique candy chains never before seen in the market.

The peculiarity of this machine is that it only produces circular chains of chewy candy blocks, represented by the letters of the English alphabet, from 'a' to 'z'. If two blocks are represented by the same letter, that means they share the same flavor.

Your challenge is to obtain a straight line of candy blocks from the circular chain, which is as long as possible without being cloying. We define a chain as "cloying" if it contains more than $$$k$$$ blocks of the same flavor. However, due to the sticky nature of the chewy candy blocks, once you select a block of a particular flavor, you must take all adjacent blocks of the same flavor.

For instance, suppose $$$k = 2$$$ and you have a circular chain of chewy candy represented by "abbcdaa". The longest chain of chewy candy you can obtain without it being cloying is "bbcd". You cannot select any 'a' flavored block, as these blocks are stuck together, forming a continuous block of "aaa", and would exceed the $$$k$$$ limit.

Your task is to determine the longest candy chain that you can extract from the machine without it being cloying.