CF526D Om Nom and Necklace

One day Om Nom found a thread with $ n $ beads of different colors. He decided to cut the first several beads from this thread to make a bead necklace and present it to his girlfriend Om Nelly. Om Nom knows that his girlfriend loves beautiful patterns. That's why he wants the beads on the necklace to form a regular pattern. A sequence of beads $ S $ is regular if it can be represented as $ S=A+B+A+B+A+...+A+B+A $ , where $ A $ and $ B $ are some bead sequences, " $ + $ " is the concatenation of sequences, there are exactly $ 2k+1 $ summands in this sum, among which there are $ k+1 $ " $ A $ " summands and $ k $ " $ B $ " summands that follow in alternating order. Om Nelly knows that her friend is an eager mathematician, so she doesn't mind if $ A $ or $ B $ is an empty sequence. Help Om Nom determine in which ways he can cut off the first several beads from the found thread (at least one; probably, all) so that they form a regular pattern. When Om Nom cuts off the beads, he doesn't change their order.

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In the first sample test a regular sequence is both a sequence of the first 6 beads (we can take $ A= $ "", $ B= $ "bca"), and a sequence of the first 7 beads (we can take $ A= $ "b", $ B= $ "ca"). In the second sample test, for example, a sequence of the first 13 beads is regular, if we take $ A= $ "aba", $ B= $ "ba".