Necklace mirror arcs

Count the stretches of a circular bead necklace that read the same forwards and backwards.

A necklace is a closed loop of beads. The string beads lists the beads' colours in order around the loop, one lowercase letter per bead, so the last bead is next to the first. A stretch is described by a starting bead i (0 <= i < n, where n is the number of beads) and a length len (1 <= len <= n): it consists of len consecutive beads going in the listed direction from bead i, continuing past the last bead back to bead 0 when needed. A stretch is mirrored when its colours read the same from either end.

Stretches are told apart by their (i, len) pair, so equal-looking stretches at different places are counted separately, and the n stretches of length n (one per starting bead) count as n different stretches. A stretch may not be longer than the necklace, so no bead appears twice in it.

Input:

• beads: a non-empty string of lowercase letters.
• min_len: a positive integer.

Output: an integer, the number of mirrored stretches whose length is at least min_len. If min_len is larger than the number of beads, return 0.

Necklaces can have thousands of beads and repeat colours heavily, so comparing every stretch bead by bead will be too slow.