Weathervane Walk

Track a courier who walks a ring of villages, where each village's weathervane decides his next direction, for up to 10^15 days.

A ring road has n villages numbered 0 to n - 1; village n - 1 is next to village 0. Every village has a weathervane pointing either clockwise (C, toward the next higher number, wrapping from n - 1 to 0) or anticlockwise (A, toward the next lower number, wrapping from 0 to n - 1).

The courier starts in village start. Each day, exactly this happens:

1. He reads the weathervane of the village he is in and walks to the neighbouring village it points toward.
2. Then the weathervane of the village he just left flips (C becomes A, A becomes C). The weathervane of the village he arrived in is not touched.

For example, on a ring of 3 villages with vanes CCA, starting in village 0: day 1 he walks to village 1 and vane 0 flips (ACA); day 2 he walks to village 2 and vane 1 flips (AAA); day 3 he reads A at village 2, walks to village 1, and vane 2 flips (AAC).

After days days, report where he is, what every weathervane shows, and how many times he has arrived in each village during those days. The starting position at day 0 is not an arrival.

Input: vanes, a string of n characters C and A (the vane of village i is vanes[i]); start, the starting village; days, the number of days.

Output: a list [village, vanes, arrivals]: his final village (an integer), the final weathervane string in the same format as the input, and a list of n integers where entry i is the number of arrivals in village i.