Implement Kac Ring Simulation with O(1) Step Query

Implement a Kac Ring data structure consisting of a circular ring of N positions, each with a color (0 or 1, or equivalently White/Black) and optional markers. When the simulation advances one step, each ball/position moves clockwise, and any position leaving a marked spot flips its color. Implement two methods: step() to advance the simulation by one step, and kstep(k) to advance by k steps, each returning the color ratio (number of 1s / N, or equivalently (W - B) / N) after the operation. Optimize from a brute-force O(N) per step approach to an O(1) per query solution using prefix sums or similar techniques.