Gator And Ducks
Suppose there are ducks floating on the pond in a circle. The pond is also home for alligator with a fondness for ducks. Beginning at a particular position (duck number 1) the alligator counts clockwise around the circle and eats every step-th duck (the circle closing as ducks are eaten).
For example, when ducks = 8 and step = 4, the following diagram shows duck number outside and consumption order inside:
The first duck is fifth on the menu, the second is forth, etc. The sequence 5, 4, 6, 1, 3, 8, 7, 2 of orders of consumption completely describes alligator's menu.
Write a script which returns the orders of consumption of the ducks given...
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