Farmer John's N (4 <= N <= 10,000) cows live at various points within a circular field. FJ wants to partition his cows by building K (3 <= K <= 1000) fences radially outward from the center of the field at evenly-spaced angles (each measuring 360/K degrees). Depending on how he rotates this system of fences, he can partition the cows into K subsets, each containing a different subset of cows (potentially an empty subset). Define the RANGE of this partition as the number of cows in the largest set minus the number of cows in the smallest set. Determine the minimum attainable RANGE value for a given set of cows.
Of course, no cow can straddle a fence. Cows must be in one partition or the other.
To avoid problems with rounding, the input data will not contain cows that are very close to an integer multiple of 360/K degrees apart.