Why does counting sort run in linear time, and what limits its applicability?

A It compares every pair of elements but uses a fast comparison function, giving O(n) B It tallies occurrences of each key value in a count array and then reconstructs the sorted output in O(n + k), but it is only practical when the range of key values k is not much larger than n C It works by recursively splitting the array into halves like merge sort D It sorts by repeatedly finding the minimum element and swapping it into place