Split Prefix Suffix

Amazon Prime Day is a day where many items are put on sale for Amazon Prime members. A list of sale items is assembled where each item is assigned a category denoted by a lowercase English letter.

Since the sale is to be held on two different days, the company has decided to split the list of items into two contiguous non-empty sub-lists - a prefix and a suffix. To ensure that both days share a sufficient number of similar items, they also need to split it in a way such that the number of distinct categories shared by both sub-lists is greater than k.

Formally, given a string, categories, find the number of ways to split the string into exactly two contiguous non-empty substrings such that the number of distinct characters occurring in both the substrings is greater than a given integer k.