Devanshi Raut wrote a secret message — a lowercase English string S.
She wants to find special hidden “patterns” inside it.
For any chosen substring T of S, imagine marking every position in S that is covered by any occurrence of T.
That means:
If T appears starting at position i, then all letters from i to i + len(T) - 1 are marked.
Some positions may be marked multiple times — that’s okay, they still count as “marked once”.
After all occurrences of T are marked, the marked cells form groups of contiguous Xs (like continuous patches on a map).
Each such patch is called an island.

For example:
S = "ababaewabaq"
T = "aba"

The marked positions look like this:
XXXXXewXXXq
The X’s appear in 2 separate groups, so substring "aba" produces 2 islands.
Your Task:
Given the string S and an integer K, count how many distinct substrings of S produce exactly K islands.

Output a single integer — the count of distinct substrings that produce exactly K islands.