Longest Substring with K-Repeating Characters

You are given a string s consisting of lowercase English letters and an integer k. Your task is to find the length of the longest substring of s in which the frequency of every character that appears in that substring is greater than or equal to k.

If no such substring exists, return 0.

Input Format:

The first line contains the string s.

The second line contains the integer k.

Output Format:

The function should return a single integer representing the length of the longest valid substring.

Note:

This problem can be elegantly solved using a divide-and-conquer strategy. The key insight is that if a character in a given string appears fewer than k times, it can never be part of a valid substring. Therefore, such a character acts as a "splitter." We can split the string by this character and recursively find the longest valid substring in the resulting parts.