*****NO ARRAY SHOULD BE USED WITHIN THE PROGRAM***** (please solve with C thanks)

Given a non-negative integer n<999999999999999999 and k, find the length of the longest sub-string T, in which the occurrence of each number is no less than k. Here are two examples:

(1). Given n=11122 and k=3, the answer is 3. In this case, the longest string is 111, in which number 1 appears 3 times, which is no less than k=3 times.

(2). Given n=121223 and k=2, the answer is 5. In this case, the longest string is 12122, in which number 1 appears 2 times, and 2 appears 3 times. Both 1 and 2 appears no less than k=2 times. n=223 is another sub-string, but it does not meet the requirement, because 2 only appears one time (less than k=2 times). n=121223 itself is also a sub-string not meeting the requirement: 3 appears only once (less than k=2 times).

Use recursion to find the answer (length of the longest sub-string T), based on the given n and k in c program.