Concatenation of credits

For her outstanding achievements, Ira was entrusted to read lectures to junior students. Having good experience in paying attention to unrelated things during classes (like in problem A), Ira found a new activity. Taking advantage of the fact that students were writing a test and gave her all their record-books, she started looking for patterns in their marks.

Teachers at the university, I must say, are quite strict. First, they never give a 100 mark. Second, they never put a mark into a record-book if it is already present there.

Thus, in each record-book, Ira saw six different marks from 10 to 99. Instead of putting there a seventh mark, she concatenated these six marks and divided the result by her favorite number. Sasha, skipping his class just to watch Ira's lesson, observed what was happening.

— You know, there are quite a lot of combinations of marks that are divisible by your favorite number. — About three? — Ira asked with barely concealed irony. — Not exactly — our university doesn't have enough students. — Well, well.