For integer a >= 0, b >= 0, let f(a, b) = 0 if b = 0; f(a div b, a mod b) + 1 otherwise. Q1: Suppose f(a, b) = n. What is the smallest possible value of a in terms of n? Q2: What is lim(a -> inf; SUM(1 <= b <= a; f(a, b)) / a)?