ILL 1990 Problem 80

Function $f(x, y): \mathbb N \times \mathbb N \to \mathbb Q$ satisfies the conditions:

(i) $f(1, 1) =1$ ,

(ii) $f(p + 1, q) + f(p, q + 1) = f(p, q)$ for all $p, q \in \mathbb N$ , and

(iii) $qf(p + 1, q) = pf(p, q + 1)$ for all $p, q \in \mathbb N$ .

Find $f(1990, 31).$