IT-CESENATICO 1989 Problem 6

Given a real number $\alpha$ , a function $f$ is defined on pairs of nonnegative integers by $f(0,0) = 1, f(m,0) = f(0,m) = 0$ for $m > 0$ , $f(m,n) = \alpha f(m,n-1)+(1- \alpha)f(m -1,n-1)$ for $m,n > 0$ . Find the values of $\alpha$ such that $| f(m,n)| < 1989$ holds for any integers $m,n \ge 0$ .