BALKAN 1999 Problem 4

Let $\{a_n\}_{n\geq 0}$ be a non-decreasing, unbounded sequence of non-negative integers with $a_0=0$ . Let the number of members of the sequence not exceeding $n$ be $b_n$ . Prove that $$(a_0 + a_1 + \cdots + a_m)( b_0 + b_1 + \cdots + b_n ) \geq (m + 1)(n + 1).$$