MathNet 2011 Question 17

Let $\{a_1, a_2, ..., a_m\}$ and $\{b_1, b_2, ..., b_n\}$ be two sets of reals with the same sum. Prove that you can find an $m \times n$ array so that the row sums are $a_1, a_2, ..., a_m$ and the column sums are $b_1, b_2, ..., b_n$.