RU-ALLRUSSIAN 1977 Problem 14

The positive integers $\mathbf{a}_1$ , $\mathbf{a}_2$ , ..., $\mathbf{a}_{\mathrm{m}}$ , $\mathbf{b}_1$ , $\mathbf{b}_2$ , ..., $\mathbf{b}_{\mathrm{n}}$ satisfy: $(\mathbf{a}_1 + \mathbf{a}_2 + \ldots + \mathbf{a}_{\mathrm{m}}) = (\mathbf{b}_1 + \mathbf{b}_2 + \ldots + \mathbf{b}_{\mathrm{n}}) < \mathrm{mn}$ . Show that we can delete some (but not all) of the numbers so that the sum of the remaining a's equals to the sum of the remaining b's.