Suppose a_{1}, a_{2}, \ldots, a_{10} are nonnegative integers such that
\sum_{k=1}^{10} a_{k}=15 \quad \text { and } \quad \sum_{k=1}^{10} k a_{k}=80
Let M and m denote the maximum and minimum respectively of \sum_{k=1}^{10} k^{2} a_{k}. Compute M-m.