Bounded Knapsack - Problem Statement

You have $n$ item types. Item $i$ has weight $w_i$, value $v_i$, and quantity limit $k_i$. Find the maximum value you can fit in a knapsack of capacity $W$.

For example: items $[(w=2, v=3, k=3), (w=3, v=4, k=2)]$ with capacity $W=10$. You can take up to 3 of the first item and up to 2 of the second. The simple solution adds another loop over quantities, but that's $O(n \times W \times k)$. When $k$ is large, this times out.