Best value from unit-weight items with limited copies

A bag holds at most capacity units of weight. There are n kinds of item; every copy of kind i weighs 1 and is worth values[i], and there are counts[i] copies of it. Return the most value you can pack.

def max_packed_value(values: list[int], counts: list[int], capacity: int) -> int: ...

n is up to 10^5 and capacity and counts are up to 10^9, so the textbook knapsack table is out of the question. Explain why the unit weights make a simpler approach correct, and watch for totals that overflow 32 bits.