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bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | # Bounded Knapsack
## Description
Given item weights, values, and available multiplicities, maximize total value without exceeding the knapsack capacity.
## Input
The verification-case input consists of parallel `weights`, `values`, and `counts` arrays, item count `n`, capacity, and work buffers.
## Output
The function produces the maximum achievable total value.
## Constraints
- $0 \le n,capacity \le 1000$; weights are positive, values and counts are nonnegative.
## Source
Classical algorithmic problem reconstructed from the verified C artifact.
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