You are packing a backpack of capacity W for an expedition with n candidate supply items. Item i has weight w_i and value v_i; each item may be taken at most once (you either bring it or you don't). Choose a set of items whose total weight does not exceed W, maximizing total value.
Input format
Line 1: two integers n W.
Line 2: n space-separated integers, the item weights (empty if n = 0).
Line 3: n space-separated integers, the item values (empty if n = 0).
Output format
A single integer: the maximum total value achievable within capacity W.
Constraints
- 0 ≤ n ≤ 200
- 0 ≤ W ≤ 2000
- 1 ≤ w_i ≤ 200, 1 ≤ v_i ≤ 1000