A vending-machine restocker is filling a shelf of capacity W. There are n item types; type i has weight w_i and value v_i, and an UNLIMITED supply is available (any non-negative number of units of each type may be placed on the shelf). Choose how many units of each type to place so 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