You are given \(n\) objects, a knapsack of capacity \(c\), array \(v\), and array \(w\). The \(i^{th}\) object has value v[i] and weight w[i].

Determine the maximum total value that you can get by selecting objects in such a manner that their sum of weights is not greater than the capacity \(c\).

Input format

• First line: Two integers \(n\) and \(c\) denoting the number of objects and capacity of the knapsack (\(1 \le n \le 10^3\) and \(0 \le c \le 2×10^6\)) 
• Second line: \(n\) integers \(v_1,\ v_2,\ ..., v_n\) (\(0 \le v_i \le 50\))
• Third line: \(n\) integers \(w_1,\ w_2,\ ...,\ w_n\) (\(0 \le w_i \le 2×10^6\))

Output format

Print a single integer denoting the maximum value that you can get by selecting the objects.