Subset Sum (APCS 2018-10 Advanced Subtask Version)

2.0s 256M

Choose any subset of positions from a positive integer sequence, using each position at most once. Find the largest sum not exceeding \(P\). The empty subset is allowed, and equal values at different positions are separate choices.

Input

Read \(n,P\), then \(n\) positive integers.

Constraints

\(1\le n\le25\); \(1\le P,a_i\le1000000009\). This package makes the value bound explicit; values above \(P\) cannot be selected.

Output

Print the maximum sum.

Sample Input

5 17
5 5 8 3 10

Sample Output

16

Source

d007 · 2018-10 APCS. Public subtask version, not the full original.

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