Best Choice (APCS 2024-06 Expert)

2.0s 256M

You are given a sequence of \(n\) positive integers. Select a prefix and a suffix that do not overlap; either may be empty. The selected numbers must contain equally many odd and even values, and their sum must not exceed \(k\). Find the maximum possible sum. Selecting nothing is allowed and gives \(0\).

Input Format

The first line contains \(n,k\). The second line contains the \(n\) values \(a_i\) in order.

Output Format

Print the maximum valid sum.

Constraints

\(1\le n\le300000\), \(1\le k\le10^9\), \(1\le a_i\le5000\). In every prefix, the absolute difference between the numbers of odd and even values is at most \(2000\).

Scoring

  • 20 points: \(n=1000\).
  • 80 points: No additional restrictions.

Each scored test is worth 5 points.

Sample Input 1

8 22
1 5 2 2 9 3 5 8

Sample Output 1

16

Sample Input 2

7 20
7 7 8 2 8 9 5

Sample Output 2

0

Source

APCS 2024-06 public archive version: o079。

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