Alan's Candy Grams

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Points: 10 (partial)
Time limit: 2.0s
Memory limit: 64M

Problem type

AlanL received candy grams from his friend [REDACTED]! He has N individual candies, which he organized in order to eat 1 for the next N days such that each day has a specific associated candy. Each candy has a sweetness value of a_i, and because [REDACTED] is sweet AlanL wishes to maximize the sweetness he eats over the N days. However, if AlanL eats a 2 candies in a row with a sum greater than K, he will spontaneously combust. Thus, sometimes AlanL must skip eating candies on certain days in order to live. Please help AlanL!

Input Specification

The first line will contain N, K\ (1 \le N \le 2 \times 10^5),\ (1 \le K \le 10^9).

The next line will contain N integers a_i\ (1 \le a_i \le 10^9).

Output Specification

The maximum sweetness that AlanL can eat from the candies.


Subtask 1 [30%]

N \le 2000

Subtask 2 [70%]

No further constraints.

Sample Input

5 5
5 1 2 3 4

Sample Output


Sample Explanation

Alan eats the second, third, and fourth candies.


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