AT_abc478_b.Topping

Takahashi is at a ramen shop.

This shop has $N$ kinds of toppings, and the $i$-th topping has a price of $i$ and a happiness of $W_i$.

Takahashi chooses three distinct kinds of toppings so that the total price is at most $V$. Find the maximum possible total happiness of the toppings he chooses.

The constraints guarantee that there is at least one way to choose three distinct kinds of toppings so that the total price is at most $V$.

高桥正在一家拉面店。

这家店有 $N$ 种配料，其中第 $i$ 种配料的价格为 $i$，带来的幸福感为 $W_i$。

高桥要从中选出三种互不相同的配料，使得它们的总价格不超过 $V$。求他所能获得的最大总幸福感。

题目保证：至少存在一种方式，能选出三种互不相同的配料，使其总价格不超过 $V$。

The input is given from Standard Input in the following format:

$N$ $V$
$W_1$ $W_2$ $\dots$ $W_N$

输入从标准输入中按以下格式给出：

$N$ $V$
$W_1$ $W_2$ $\dots$ $W_N$

Output the answer in one line.

一行输出答案。

Sample 1 Explanation:
When choosing the first, third, and fifth toppings, the total price is $1+3+5=9$, and the total happiness is $31+59+53=143$.

Sample 2 Explanation:
When choosing the second, sixth, and seventh toppings, the total price is $2+6+7=15$, and the total happiness is $448944+670309+976672=2095925$.

Constraints

• $3 \leq N \leq 100$
• $6 \leq V \leq 3N-3$
• $1 \leq W_i \leq 10^6$
• All input values are integers.

样例 1 解释：
选择第 1、第 3 和第 5 种配料时，总价格为 $1+3+5=9$，总幸福值为 $31+59+53=143$。

样例 2 解释：
选择第 2、第 6 和第 7 种配料时，总价格为 $2+6+7=15$，总幸福值为 $448944+670309+976672=2095925$。

约束条件

• $3 \leq N \leq 100$
• $6 \leq V \leq 3N-3$
• $1 \leq W_i \leq 10^6$
• 所有输入值均为整数。