AT_abc478_b [ABC478B] 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 $ .

The input is given from Standard Input in the following format: > $ N $ $ V $ $ W_1 $ $ W_2 $ $ \dots $ $ W_N $

Output the answer in one line.

### Sample Explanation 1 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 Explanation 2 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.