After an exhausting day of preparing COCI, after sleeping for only three hours
and in intervals of 20 minutes, and finally after naughty Patrick and Josip got on
his nerves, Vito fell asleep.
Vito was always a pacifist and as a sign of his resignation in front of the disobedience
of his (un)reliable friends, Vito dreamed of \(n\) white flags. The white flags had the
shape of a right triangle swirling in the air with one of their sides parallel to the
ground. In the morning, Vito could only remember a few key details... the length
of the hypotenuse of the \(i-th\) flag was \(r_{i}\) and the total sum of heights of the flags was at most \(S\).
Now awake, he decided he shall fight on the beaches and never surrender! He rushed to the nearest paint
shop so that next time he dreams of the \(n\) white flags he can paint them over! But he quickly realized, he
isn’t sure how much paint he has to buy. So he asked you to calculate the maximum possible total area of
the \(n\) white flags satisfying the constraints!

Subtask
Constraints
Restrictions
1
41
\(n \le 100\)
2
22
\(n \le 1000\)
3
47
No additional constraints.

The first line contains the integers \(n\) and \(S\) (\(1 \le n \le 100\,000\), \(1 \le S \le 10^{10}\)), the number of flags and the
maximum possible sum of heights of the flags.
In the next line there are \(n\) integers \(r@@RISE_MATH_BLOCK_0@@i \le 100\,000\)).

In the only line, output the maximum possible sum of areas of the flags. Your solution will be considered
correct if the absolute or relative error is smaller than \(10^{−}\)^{6}.

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출처 COCI 2022/2023 Contest 5