Survey

You are running a survey and want to find respondents in your social group. The group has $n$ members, and you have a budget of $m$ dollars. Divide the $m$ dollars into $n$ shares. Each member receives one of the shares, chosen uniformly at random. Each share can be any non-negative real number.

Each person has a reward threshold $x$. A person participates in the survey if and only if they receive a share of at least $x$ dollars. Otherwise, they accept the payment and do not participate.

Divide the budget so that the expected number of participating members is as large as possible.

The first line contains two integers $n$ ($1 \le n \le 1000$) and $m$ ($1 \le m \le 5000$), the number of group members and the budget.

The second line contains $n$ integers $x_1, x_2, \ldots, x_n$ ($0 \le x_i \le m$), the reward threshold of each member.

Print one real number: the maximum expected number of members who participate. An answer is accepted if its absolute or relative error is at most $10^{-9}$.