A7752 | Average Superhero Gang Power

Every superhero has been given a power value by the Felicity Committee. The avengers crew wants to maximize the average power of the superheroes in their team by performing certain operations.

Initially, there are $n$ superheroes in avengers team having powers $a_1, a_2, \ldots, a_n$ , respectively. In one operation, they can remove one superhero from their team (if there are at least two) or they can increase the power of a superhero by $1$ . They can do at most $m$ operations. Also, on a particular superhero at most $k$ operations can be done.

Can you help the avengers team to maximize the average power of their crew?

The first line contains three integers $n$ , $k$ and $m$ ( $1 \le n \le 10^{5}$ , $1 \le k \le 10^{5}$ , $1 \le m \le 10^{7}$ ) — the number of superheroes, the maximum number of times you can increase power of a particular superhero, and the total maximum number of operations.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^{6}$ ) — the initial powers of the superheroes in the cast of avengers.

Output a single number — the maximum final average power.

Your answer is considered correct if its absolute or relative error does not exceed $10^{-6}$ .

Formally, let your answer be $a$ , and the jury's answer be $b$ . Your answer is accepted if and only if $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$ .