Problem:
Score : 400 points

Problem Statement

We have N dice arranged in a line from left to right. The i-th die from the left shows p_i numbers from 1 to p_i with equal probability when thrown.

We will choose K adjacent dice, throw each of them independently, and compute the sum of the numbers shown. Find the maximum possible value of the expected value of this sum.

Constraints

1 ≤ K ≤ N ≤ 200000

1 ≤ p_i ≤ 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
p_1 ... p_N

Output

Print the maximum possible value of the expected value of the sum of the numbers shown.

Your output will be considered correct when its absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

5 3
1 2 2 4 5

Sample Output 1

7.000000000000

When we throw the third, fourth, and fifth dice from the left, the expected value of the sum of the numbers shown is 7. This is the maximum value we can achieve.

Sample Input 2

4 1
6 6 6 6

Sample Output 2

3.500000000000

Regardless of which die we choose, the expected value of the number shown is 3.5.

Sample Input 3

10 4
17 13 13 12 15 20 10 13 17 11

Sample Output 3

32.000000000000

Solution in Rust (1.15.1) (judge verdict: Runtime Error)

use std::collections::HashSet;
fn main() {
    // loop{ //For test
        solve();
    // }
}

#[allow(dead_code)]
fn solve(){
    let mut nk: Vec<i32> = read_vec();
    let mut p: Vec<i32> = read_vec();
    let mut ans:f32 = 0.0;   
    let mut memo :Vec<f32> = Vec::new();
    for i in 0..1001 {
      memo.push(-1.0);
    }
    for i in 0..(nk[0]-nk[1]+1) {
        //println!("====");
        let mut tmp_sum:f32 =0.0;
        for j in i..(i+nk[1]) {
            //println!("{}", p[j as usize]);
            if memo[j as usize] == -1.0 {
                memo[j as usize] = ave(&p[j as usize]);
            }
            tmp_sum += memo[j as usize];
        }
        if ans < tmp_sum {
            ans = tmp_sum;
        }
        //println!("ans:{} tmp:{}", ans as f32, tmp_sum as f32);
    }
    println!("{}", ans);
}

fn ave(x:&i32) -> f32 {
    let sum= (1..x+1).sum::<i32>();
    (sum as f32) / (*x as f32)
}

/// 標準入力から一行を読み取り、指定の型に変換する関数
#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    let _ = std::io::stdin().read_line(&mut s);
    s.trim().parse().ok().unwrap()
}

/// 標準入力から一行を読み取り、空白文字で分割し、各要素を指定の型に変換する関数
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

/// 標準入力からn行を読み取り、各行を空白文字で分割し、各要素を指定の型に変換する関数
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}