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 Python (3.4.3) (judge verdict: Runtime Error)

import java.util.*;

//update 2020/1/1 23:01

public class Main{

  static Scanner sc = new Scanner(System.in);
  static StringBuilder sb = new StringBuilder();

  public static void main(String[] args) {

    int n = nextInt();
    int k = nextInt();
    double[] p = new double[n];
    for(int i=0;i<n;i++){
      p[i] = nextDouble();
    }

    double[] eachK = new double[n-k+1];

    double Sum = 0;

    for(int i=0;i<k;i++){
      Sum += (1+p[i])/2;
    }

    double max = Sum;

    for(int i=1;i<n-k+1;i++){
      Sum -= (1+p[i-1])/2;
      Sum += (1+p[i+k-1])/2;
      max = Math.max(max,Sum);
    }


    System.out.println(max);

  }
  /*
    static String toSmall(String s){
      char c = s.charAt(0);
      //if(Character.isUpperCase(c)){
      if(c<=90){
        c += 32;
      }
      return String.valueOf(c);
    }
    static String toBig(String s){
      char c = s.charAt(0);
      //if(Character.isLowerCase(c)){
      if(c>=97){
        c -= 32;
      }
      return String.valueOf(c);
    }
  */

  static String toSmall(String s){
    return s.toLowerCase();
  }

  static String toBig(String s){
    return s.toUpperCase();
  }

  static String next(){
    return sc.next();
  }

  static int nextInt(){
    return Integer.parseInt(sc.next());
  }

  static long nextLong(){
    return Long.parseLong(sc.next());
  }

  static double nextDouble(){
    return Double.parseDouble(sc.next());
  }

  static String[] splitString(String s){
    return s.split("");
  }

  static char[] splitChar(String s){
    return s.toCharArray();
  }

  static int charToInt(char a){
    return a - 48;
  }

////////////////////////////////////////////
  public static int max(int[] a){
    int lng = a.length;
    int max = a[0];
    for(int i=1;i<lng;i++){
      max = Math.max(max,a[i]);
    }
    return max;
  }
  public static long max(long[] a){
    int lng = a.length;
    long max = a[0];
    for(int i=1;i<lng;i++){
      max = Math.max(max,a[i]);
    }
    return max;
  }
////////////////////////////////////////////

////////////////////////////////////////////
  public static int min(int[] a){
    int lng = a.length;
    int min = a[0];
    for(int i=1;i<lng;i++){
      min = Math.min(min,a[i]);
    }
    return min;
  }
  public static long min(long[] a){
    int lng = a.length;
    long min = a[0];
    for(int i=1;i<lng;i++){
      min = Math.min(min,a[i]);
    }
    return min;
  }
////////////////////////////////////////////

}