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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using static program.Input;
using static program.MyMath;
using static System.Console;
using static program.Const;

namespace program
{
  class Program
  {
    static void Main()
    {
      var n = ScanIntArray();
      var e = ScanLongArray().Select(_=>1+_).ToArray();
      long s = 0;
      for(int i=0; i<n[1]; i++){
        s += e[i];
      }
      long max = s;
      for(int i=n[1]; i<n[0]; i++){
        s -= e[i-n[1]];
        s += e[i];
        max = Math.Max(max, s);
      }
      WriteLine((double)max / 2);
    }
  }

  static class Const
  {
    public static string alp = "abcdefghijklmnopqrstuvwxyz";
    public static string Alp = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    public static long MOD = 1000000007;
    public static int INF = int.MaxValue;
    public static long INFL = long.MaxValue;
  }
  static class Input
  {
    static public int ScanInt() { return int.Parse(Console.ReadLine()); }
    static public uint ScanUint() { return uint.Parse(Console.ReadLine()); }
    static public double ScanDouble() { return double.Parse(Console.ReadLine()); }
    static public long ScanLong() { return long.Parse(Console.ReadLine()); }
    static public ulong ScanUlong() { return ulong.Parse(Console.ReadLine()); }
    static public int[] ScanIntArray() { return Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray(); }
    static public uint[] ScanUintArray() { return Console.ReadLine().Split().Select(x => uint.Parse(x)).ToArray(); }
    static public double[] ScanDoubleArray() { return Console.ReadLine().Split().Select(x => double.Parse(x)).ToArray(); }
    static public long[] ScanLongArray() { return Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray(); }
    static public ulong[] ScanUlongArray() { return Console.ReadLine().Split().Select(x => ulong.Parse(x)).ToArray(); }

    static public string ScanStr() { return Console.ReadLine(); }
    static public string[] ScanStrArray() { return ScanStr().Split(); }
    static public string RegaxReplace(this string arg1, string pattern, string replacement) { return Regex.Replace(arg1, pattern, replacement); }
    static public string Join<T>(this IEnumerable<T> source, string separator) { return string.Join(separator, source); }
  }

  static class MyMath
  {
    static public int Floor2(this int a)
    {
      int N = 1;
      while (N < a) N *= 2;
      return N / 2;
    }
    static public long Floor2(this long a)
    {
      long N = 1;
      while (N < a) N *= 2;
      return N / 2;
    }
    static public int Ceiling2(this int a)
    {
      int N = 1;
      while (N < a) N *= 2;
      return N;
    }
    static public long Ceiling2(this long a)
    {
      long N = 1;
      while (N < a) N *= 2;
      return N;
    }
    static public long[] CumSum(this long[] a)
    {
      var res = new long[a.Length];
      long s = 0;
      for (int i = 0; i < a.Length; i++) res[i] = (s += a[i]);
      return res;
    }
    static public IEnumerable<int> PrimeFactors(this int n)
    {
      int tmp = n;
      for (int i = 2; i * i <= n; i++)
      {
        while (tmp % i == 0)
        {
          tmp /= i;
          yield return i;
        }
      }
      if (tmp != 1) yield return tmp;
    }
    static public IEnumerable<long> PrimeFactors(this long n)
    {
      var tmp = n;
      for (long i = 2; i * i <= n; i++)
      {
        while (tmp % i == 0)
        {
          tmp /= i;
          yield return i;
        }
      }
      if (tmp != 1) yield return tmp;
    }
    static public int Digit(this int n, int d) { if (d < 0) return 0; return (n % (int)Math.Pow(10, d + 1)) / (int)Math.Pow(10, d); }
    static public int Length(this int n) { if (n < 0) return 0; return (int)Math.Log10(n) + 1; }
    static public int Top(this int n) { return n.Digit(n.Length() - 1); }
    public static bool isPrime(this int p)
    {
      if (p <= 1) return false;
      for (int i = 2; i * i <= p; i++)
        if (p % i == 0) return false;
      return true;
    }
    public static bool isPrime(this long p)
    {
      if (p <= 1) return false;
      for (long i = 2; i * i <= p; i++)
        if (p % i == 0) return false;
      return true;
    }
    public static int GCD(int a, int b)
    {
      Func<int, int, int> gcd = null;
      gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
      return a > b ? gcd(a, b) : gcd(b, a);
    }
    public static long GCD(long a, long b)
    {
      Func<long, long, long> gcd = null;
      gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
      return a > b ? gcd(a, b) : gcd(b, a);
    }
    public static ulong extGCD(ulong a, ulong b, ref ulong x, ref ulong y)
    {
      if (b == 0)
      {
        x = 1;
        y = 0;
        return a;
      }
      var d = extGCD(b, a % b, ref y, ref x);
      y -= a / b * x;
      return d;
    }
    public static int LCM(int a, int b) { return a * b / GCD(a, b); }
    public static long LCM(long a, long b) { return a * b / GCD(a, b); }
    public static long Inv(this long a, long m = 1000000007)
    {
      long b = m, u = 1, v = 0;
      while (b != 0)
      {
        long t = a / b;
        a -= t * b;
        swap(ref a, ref b);
        u -= t * v;
        swap(ref u, ref v);
      }
      u %= m;
      if (u < 0) u += m;
      return u;
    }
    private static void swap(ref long a, ref long b)
    {
      var t = a;
      a = b;
      b = t;
    }
  }


}