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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;


namespace AtCoder
{

    struct mint : IEquatable<mint>
    {
        //static uint mod = 998244353;
        static uint mod = 1000000007;
        uint _v;

        public mint(long v) : this((uint)(v % mod + mod)){ }
        private mint(uint v)
        {
            _v = v < mod ? v : (v - mod);
        }

        public static void SetMod(uint p)
        {
            mod = p;
        }

        public static mint operator+(mint lhs, mint rhs)
        {
            return new mint(lhs._v + rhs._v);
        }
        public static mint operator-(mint lhs, mint rhs)
        {
            return new mint(lhs._v + mod - rhs._v);
        }
        public static mint operator*(mint lhs, mint rhs)
        {
            return new mint((uint)((ulong)lhs._v * rhs._v % mod));
        }
        public static mint operator/(mint lhs, mint rhs)
        {
            return lhs * rhs.Inv();
        }
        public static mint operator^(mint x, int n)
        {
            return Pow(x, n);
        }
        public static bool operator==(mint l, mint r)
        {
            return l._v == r._v;
        }
        public static bool operator!=(mint l, mint r)
        {
            return !(l == r);
        }
        public static bool operator<(mint l, mint r)
        {
            return l._v < r._v;
        }
        public static bool operator>(mint l, mint r)
        {
            return l._v > r._v;
        }

        public static mint Pow(mint x, int n)
        {
            var r = new mint(1);
            while (n > 0)
            {
                if ((n & 1) > 0) r *= x;
                x *= x;
                n >>= 1;
            }
            return r;
        }
        
        public mint Pow(int n)
        {
            return Pow(this, n);
        }
        public mint Inv()
        {
            return Pow((int)mod - 2);
        }
        
        public bool Equals(mint o)
        {
            return this == o;
        }

        public override bool Equals(object obj)
        {
            if (obj is mint) return this == (mint)obj;
            else return false;
        }
        public override int GetHashCode()
        {
            return _v.GetHashCode();
        }
        public override string ToString()
        {
            return _v.ToString();
        }

        public static implicit operator mint(int i)
        {
            return new mint(i);
        }
        public static implicit operator mint(long i)
        {
            return new mint(i);
        }


        private static mint[] _fact;
        public static void SetFact(int n)
        {
            _fact = new mint[n + 1];
            _fact[0] = 1;
            for (int i = 1; i < n + 1; i++)
            {
                _fact[i] = _fact[i - 1] * i;
            }
        }
        public static mint Fact(int n)
        {
            if (_fact == null || _fact.Length <= n)
            {
                SetFact(n * 2);
            }
            return _fact[n];
        }

        public static mint Combination(int n, int r)
        {
            return Fact(n) / (Fact(n - r) * Fact(r));
        }
    }
    static class Extensions
    {
        public static int LowerBound<T>(this IList<T> list, T value, IComparer<T> comp=null)
        {
            if (comp == null) comp = Comparer<T>.Default;

            var l = 0;
            var r = list.Count;

            while (l < r)
            {
                var m = (l + r) / 2;
                var c = comp.Compare(value, list[m]);
                if (c > 0) l = m + 1;
                else  r = m;
            }

            return l;
        }
        public static int UpperBound<T>(this IList<T> list, T value, IComparer<T> comp=null)
        {
            if (comp == null) comp = Comparer<T>.Default;

            var l = 0;
            var r = list.Count;

            while (l < r)
            {
                var m = (l + r) / 2;
                var c = comp.Compare(value, list[m]);
                if (c >= 0) l = m + 1;
                else r = m;
            }

            return r;
        }
    }
    class Program
    {
		static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }
        static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }
        static int[] ReadIntArray(int n)
        {
            var a = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = ReadInt();
            }
            return a;
        }
        static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }
        static long[] ReadLongArray(int n)
        {
            var a = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = ReadLong();
            }
            return a;
        }
        static List<T> ReadObjects<T>(int n, Func<int[], T> creator)
        {
            var l = new List<T>(n);

            for (int i = 0; i < n; i++)
            {
                var a = ReadIntArray();
                l.Add(creator(a));
            }

            return l;
        }

        static int[,] ReadMatrix(int n, int m)
        {
            var r = new int[n, m];
            for (int i = 0; i < n; i++)
            {
                var a = ReadIntArray();
                for (int j = 0; j < m; j++)
                {
                    r[i, j] = a[j];
                }
            }
            return r;
        }
		
        public static int[] ZAlgotithm(string s)
        {
            var len = s.Length;

            var a = new int[len];
            a[0] = len;
            var i = 1;
            var j = 0;
            while (i < len)
            {
                while (i + j < len && s[j] == s[i + j]) j++;
                a[i] = j;

                if (j == 0)
                {
                    i++;
                    continue;
                }

                var k = 1;
                while (i + k < len && k + a[k] < j)
                {
                    a[i + k] = a[k];
                    k++;
                }
                i += k;
                j -= k;
            }

            return a;
        }
        public class MaxHeap<T> : IEnumerable<T>
        {
            private List<T> _list;
            private Comparer<T> _comp;
			
            public int Count
            {
                get
                {
                    return _list.Count;
                }
            }
            public MaxHeap() : this(0) { }
            public MaxHeap(int capacity, Comparison<T> comp=null)
            {
                _list = new List<T>(capacity);

                if (comp == null)
                {
                    _comp = Comparer<T>.Default;
                }
                else
                {
                    _comp = Comparer<T>.Create(comp);
                }
            }
            
            public void Push(T elem)
            {
                Upheap(elem);
            }

            public T Pop()
            {
                return Downheap();
            }

            public T Peek()
            {
                return _list[0];
            }

            
            private void Swap(int i, int j)
            {
                var a = _list[j];
                _list[j] = _list[i];
                _list[i] = a;
            }

            private void Upheap(T elem)
            {
                _list.Add(elem);
                var i = _list.Count - 1;

                while (true)
                {
                    if (i == 0) return;
                    var j = (i - 1) / 2;

                    var e = _list[i];
                    var p = _list[j];

                    var c = _comp.Compare(e, p);
                    if (c > 0)
                    {
                        Swap(i, j);
                        i = j;
                        continue;
                    }
                    else
                    {
                        break;
                    }
                }
            }

            private T Downheap()
            {
                var result = _list[0];

                var last = _list.Count - 1;
                Swap(0, last);
                _list.RemoveAt(last);
                if (_list.Count == 0) return result;

                var i = 0;
                while (true)
                {
                    if (i == _list.Count - 1) return result;
                    var p = _list[i];

                    var j = i * 2 + 1;
                    if (j >= _list.Count) return result;

                    if(j+1 < _list.Count && _comp.Compare(_list[j], _list[j+1]) < 0)
                    {
                        j++;
                    }

                    if (_comp.Compare(_list[i], _list[j]) < 0)
                    {
                        Swap(i, j);
                        i = j;
                    }
                    else
                    {
                        return result;
                    }
                }
            }
            public MaxHeap<T> Copy(Comparison<T> comp=null)
            {
                var c = new MaxHeap<T>(0, comp);
                c._list = _list.ToList();

                return c;
            }
            public MaxHeap(List<T> list)
            {
                _list = list;

                _comp = Comparer<T>.Default;
            }

            public List<T> GetList()
            {
                return _list;
            }

            public IEnumerator<T> GetEnumerator()
            {
                return _list.GetEnumerator();
            }

            IEnumerator IEnumerable.GetEnumerator()
            {
                return GetEnumerator();
            }
        }
		
        public class MinHeap<T> : IEnumerable<T>
        {
            private List<T> _list;
            private Comparer<T> _comp;

            public int Count
            {
                get
                {
                    return _list.Count;
                }
            }

            public MinHeap() : this(0) { }
            public MinHeap(int capacity, Comparison<T> comp = null)
            {
                _list = new List<T>(capacity);

                if (comp == null)
                {
                    _comp = Comparer<T>.Default;
                }
                else
                {
                    _comp = Comparer<T>.Create(comp);
                }
            }

            public void Push(T elem)
            {
                Upheap(elem);
            }

            public T Pop()
            {
                return Downheap();
            }

            public T Peek()
            {
                return _list[0];
            }


            private void Swap(int i, int j)
            {
                var a = _list[j];
                _list[j] = _list[i];
                _list[i] = a;
            }

            private void Upheap(T elem)
            {
                _list.Add(elem);
                var i = _list.Count - 1;

                while (true)
                {
                    if (i == 0) return;
                    var j = (i - 1) / 2;

                    var e = _list[i];
                    var p = _list[j];

                    var c = _comp.Compare(e, p);
                    if (c < 0)
                    {
                        Swap(i, j);
                        i = j;
                        continue;
                    }
                    else
                    {
                        break;
                    }
                }
            }

            private T Downheap()
            {
                var result = _list[0];

                var last = _list.Count - 1;
                Swap(0, last);
                _list.RemoveAt(last);
                if (_list.Count == 0) return result;

                var i = 0;
                while (true)
                {
                    if (i == _list.Count - 1) return result;
                    var p = _list[i];

                    var j = i * 2 + 1;
                    if (j >= _list.Count) return result;

                    if (j + 1 < _list.Count && _comp.Compare(_list[j], _list[j + 1]) > 0)
                    {
                        j++;
                    }

                    if (_comp.Compare(_list[i], _list[j]) > 0)
                    {
                        Swap(i, j);
                        i = j;
                    }
                    else
                    {
                        return result;
                    }
                }
            }

            public MinHeap<T> Copy(Comparison<T> comp = null)
            {
                var c = new MinHeap<T>(0, comp);
                c._list = _list.ToList();

                return c;
            }
            public MinHeap(List<T> list)
            {
                _list = list;

                _comp = Comparer<T>.Default;
            }

            public List<T> GetList()
            {
                return _list;
            }

            public IEnumerator<T> GetEnumerator()
            {
                return _list.GetEnumerator();
            }

            IEnumerator IEnumerable.GetEnumerator()
            {
                return GetEnumerator();
            }
        }
        class InputLine
        {
            private string[] _inputs;
            private int _index = 0;

            InputLine(string input)
            {
                _inputs = input.Split();
                _index = 0;
            }

            public static InputLine Read()
            {
                return new InputLine(Console.ReadLine());
            }

            public int NextInt()
            {
                return int.Parse(_inputs[_index++]);
            }
            public long NextLong()
            {
                return long.Parse(_inputs[_index++]);
            }
            public double NextDouble()
            {
                return double.Parse(_inputs[_index++]);
            }
        }
        public static int GCD(int x, int y)
        {
            var a = Math.Max(x, y);
            var b = x + y - a;

            while (b != 0)
            {
                var c = b;
                b = a % b;
                a = c;
            }

            return a;
        }
        public static long GCD(long x, long y)
        {
            var a = Math.Max(x, y);
            var b = x + y - a;

            while (b != 0)
            {
                var c = b;
                b = a % b;
                a = c;
            }

            return a;
        }
        public static long LCM(long x, long y)
        {
            var gcd = GCD(x, y);
            return x * y / gcd;
        }
        static long ModPower(long x, long y, long mod)
        {
            var bytes = BitConverter.GetBytes(y);
            var bits = new System.Collections.BitArray(bytes);

            var max2 = 0;
            for (int i = bits.Length - 1; i >= 0; i--)
            {
                if (bits[i])
                {
                    max2 = i;
                    break;
                }
            }

            long result = 1;
            for (int i = max2; i >= 0; i--)
            {
                result = (result * result) % mod;
                if (bits[i])
                {
                    result = (result * x) % mod;
                }
            }

            return result;
        }
        
        static long ModFact(long n, long mod)
        {
            long result = 1;

            for (int i = 1; i <= n; i++)
            {
                result = result * i % mod;
            }
            return result;
        }
		
        static long ModAdd(long x, long y, long mod)
        {
            return ((x % mod) + (y % mod)) % mod;
        }
        static long ModMul(long x, long y, long mod)
        {
            return ((x % mod) * (y % mod)) % mod;
        }

        static long ModDiv(long x, long y, long mod)
        {
            //フェルマーの小定理より、a^(-1) = a^(p-2)
            return ModMul(x, ModPower(y, mod - 2, mod), mod);
        }
        static long ModComb(long n, long r, long mod)
        {
            long numerator = 1;
            for (int i = 0; i < r; i++)
            {
                numerator = ModMul(numerator, n - i, mod);
            }

            long denominator = ModFact(r, mod);

            return ModDiv(numerator, denominator, mod);
        }
        class Graph
        {
            private int _size;
            private List<int>[] _edges;
            
            public Graph(int size)
            {
                _size = size;
                _edges = new List<int>[size];
            }

            public List<int> this[int i]
            {
                get
                {
                    if (_edges[i] == null) _edges[i] = new List<int>();
                    return _edges[i];
                }
            }
        }
        class Graph<T>
        {
            private int _size;
            private List<T>[] _edges;

            public Graph(int size)
            {
                _size = size;
                _edges = new List<T>[size];
            }

            public List<T> this[int i]
            {
                get
                {
                    if (_edges[i] == null) _edges[i] = new List<T>();
                    return _edges[i];
                }
            }
        }
        static Graph<T> NewGraph<T>(int size, T template)
        {
            return new Graph<T>(size);
        }
        static List<T> NewList<T>(T template)
        {
            return new List<T>();
        }
        static T[] NewArray<T>(int size, T template)
        {
            return new T[size];
        }
        static long p1097 = 1000000007;
        static void Main(string[] args)
        {
			//↓

            var nk = ReadIntArray();
            var n = nk[0];
            var k = nk[1];
            var ps = ReadIntArray();
            var es = new double[n];

            for (int i = 0; i < n; i++)
            {
                var p = ps[i];
                es[i] = (double)(p + 1) / 2;
            }

            var ss = new double[n];

            double max = 0;
            double sum = 0;
            for (int i = 0; i < n; i++)
            {
                var e = es[i];
                sum += e;
                if (i < k) continue;

                max = Math.Max(max, sum);
                sum -= es[i - k];
            }

            Console.WriteLine(max);


			//↑
        }

	}
}