using System; using System.IO; using System.Linq; using System.Text; using System.Text.RegularExpressions; using System.Collections.Generic; using System.Diagnostics; using System.Numerics; using Enu = System.Linq.Enumerable; public class Program { static readonly double INF = 1e100; int N, D; int[] Cost; double?[,] ans; public void Solve() { N = Reader.Int(); D = Reader.Int(); Cost = new[] { 0 }.Concat(Reader.IntArray(N - 2)).Concat(new[] { 0 }).ToArray(); ans = new double?[N, 2]; Console.WriteLine(Rec(0, 0, 0)); } private double Rec(int at, int used, int depth) { if (depth > N) return INF; if (at == N - 1) return 0; if (used == 0 && at + D >= N - 1) return Cost[at]; if (ans[at, used].HasValue) return ans[at, used].Value; var nextProb = new double[N]; for (int i = 1; i <= D; i++) { int next = at + i; if (next >= N) next = N - 2 - (next - N); nextProb[next] += 1.0 / D; } double res0 = 0; double res1 = INF; for (int next = 0; next < N; next++) if (next != at && nextProb[next] > 0) { res0 += nextProb[next] * Rec(next, used, depth + 1); if (used == 0) res1 = Math.Min(res1, Rec(next, 1, depth + 1)); } res0 /= 1 - nextProb[at]; double res = Cost[at] + Math.Min(res0, res1); ans[at, used] = res; return res; } } class Entry { static void Main() { new Program().Solve(); } } class Reader { static TextReader reader = Console.In; static readonly char[] separator = { ' ' }; static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries; static string[] A = new string[0]; static int i; static void Init() { A = new string[0]; } public static void Set(TextReader r) { reader = r; Init(); } public static void Set(string file) { reader = new StreamReader(file); Init(); } public static bool HasNext() { return CheckNext(); } public static string String() { return Next(); } public static int Int() { return int.Parse(Next()); } public static long Long() { return long.Parse(Next()); } public static double Double() { return double.Parse(Next()); } public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); } public static int[] IntArray(int N) { return Range(N, Int); } public static int[][] IntTable(int H) { return Range(H, IntLine); } public static string[] StringArray(int N) { return Range(N, Next); } public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); } public static string Line() { return reader.ReadLine().Trim(); } public static T[] Range(int N, Func f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; } static string[] Split(string s) { return s.Split(separator, op); } static string Next() { CheckNext(); return A[i++]; } static bool CheckNext() { if (i < A.Length) return true; string line = reader.ReadLine(); if (line == null) return false; if (line == "") return CheckNext(); A = Split(line); i = 0; return true; } }