using System; using System.Linq; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Point = System.Numerics.Complex; using Number = System.Int64; using C = System.Int32; namespace Program { public class Solver { public void Solve() { var s = Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); var n = s[0].Validate(x => 2 <= x && x <= 100); var m = s[1].Validate(x => 1 <= x && x <= n); var A = new int[n + 1]; s = Console.ReadLine().Split(' ').Select(int.Parse).ToArray().ValidateArray(x => 0 <= x && x <= 1000000000); for (int i = 2; i < n; i++) A[i] = s[i - 2]; var dp = Enumerate(200, x => new double[n + 1]); for (int k = 0; k < 200; k++) for (int i = 0; i < n; i++) dp[k][i] = -1; Func dfs = null; dfs = (k, i) => { if (k < 0) return 0.0; if (dp[k][i] > -0.5) return dp[k][i]; var ret = 0.0; for (int j = 1; j <= m; j++) { var go = i + j; if (go > n) go = n - (go - n); ret += A[go]; ret += dfs(k - 1, go); } ret /= m; return dp[k][i] = ret; }; var DP = new double[n + 1]; for (int i = 0; i <= n; i++) DP[i] = -1; Func efs = null; efs = i => { Debug.WriteLine(i); if (DP[i] > -0.5) return DP[i]; if (i + m >= n) return 0; var ret = 0.0; var min = double.MaxValue; for (int j = 1; j <= m; j++) { var go = i + j; if (go > n) go = n - (go - n); ret += A[go]; ret += efs(go); min = Math.Min(min, A[go] + dfs(199, go)); } ret /= m; ret = Math.Min(ret, min); return DP[i] = ret; }; IO.Printer.Out.WriteLine("{0:0.000000000}", efs(1)); } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer: StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b)); if (b == 0) return long.MinValue; if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } #endregion static public class Validator { static public T Validate(this T input, Func f) { if (!f(input)) throw new Exception("invalid input"); return input; } static public T[] ValidateArray(this T[] input, Func f) { foreach (var x in input) if (!f(x)) throw new Exception("invalid input"); return input; } }