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(); s.Validate(x => x.Length == 2); 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]; if (n > 2) { s = Console.ReadLine().Split(' ').Select(int.Parse).ToArray().ValidateArray(x => 0 <= x && x <= 1000000000); s.Validate(x => x.Length == n - 2); for (int i = 2; i < n; i++) A[i] = s[i - 2]; } Debug.WriteLine(A.AsJoinedString()); 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(49, go)); } ret /= m; ret = Math.Min(ret, min); return DP[i] = ret; }; Console.WriteLine("{0:0.000000000}", efs(1)); } 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(); } } #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; } }