import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.numeric, std.range, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } void chmin(T)(ref T t, in T f) { if (t > f) t = f; } void chmax(T)(ref T t, in T f) { if (t < f) t = f; } int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = cast(int)(as.length); for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a < val)); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a <= val)); } int N, M; real[] C; void main() { try { for (; ; ) { N = readInt(); M = readInt(); C = new real[N]; C[0] = C[N - 1] = 0.0; foreach (i; 1 .. N - 1) { C[i] = readReal(); } auto a = new real[][](N, N); auto b = new real[N]; foreach (i; 0 .. N - 1) { a[i][] = 0.0; a[i][i] = 1.0; foreach (j; 1 .. M + 1) { const ii = (i + j > N - 1) ? ((N - 1) * 2 - (i + j)) : (i + j); a[i][ii] -= 1.0 / M; b[i] += C[i] / M; } } a[N - 1][] = 0.0; a[N - 1][N - 1] = 1.0; b[N - 1] = 0.0; debug { foreach (i; 0 .. N) { writeln(a[i], " ", b[i]); } } foreach (h; 0 .. N) { foreach (i; h + 1 .. N) { if (abs(a[h][h]) < abs(a[i][h])) { swap(a[h], a[i]); swap(b[h], b[i]); } } foreach (j; h + 1 .. N) { a[h][j] /= a[h][h]; } a[h][h] = 1.0; foreach (i; h + 1 .. N) { foreach (j; h + 1 .. N) { a[i][j] -= a[i][h] * a[h][j]; } b[i] -= a[i][h] * b[h]; a[i][h] = 0.0; } } foreach_reverse (i; 0 .. N) { foreach (j; i + 1 .. N) { b[i] -= a[i][j] * b[j]; } } debug { writeln(b); } auto dp = new real[N]; foreach_reverse (i; 0 .. N) { if (i + M >= N - 1) { dp[i] = 0.0; } else { // no magic dp[i] = 0.0; foreach (j; 1 .. M + 1) { dp[i] += (C[i + j] + dp[i + j]) / M; } // magic foreach (j; 1 .. M + 1) { chmin(dp[i], b[i + j]); } } } debug { writeln("dp = ", dp); } writefln("%.10f", dp[0]); } } catch (EOFException e) { } }