import std.stdio, std.array, std.string, std.conv, std.algorithm; import std.typecons, std.range, std.random, std.math, std.container; import std.numeric, std.bigint, core.bitop, core.stdc.stdio; int gaussianElimination(ref real[][] org_mat, ref real[] ret) { int N = org_mat.length.to!int; auto mat = new real[][](N, N+1); foreach (i; 0..N) foreach (j; 0..N+1) mat[i][j] = org_mat[i][j]; foreach (i; 0..N) { real maxval = 0; int maxrow = -1; foreach (j; i..N) if (abs(mat[j][i]) > maxval) maxval = abs(mat[j][i]), maxrow = j; if (maxval == 0) return -1; swap(mat[i], mat[maxrow]); foreach (j; i+1..N+1) mat[i][j] /= mat[i][i]; mat[i][i] = 1; foreach (j; 0..N) { if (j == i) continue; real mul = mat[j][i]; foreach (k; i..N+1) mat[j][k] -= mul*mat[i][k]; } } foreach (i; 0..N) ret[i] = mat[i][N]; return 0; } void main() { auto s = readln.split.map!(to!int); auto N = s[0]; auto M = s[1]; auto C = [0] ~ readln.split.map!(to!int).array ~ [0]; auto mat = new real[][](N, N+1); foreach (i; 0..N) foreach(j; 0..N+1) mat[i][j] = 0; mat[N-1][N-1] = -1; foreach (i; 0..N-1) { foreach (j; 1..M+1) { auto next = (i+j < N) ? i+j : 2*N-i-j-2; mat[i][next] += 1.0L / M; } mat[i][i] -= 1; mat[i][N] = -C[i]; } auto E = new real[](N); gaussianElimination(mat, E); auto dp = new real[](N); foreach (i; iota(N-1, -1, -1)) { if (i+M >= N-1) dp[i] = C[i]; else { // mahou tsukawanai dp[i] = C[i]; foreach (j; 1..M+1) dp[i] += dp[i+j] / M; // tsukau foreach (j; 1..M+1) dp[i] = min(dp[i], C[i]+E[i+j]); } } writefln("%.9f", dp[0]); }