package adv2016; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class N463_2 { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int n = ni(), m = ni(); if(n == 2){ out.println(0); return; } if(m == n-1){ out.println(0); return; } int[] c = na(n-2); double[][] M = new double[2*n][2*n]; for(int i = 0;i < n;i++){ if(i < n-1){ for(int j = 1;j <= m;j++){ int x = i + j; if(x >= n)x = 2*n-2-x; M[i][x] += 1./m; M[i+n][x+n] += 1./m; if(x >= 1 && x-1 < c.length)M[i][x+n] += (double)c[x-1]/m; } } } double[] start = new double[2*n]; start[2*n-1] = 1; double[] es0 = S(M, start); double[] es1 = new double[n]; for(int i = n-m-1;i >= 0;i--){ double e = 0; for(int j = 1;j <= m;j++){ e += 1./m*(es1[i+j] + (i+j-1 < c.length ? c[i+j-1] : 0.)); } for(int j = 1;j <= m;j++){ e = Math.min(e, es0[i+j]+(i+j-1 < c.length ? c[i+j-1] : 0.)); } es1[i] = e; } // tr(es1); out.printf("%.14f\n", es1[0]); } public static double[] S(double[][] T, double[] v) { int n = T.length; // ...(1+T^4)(1+T^2)(1+T)v while(true){ double[] w = new double[n]; for(int i = 0;i < n;i++){ double sum = v[i]; for(int k = 0;k < n;k++){ sum += T[i][k] * v[k]; } w[i] = sum; } double[][] U = p2(T); double norm = 0; for(int i = 0;i < n;i++){ double d = v[i]-w[i]; norm += d*d; } if(norm == 0)break; v = w; T = U; } return v; } public static double[] mul(double[][] A, double[] v) { int m = A.length; int n = v.length; double[] w = new double[m]; for(int i = 0;i < m;i++){ double sum = 0; for(int k = 0;k < n;k++){ sum += A[i][k] * v[k]; } w[i] = sum; } return w; } public static double[][] p2(double[][] A) { int n = A.length; double[][] C = new double[n][n]; for(int i = 0;i < n;i++){ for(int k = 0;k < n;k++){ for(int j = 0;j < n;j++){ C[i][j] += A[i][k] * A[k][j]; } } } return C; } public static double[] solve(double[][] a, double[] c) { int n = a.length; int[] ps = new int[n]; for(int i = 0;i < n;i++)ps[i] = i; // Forward Elimination for(int i = 0;i < n;i++){ int pivot = -1; int from = -1; double amax = 0; for(int j = i;j < n;j++){ if(Math.abs(a[ps[j]][i]) > amax){ amax = Math.abs(a[ps[j]][i]); pivot = ps[j]; from = j; } } if(pivot == -1)return null; int d = ps[i]; ps[i] = ps[from]; ps[from] = d; for(int j = i+1;j < n;j++){ a[ps[i]][j] /= a[ps[i]][i]; } c[ps[i]] /= a[ps[i]][i]; a[ps[i]][i] = 1.0; for(int j = i+1;j < n;j++){ for(int k = i+1;k < n;k++){ a[ps[j]][k] -= a[ps[j]][i] * a[ps[i]][k]; } c[ps[j]] -= a[ps[j]][i] * c[ps[i]]; a[ps[j]][i] = 0.0; } } // Back Substitution for(int i = n-1;i >= 0;i--){ for(int j = i-1;j >= 0;j--){ c[ps[j]] -= a[ps[j]][i] * c[ps[i]]; } } double[] ret = new double[n]; for(int i = 0;i < n;i++){ ret[i] = c[ps[i]]; } return ret; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new N463_2().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }