using System; using System.Collections.Generic; using System.IO; using System.Linq; using System.Runtime.CompilerServices; using System.Numerics; using System.Threading; partial class Program { int[] dx = new int[] { 1, 0, -1, 0, 1, -1, -1, 1 }; int[] dy = new int[] { 0, 1, 0, -1, 1, 1, -1, -1 }; //long mod = 1000000007; long mod = 998244353; public void Solve() { var (N, M) = io.GetMulti(); var B = io.GetLongArray(); var cum = B.GetCum(true, 0, (a, b) => a + b); var last = 1; for (; last <= M; last++) { if ((cum[^1] - cum[last] - B[last - 1] * (M - last)) < M) { break; } } last--; long nokori = 0; for (int i = last; i < M; i++) nokori += (N-B[i]); var hoge = last == 0 ? 0 : M * 1.0 / (M - last); io.Print(nokori*1.0 / (M-last) + hoge+B[0]-1); } IO io = new IO(); static void Main() { Console.SetIn(new StreamReader(Console.OpenStandardInput(8192))); Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); var program = new Program(); //var t = new Thread(program.Solve, 134217728); //t.Start(); //t.Join(); program.Solve(); Console.Out.Flush(); Console.Read(); } } //------------------------------------------------------------------------------------------------------------------ public static class Ex { public static bool IsNullOrEmpty(this string s) { return string.IsNullOrEmpty(s); } public static void yesno(this bool b) => Console.WriteLine(b ? "yes" : "no"); public static void YesNo(this bool b) => Console.WriteLine(b ? "Yes" : "No"); public static void YESNO(this bool b) => Console.WriteLine(b ? "YES" : "NO"); public static void Yes() => Console.WriteLine("Yes"); public static void YES() => Console.WriteLine("YES"); public static void No() => Console.WriteLine("No"); public static void NO() => Console.WriteLine("NO"); public static void M1() => Console.WriteLine("-1"); ////[MethodImpl(MethodImplOptions.AggressiveInlining)] ////public static bool Chmax(ref this int a, int b) ////{ //// if (a < b) { a = b; return true; } //// else return false; ////} ////[MethodImpl(MethodImplOptions.AggressiveInlining)] ////public static bool Chmin(ref this int a, int b) ////{ //// if (a > b) { a = b; return true; } //// else return false; ////} ////[MethodImpl(MethodImplOptions.AggressiveInlining)] ////public static bool Chmax(ref this long a, long b) ////{ //// if (a < b) { a = b; return true; } //// else return false; ////} ////[MethodImpl(MethodImplOptions.AggressiveInlining)] ////public static bool Chmin(ref this long a, long b) ////{ //// if (a > b) { a = b; return true; } //// else return false; ////} ////[MethodImpl(MethodImplOptions.AggressiveInlining)] ////public static bool Chmax(ref this T a, T b) where T : struct, IComparable ////{ //// if (b.CompareTo(a) > 0) { a = b; return true; } //// else return false; ////} ////[MethodImpl(MethodImplOptions.AggressiveInlining)] ////public static bool Chmin(ref this T a, T b) where T : struct, IComparable ////{ //// if (b.CompareTo(a) < 0) { a = b; return true; } //// else return false; ////} /// /// constraintを満たす最小のインデックスを返します。 /// /// T key が満たすべき制約 /// 制約を満たす最小のインデックス(0-indexed) [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int LowerBound(this IList ls, Func constraint) { var ng = -1; var ok = ls.Count; while (ok - ng > 1) { var mid = (ok + ng) / 2; if (constraint(ls[mid])) ok = mid; else ng = mid; } return ok; } /// /// 配列の累積演算結果の配列を返します。 /// /// 左から順に計算するか? /// 単位元 /// 演算 /// 要素数N+1の累積演算テーブル [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[] GetCum(this IList ls, bool fromLeft, T gen, Func func) { var res = new T[ls.Count + 1]; res.AsSpan().Fill(gen); if (fromLeft) { for (int i = 0; i < ls.Count; i++) res[i + 1] = func(res[i], ls[i]); } else { for (int i = ls.Count; i > 0; i--) res[i - 1] = func(res[i], ls[i - 1]); } return res; } /// /// 文字列のIListを昇順にソートして返します。 /// /// /// 昇順の文字列配列 public static string[] StringListFastSort(this IList ls) { var res = ls.ToArray(); Array.Sort(res, StringComparer.OrdinalIgnoreCase); return res; } /// /// 立っているビットの数を返します。 /// public static int PopCount(this uint bits) { bits = bits - ((bits >> 1) & 0x55555555); bits = (bits & 0x33333333) + ((bits >> 2) & 0x33333333); return (int)(((bits + (bits >> 4) & 0xF0F0F0F) * 0x1010101) >> 24); } /// /// elementで満たされた一次元配列を返します。 /// public static T[] Repeat(this T element, int N) { var res = new T[N]; res.AsSpan().Fill(element); return res; } /// /// elementで満たされた二次元配列を返します。 /// public static T[][] Repeat(this T element, int H, int W) { var res = new T[H][]; for (int i = 0; i < H; i++) { res[i] = new T[W]; res[i].AsSpan().Fill(element); } return res; } /// /// elementで満たされた三次元配列を返します。 /// public static T[][][] Repeat(this T element, int H, int W, int R) { var res = new T[H][][]; for (int i = 0; i < H; i++) { res[i] = new T[W][]; for (int j = 0; j < W; j++) { res[i][j] = new T[R]; res[i][j].AsSpan().Fill(element); } } return res; } } class IO { [MethodImpl(MethodImplOptions.AggressiveInlining)] public string GetStr() => Console.ReadLine().Trim(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public char GetChar() => Console.ReadLine().Trim()[0]; [MethodImpl(MethodImplOptions.AggressiveInlining)] public int GetInt() => int.Parse(Console.ReadLine().Trim()); [MethodImpl(MethodImplOptions.AggressiveInlining)] public long GetLong() => long.Parse(Console.ReadLine().Trim()); [MethodImpl(MethodImplOptions.AggressiveInlining)] public double GetDouble() => double.Parse(Console.ReadLine().Trim()); [MethodImpl(MethodImplOptions.AggressiveInlining)] public decimal GetDecimal() => decimal.Parse(Console.ReadLine().Trim()); [MethodImpl(MethodImplOptions.AggressiveInlining)] public string[] GetStrArray() => Console.ReadLine().Trim().Split(' '); [MethodImpl(MethodImplOptions.AggressiveInlining)] public string[][] GetStrArray(int N) { var res = new string[N][]; for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' '); return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int[] GetIntArray() => Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public int[][] GetIntArray(int N) { var res = new int[N][]; for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public long[] GetLongArray() => Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public long[][] GetLongArray(int N) { var res = new long[N][]; for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public decimal[] GetDecimalArray() => Console.ReadLine().Trim().Split(' ').Select(decimal.Parse).ToArray(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public decimal[][] GetDecimalArray(int N) { var res = new decimal[N][]; for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(decimal.Parse).ToArray(); return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public char[] GetCharArray() => Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public double[] GetDoubleArray() => Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public double[][] GetDoubleArray(int N) { var res = new double[N][]; for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); return res; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public char[][] GetGrid(int H) { var res = new char[H][]; for (int i = 0; i < H; i++) res[i] = Console.ReadLine().Trim().ToCharArray(); return res; } public List[] GetUnweightedAdjanceyList(int V, int E, bool isDirected, bool isNode_0indexed) { var ls = new List[V]; for (int i = 0; i < V; i++) ls[i] = new List(); for (int i = 0; i < E; i++) { var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); if (isNode_0indexed == false) { input[0]--; input[1]--; } ls[input[0]].Add(input[1]); if (isDirected == false) ls[input[1]].Add(input[0]); } return ls; } public Dictionary> GetUnweightedAdjacencyDict(int V, int E, bool isDirected, bool isNode_0indexed) { var dic = new Dictionary>(); foreach (var e in Enumerable.Range(0, V)) { dic.Add(e, new List()); } for (int i = 0; i < E; i++) { var input = GetIntArray(); var a = isNode_0indexed ? input[0] : input[0] - 1; var b = isNode_0indexed ? input[1] : input[1] - 1; dic[a].Add(b); if (isDirected == false) dic[b].Add(a); } return dic; } public List<(int to, long dist)>[] GetWeightedAdjacencyList(int V, int E, bool isDirected, bool isNode_0indexed) { var ls = new List<(int to, long dist)>[V]; for (int i = 0; i < V; i++) ls[i] = new List<(int to, long dist)>(); for (int i = 0; i < E; i++) { var hoge = Console.ReadLine().Split(' '); var a = int.Parse(hoge[0]); var b = int.Parse(hoge[1]); var c = long.Parse(hoge[2]); if (isNode_0indexed == false) { a--; b--; } ls[a].Add((b, c)); if (isDirected == false) ls[b].Add((a, c)); } return ls; } //public Dictionary> GetWeightedAdjacencyDict(int N, int M, bool isDirected, bool isNode_0indexed) //{ // var dic = new Dictionary>(); // foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<(int, long)>()); } // for (int i = 0; i < M; i++) // { // var input = GetIntArray(); // var a = isNode_0indexed ? input[0] : input[0] - 1; // var b = isNode_0indexed ? input[1] : input[1] - 1; // var c = input[2]; // dic[a].Add((b, c)); // if (isDirected == false) dic[b].Add((a, c)); // } // return dic; //} [MethodImpl(MethodImplOptions.AggressiveInlining)] bool eq() => typeof(T).Equals(typeof(U)); [MethodImpl(MethodImplOptions.AggressiveInlining)] T ct(U a) => (T)Convert.ChangeType(a, typeof(T)); [MethodImpl(MethodImplOptions.AggressiveInlining)] T cv(string s) => eq() ? ct(int.Parse(s)) : eq() ? ct(long.Parse(s)) : eq() ? ct(double.Parse(s)) : eq() ? ct(decimal.Parse(s)) : eq() ? ct(s[0]) : ct(s); [MethodImpl(MethodImplOptions.AggressiveInlining)] void Multi(out T a) => a = cv(GetStr()); [MethodImpl(MethodImplOptions.AggressiveInlining)] void Multi(out T a, out U b) { var ar = GetStrArray(); a = cv(ar[0]); b = cv(ar[1]); } [MethodImpl(MethodImplOptions.AggressiveInlining)] void Multi(out T a, out U b, out V c) { var ar = GetStrArray(); a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); } [MethodImpl(MethodImplOptions.AggressiveInlining)] void Multi(out T a, out U b, out V c, out W d) { var ar = GetStrArray(); a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); } [MethodImpl(MethodImplOptions.AggressiveInlining)] void Multi(out T a, out U b, out V c, out W d, out X e) { var ar = GetStrArray(); a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); } [MethodImpl(MethodImplOptions.AggressiveInlining)] void Multi(out T a, out U b, out V c, out W d, out X e, out Y f) { var ar = GetStrArray(); a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); f = cv(ar[5]); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public (T, U) GetMulti() { var ar = Console.ReadLine().Split(' '); return (cv(ar[0]), cv(ar[1])); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public (T, U, V) GetMulti() { var ar = Console.ReadLine().Split(' '); return (cv(ar[0]), cv(ar[1]), cv(ar[2])); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public (T, U, V, W) GetMulti() { var ar = Console.ReadLine().Split(' '); return (cv(ar[0]), cv(ar[1]), cv(ar[2]), cv(ar[3])); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public (T, U, V, W, X) GetMulti() { var ar = Console.ReadLine().Split(' '); return (cv(ar[0]), cv(ar[1]), cv(ar[2]), cv(ar[3]), cv(ar[4])); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public (T, U, V, W, X, Y) GetMulti() { var ar = Console.ReadLine().Split(' '); return (cv(ar[0]), cv(ar[1]), cv(ar[2]), cv(ar[3]), cv(ar[4]), cv(ar[5])); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Print() => Console.WriteLine(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Print(T t) => Console.WriteLine(t); [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Print(string separator, IList ls) => Console.WriteLine(string.Join(separator, ls)); public void Debug(IList ls) { Console.Error.WriteLine(); Console.Error.WriteLine("[" + string.Join(",", ls) + "]"); } public void Debug(IList> ls) { Console.Error.WriteLine(); foreach (var l in ls) { Console.Error.WriteLine("[" + string.Join(",", l) + "]"); } Console.Error.WriteLine(); } }