using System; using System.IO; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; namespace AtCoder.Contest.D { static class Program { public static void Main(string[] args) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); var cin = new Scanner(); long n = cin.NextLong(); var p = new List(); p.Add(1); ModInt inv = ModInt.Inverse(6); var vec = new Matrix(6, 1); var t = new Matrix(6, 6); vec[0, 0] = 1; vec[1, 0] = 166666668; vec[2, 0] = 194444446; vec[3, 0] = 893518525; vec[4, 0] = 209104940; vec[5, 0] = 577289099; for (int i = 0; i < 6; i++) { for (int j = 0; j < 6; j++) { if(i != 5) { if (i == j - 1) t[i, j] = 1; else t[i, j] = 0; } else { t[i, j] = inv; } } } if (n < 6) Console.WriteLine(vec[(int)n, 0]); else { var ans = Matrix.Pow(t, n - 5) * vec; Console.WriteLine(ans[5, 0]); } var aa = new List(); for (int i = 0; i < 6; i++) { aa.Add(vec[i, 0]); } for (int i = 6; i <= n; i++) { aa.Add((aa[i - 1] + aa[i - 2] + aa[i - 3] + aa[i - 4] + aa[i - 5] + aa[i - 6]) * inv); } Console.Out.Flush(); } } public class Matrix { int row, col; public ModInt[] mat; /// /// 列目の要素へのアクセスを提供します。 /// /// 行の番号 /// 列の番号 public ModInt this[int r, int c] { get { return mat[r * col + c]; } set { mat[r * col + c] = value; } } public Matrix(int r, int c) { row = r; col = c; mat = new ModInt[row * col]; } public static Matrix operator *(Matrix l, Matrix r) { System.Diagnostics.Debug.Assert(l.col == r.row); var ret = new Matrix(l.row, r.col); for (int i = 0; i < l.row; i++) for (int k = 0; k < l.col; k++) for (int j = 0; j < r.col; j++) ret.mat[i * r.col + j] = (ret.mat[i * r.col + j] + l.mat[i * l.col + k] * r.mat[k * r.col + j]); return ret; } /// /// ^ を O(^3 log ) で計算します。 /// public static Matrix Pow(Matrix m, long n) { var ret = new Matrix(m.row, m.col); for (int i = 0; i < m.row; i++) ret.mat[i * m.col + i] = 1; for (; n > 0; m *= m, n >>= 1) if ((n & 1) == 1) ret = ret * m; return ret; } public ModInt[][] Items { get { var a = new ModInt[row][]; for (int i = 0; i < row; i++) { a[i] = new ModInt[col]; for (int j = 0; j < col; j++) a[i][j] = mat[i * col + j]; } return a; } } } public struct ModInt : IComparable, IEquatable { public static long MOD = 1000000007; private readonly long num; public ModInt(long n) { num = n; } public override string ToString() => num.ToString(); public static ModInt operator +(ModInt l, ModInt r) { long x = l.num + r.num; if (x >= MOD) x -= MOD; return new ModInt(x); } public static ModInt operator -(ModInt l, ModInt r) { long x = l.num - r.num; if (x < 0) x += MOD; return new ModInt(x); } public static ModInt operator *(ModInt l, ModInt r) => new ModInt((l.num * r.num) % MOD); public static ModInt operator /(ModInt l, ModInt r) => l * r.Inverse(); public static ModInt operator ++(ModInt x) { var tmp = x + new ModInt(1); return tmp; } public static ModInt operator --(ModInt x) { var tmp = x - new ModInt(1); return tmp; } public static bool operator >(ModInt l, ModInt r) => l.CompareTo(r) > 0; public static bool operator <(ModInt l, ModInt r) => l.CompareTo(r) < 0; public static bool operator >=(ModInt l, ModInt r) => l.CompareTo(r) >= 0; public static bool operator <=(ModInt l, ModInt r) => l.CompareTo(r) <= 0; public static bool operator ==(ModInt l, ModInt r) => l.Equals(r); public static bool operator !=(ModInt l, ModInt r) => !l.Equals(r); public static implicit operator long(ModInt x) => x.num; public static implicit operator ModInt(long n) { n %= MOD; if (n < 0) n += MOD; return new ModInt(n); } public ModInt Inverse() => Inverse(this, MOD); public static ModInt Inverse(ModInt x) => Inverse(x.num, MOD); public static long Inverse(long x, long m) { if (x % m == 0) throw new DivideByZeroException(); long a = x, b = m, u = 1, v = 0; while (b > 0) { long t = a / b; a -= t * b; long p = a; a = b; b = p; // swap(a, b); u -= t * v; p = u; u = v; v = p; // swap(u, v); } u %= m; if (u < 0) u += m; return u; } public static ModInt Pow(ModInt x, long n) => Pow(x.num, n); public static ModInt Pow(long x, long n) { if (n == 0) return x; long now = 1; for (n %= MOD - 1; n > 0; n /= 2, x = x * x % MOD) { if (n % 2 == 1) now = now * x % MOD; } return new ModInt(now); } public int CompareTo(ModInt x) { if (num == x.num) return 0; if (num > x.num) return 1; return -1; } public bool Equals(ModInt x) => num == x.num; public override bool Equals(object obj) => obj is ModInt m && num == m.num; public override int GetHashCode() { return HashCode.Combine(num); } } class Scanner { string[] s; int i; char[] cs = new char[] { ' ' }; public Scanner() { s = new string[0]; i = 0; } public string Next() { if (i < s.Length) return s[i++]; string st = Console.ReadLine(); while (st == "") st = Console.ReadLine(); s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries); if (s.Length == 0) return Next(); i = 0; return s[i++]; } public int NextInt() { return int.Parse(Next()); } public int[] ArrayInt(int N, int add = 0) { int[] Array = new int[N]; for (int i = 0; i < N; i++) { Array[i] = NextInt() + add; } return Array; } public long NextLong() { return long.Parse(Next()); } public long[] ArrayLong(int N, long add = 0) { long[] Array = new long[N]; for (int i = 0; i < N; i++) { Array[i] = NextLong() + add; } return Array; } public double NextDouble() { return double.Parse(Next()); } public double[] ArrayDouble(int N, double add = 0) { double[] Array = new double[N]; for (int i = 0; i < N; i++) { Array[i] = NextDouble() + add; } return Array; } } }