#include #define rep(i, n) for (int i = 0; i < (n); i++) #define repr(i, n) for (int i = (n) - 1; i >= 0; i--) #define rep2(i, l, r) for (int i = (l); i < (r); i++) #define rep2r(i, l, r) for (int i = (r) - 1; i >= (l); i--) #define range(a) a.begin(), a.end() using namespace std; using ll = long long; constexpr int MOD = 1000000007; class mint { int n; public: mint(int n_ = 0) : n(n_) {} explicit operator int() { return n; } friend mint operator-(mint a) { return -a.n + MOD * (a.n != 0); } friend mint operator+(mint a, mint b) { int x = a.n + b.n; return x - (x >= MOD) * MOD; } friend mint operator-(mint a, mint b) { int x = a.n - b.n; return x + (x < 0) * MOD; } friend mint operator*(mint a, mint b) { return (long long)a.n * b.n % MOD; } friend mint &operator+=(mint &a, mint b) { return a = a + b; } friend mint &operator-=(mint &a, mint b) { return a = a - b; } friend mint &operator*=(mint &a, mint b) { return a = a * b; } friend bool operator==(mint a, mint b) { return a.n == b.n; } friend bool operator!=(mint a, mint b) { return a.n != b.n; } friend istream &operator>>(istream &i, mint &a) { return i >> a.n; } friend ostream &operator<<(ostream &o, mint a) { return o << a.n; } }; mint operator "" _m(unsigned long long n) { return n; } mint modinv(mint n) { int a = (int)n, b = MOD; int s = 1, t = 0; while (b != 0) { int q = a / b; a -= q * b; s -= q * t; swap(a, b); swap(s, t); } return s >= 0 ? s : s + MOD; } vector berlekamp_massey(vector s) { const int N = s.size(); vector C(N); vector B(N); C[0] = 1; B[0] = 1; int L = 0; int m = 1; mint b = 1; for (int n = 0; n < N; n++) { mint d = s[n]; for (int i = 1; i <= L; i++) d += C[i] * s[n - i]; mint inv_b = modinv(b); if (d == 0) { m++; } else if (2 * L <= n) { auto T = C; for (int i = 0; i + m < N; i++) C[i + m] -= B[i] * d * inv_b; L = n + 1 - L; B = T; b = d; m = 1; } else { for (int i = 0; i + m < N; i++) C[i + m] -= B[i] * d * inv_b; m++; } } C.resize(L + 1); reverse(C.begin(), C.end()); assert(L < N - 1); C.pop_back(); for (int i = 0; i < C.size(); i++) { C[i] = -C[i]; } return C; } vector poly_mod(vector a, const vector &m) { const int n = m.size(); for (int i = a.size() - 1; i >= m.size(); i--) { for (int j = 0; j < m.size(); j++) { a[i - n + j] += a[i] * m[j]; } } a.resize(m.size()); return a; } // a*b mod m(x) vector poly_mul(const vector &a, const vector &b, const vector &m) { vector ret(a.size() + b.size() - 1); for (int i = 0; i < a.size(); i++) { for (int j = 0; j < b.size(); j++) { ret[i + j] += a[i] * b[j]; } } return poly_mod(ret, m); } // x^n mod m(x) vector nth_power(long long n, const vector &m) { vector ret(1); vector x(2); ret[0] = x[1] = 1; while (n > 0) { if (n & 1) ret = poly_mul(ret, x, m); x = poly_mul(x, x, m); n /= 2; } return poly_mod(ret, m); } mint predict_nth(vector a, long long n) { auto b = nth_power(n, berlekamp_massey(a)); mint res = 0; for (int i = 0; i < b.size(); i++) { res += a[i] * b[i]; } return res; } /* 1/(1-x)(1-x^2)(1-x^3) = 1 + x + 2 x + 3 x + 4 x + 5 x + 7 x + 8 x + 10 x + 12 x 10 11 12 13 14 15 16 17 + 14 x + 16 x + 19 x + 21 x + 24 x + 27 x + 30 x + 33 x 18 19 20 + 37 x + 40 x + 44 x */ int main() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); vector p{0,0,0,0,1,1,2,3,4,5,7,8,10,12,14,16}; ll n; cin >> n; cout << predict_nth(p, n) << endl; }