#include using namespace std; const int MOD = 1e9 + 9; template struct Matrix { vector> A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector(m, 0)) {} Matrix(size_t n) : A(n, vector(n, 0)){}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector& operator[](int k) const { return (A.at(k)); } inline vector& operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for (int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix& operator+=(const Matrix& B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix& operator-=(const Matrix& B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix& operator*=(const Matrix& B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector> C(n, vector(m, 0)); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) for (int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix& operator^=(long long k) { Matrix B = Matrix::I(height()); while (k > 0) { if (k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix& B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix& B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix& B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } friend ostream& operator<<(ostream& os, Matrix& p) { size_t n = p.height(), m = p.width(); for (int i = 0; i < n; i++) { os << "["; for (int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for (int i = 0; i < width(); i++) { int idx = -1; for (int j = i; j < width(); j++) { if (B[j][i] != 0) idx = j; } if (idx == -1) return (0); if (i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for (int j = 0; j < width(); j++) { B[i][j] /= vv; } for (int j = i + 1; j < width(); j++) { T a = B[j][i]; for (int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; template struct ModInt { using M = ModInt; const static M G; uint v; ModInt(long long _v = 0) { set_v(uint(_v % Mod + Mod)); } M& set_v(uint _v) { v = (_v < Mod) ? _v : _v - Mod; return *this; } explicit operator bool() const { return v != 0; } M operator-() const { return M() - *this; } M operator+(const M& r) const { return M().set_v(v + r.v); } M operator-(const M& r) const { return M().set_v(v + Mod - r.v); } M operator*(const M& r) const { return M().set_v((unsigned long long)v * r.v % Mod); } M operator/(const M& r) const { return *this * r.inv(); } M& operator+=(const M& r) { return *this = *this + r; } M& operator-=(const M& r) { return *this = *this - r; } M& operator*=(const M& r) { return *this = *this * r; } M& operator/=(const M& r) { return *this = *this / r; } bool operator==(const M& r) const { return v == r.v; } M pow(long long n) const { M x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } M inv() const { return pow(Mod - 2); } friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; } friend istream& operator>>(istream& is, M& r) { return is >> r.v; } }; int main() { const int C[] = {1, 5, 10, 50, 100, 500}; ModInt dp[510][10] = {}; dp[0][0] = 1; for (int i = 0; i < 6; i++) { for (int c = 0; c <= 500; c++) { if (c + C[i] <= 500) dp[c + C[i]][i] += dp[c][i]; dp[c][i + 1] += dp[c][i]; } } Matrix> Mat(6); for (int t = 0; t < 6; t++) { ModInt dp[510][10] = {}; dp[0][t] = 1; for (int i = 0; i < 6; i++) { for (int c = 0; c <= 500; c++) { if (c + C[i] <= 500) dp[c + C[i]][i] += dp[c][i]; if (c > 0) dp[c][i + 1] += dp[c][i]; } } for (int i = 0; i < 6; i++) { Mat[i][t] = dp[500][i]; } } int T; cin >> T; while (T--) { long long M; cin >> M; Matrix> Vec(6, 1); for (int i = 0; i < 6; i++) { Vec[i][0] = dp[M % 500][i]; } Matrix> Mat_M = (Mat ^ (M / 500)); Vec = Mat_M * Vec; cout << Vec[5][0] << endl; } }