#include #pragma GCC diagnostic ignored "-Wsign-compare" #pragma GCC diagnostic ignored "-Wsign-conversion" #define NDEBUG #define SHOW(...) static_cast(0) //!===========================================================!// //! dP dP dP !// //! 88 88 88 !// //! 88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b. !// //! 88 88 88ooood8 88' '88 88' '88 88ooood8 88' '88 !// //! 88 88 88. ... 88. .88 88. .88 88. ... 88 !// //! dP dP '88888P' '88888P8 '88888P8 '88888P' dP !// //!===========================================================!// template T read() { T v; return std::cin >> v, v; } template std::vector readVec(const std::size_t l) { std::vector v(l); for (auto& e : v) { std::cin >> e; } return v; } using ld = long double; using uint = unsigned int; using ll = long long; using ull = unsigned long long; constexpr unsigned int MOD = 1000000007; template constexpr T INF = std::numeric_limits::max() / 4; template constexpr F PI = static_cast(3.1415926535897932385); std::mt19937 mt{std::random_device{}()}; template bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); } template bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); } template std::vector Vec(const std::size_t n, T v) { return std::vector(n, v); } template auto Vec(const std::size_t n, Args... args) { return std::vector(n, Vec(args...)); } template constexpr T popCount(const T u) { #ifdef __has_builtin return u == 0 ? T(0) : (T)__builtin_popcountll(u); #else unsigned long long v = static_cast(u); return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast(v * 0x0101010101010101ULL >> 56 & 0x7f); #endif } template constexpr T log2p1(const T u) { #ifdef __has_builtin return u == 0 ? T(0) : T(64 - __builtin_clzll(u)); #else unsigned long long v = static_cast(u); return v = static_cast(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v); #endif } template constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); } template constexpr T msbp1(const T v) { return log2p1(v); } template constexpr T lsbp1(const T v) { #ifdef __has_builtin return __builtin_ffsll(v); #else return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1); #endif } template constexpr bool ispow2(const T v) { return popCount(v) == 1; } template constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); } template constexpr T floor2(const T v) { return v == 0 ? T(0) : T(1) << (log2p1(v) - 1); } //!===============================================================!// //! 88888888b dP .88888. a88888b. 888888ba !// //! 88 88 d8' '88 d8' '88 88 '8b !// //! a88aaaa dP. .dP d8888P 88 88 88 88 !// //! 88 '8bd8' 88 88 YP88 88 88 88 !// //! 88 .d88b. 88 Y8. .88 Y8. .88 88 .8P !// //! 88888888P dP' 'dP dP '88888' Y88888P' 8888888P !// //!===============================================================!// template constexpr std::pair extgcd(const T a, const T b) { if (b == 0) { return std::pair{1, 0}; } const auto p = extgcd(b, a % b); return {p.second, p.first - p.second * (a / b)}; } template constexpr T inverse(const T a, const T mod) { return (mod + extgcd((mod + a % mod) % mod, mod).first % mod) % mod; } //!========================================================!// //! 8888ba.88ba dP dP dP !// //! 88 '8b '8b 88 88 88 !// //! 88 88 88 .d8888b. .d888b88 88 88d888b. d8888P !// //! 88 88 88 88' '88 88' '88 88 88' '88 88 !// //! 88 88 88 88. .88 88. .88 88 88 88 88 !// //! dP dP dP '88888P' '88888P8 dP dP dP dP !// //!========================================================!// template class ModInt { private: uint v; static uint norm(const uint& x) { return x < mod ? x : x - mod; } static ModInt make(const uint& x) { ModInt m; return m.v = x, m; } static ModInt power(ModInt x, ll n) { ModInt ans = 1; for (; n; n >>= 1, x *= x) { if (n & 1) { ans *= x; } } return ans; } static ModInt inv(const ModInt& x) { return ModInt{inverse(static_cast(x.v), static_cast(mod))}; } public: ModInt() : v{0} {} ModInt(const ll val) : v{norm(uint(val % static_cast(mod) + static_cast(mod)))} {} ModInt(const ModInt& n) : v{n()} {} explicit operator bool() const { return v != 0; } ModInt& operator=(const ModInt& m) { return v = m(), (*this); } ModInt& operator=(const ll val) { return v = norm(uint(val % static_cast(mod) + static_cast(mod))), (*this); } friend ModInt operator+(const ModInt& m) { return m; } friend ModInt operator-(const ModInt& m) { return make(norm(mod - m.v)); } friend ModInt operator+(const ModInt& m1, const ModInt& m2) { return make(norm(m1.v + m2.v)); } friend ModInt operator-(const ModInt& m1, const ModInt& m2) { return make(norm(m1.v + mod - m2.v)); } friend ModInt operator*(const ModInt& m1, const ModInt& m2) { return make(static_cast(static_cast(m1.v) * static_cast(m2.v) % static_cast(mod))); } friend ModInt operator/(const ModInt& m1, const ModInt& m2) { return m1 * inv(m2.v); } friend ModInt operator+(const ModInt& m, const ll val) { return ModInt{static_cast(m.v) + val}; } friend ModInt operator-(const ModInt& m, const ll val) { return ModInt{static_cast(m.v) - val}; } friend ModInt operator*(const ModInt& m, const ll val) { return ModInt{static_cast(m.v) * (val % static_cast(mod))}; } friend ModInt operator/(const ModInt& m, const ll val) { return ModInt{static_cast(m.v) * inv(val)}; } friend ModInt operator+(const ll val, const ModInt& m) { return ModInt{static_cast(m.v) + val}; } friend ModInt operator-(const ll val, const ModInt& m) { return ModInt{static_cast(m.v) - val}; } friend ModInt operator*(const ll val, const ModInt& m) { return ModInt{static_cast(m.v) * (val % static_cast(mod))}; } friend ModInt operator/(const ll val, const ModInt& m) { return ModInt{static_cast(m.v) * inv(val)}; } friend ModInt& operator+=(ModInt& m1, const ModInt& m2) { return m1 = m1 + m2; } friend ModInt& operator-=(ModInt& m1, const ModInt& m2) { return m1 = m1 - m2; } friend ModInt& operator*=(ModInt& m1, const ModInt& m2) { return m1 = m1 * m2; } friend ModInt& operator/=(ModInt& m1, const ModInt& m2) { return m1 = m1 / m2; } friend ModInt& operator+=(ModInt& m, const ll val) { return m = m + val; } friend ModInt& operator-=(ModInt& m, const ll val) { return m = m - val; } friend ModInt& operator*=(ModInt& m, const ll val) { return m = m * val; } friend ModInt& operator/=(ModInt& m, const ll val) { return m = m / val; } friend ModInt operator^(const ModInt& m, const ll n) { return power(m.v, n); } friend ModInt& operator^=(ModInt& m, const ll n) { return m = m ^ n; } friend bool operator==(const ModInt& m1, const ModInt& m2) { return m1.v == m2.v; } friend bool operator!=(const ModInt& m1, const ModInt& m2) { return not(m1 == m2); } friend bool operator==(const ModInt& m, const ll val) { return m.v == norm(static_cast(static_cast(mod) + val % static_cast(mod))); } friend bool operator!=(const ModInt& m, const ll val) { return not(m == val); } friend bool operator==(const ll val, const ModInt& m) { return m.v == norm(static_cast(static_cast(mod) + val % static_cast(mod))); } friend bool operator!=(const ll val, const ModInt& m) { return not(m == val); } friend std::istream& operator>>(std::istream& is, ModInt& m) { uint v; return is >> v, m = v, is; } friend std::ostream& operator<<(std::ostream& os, const ModInt& m) { return os << m(); } static std::vector invVec(const std::size_t N) { std::vector ans(N + 1, 1); for (std::size_t i = 2; i <= N; i++) { ans[i] = -ans[mod % i] * (mod / i); } return ans; } uint operator()() const { return v; } }; template class Lagrange { using mint = ModInt; public: Lagrange(const std::vector& x, const std::vector& f) : N{x.size()}, a(N, 0), x{x} { assert(x.size() == f.size()); if (isSeq(x)) { auto v = mint::invVec(N - 1); for (std::size_t i = 1; i < N; i++) { v[i] *= v[i - 1]; } for (std::size_t i = 0; i < N; i++) { for (std::size_t j = 0; j <= i; j++) { const auto b = v[i - j] * v[j]; a[i] += ((i - j) % 2 == 0 ? b : -b) * f[j]; } } } else { for (std::size_t i = 0; i < N; i++) { for (std::size_t j = 0; j <= i; j++) { mint p = 1; for (std::size_t k = 0; k <= i; k++) { if (j == k) { continue; } p *= (x[j] - x[k]); } a[i] += f[j] / p; } } } } mint eval(const ll v) const { mint ans = 0, base = 1; for (std::size_t i = 0; i < N; base *= (v - x[i++])) { ans += base * a[i]; } return ans; } private: bool isSeq(const std::vector& x) { return (x.back() - x.front() + 1LL) == N; } std::size_t N; std::vector a; std::vector x; }; //!=====================================!// //! 8888ba.88ba oo !// //! 88 '8b '8b !// //! 88 88 88 .d8888b. dP 88d888b. !// //! 88 88 88 88' '88 88 88' '88 !// //! 88 88 88 88. .88 88 88 88 !// //! dP dP dP '88888P8 dP dP dP !// //!=====================================!// int main() { constexpr uint MOD = 1000000009; using mint = ModInt; constexpr int C[6] = {1, 5, 10, 50, 100, 500}; std::vector> F; F.push_back(Lagrange({0, 1, 2, 3, 4, 5}, {1, 1, 1, 1, 1, 1})); for (int i = 1; i < 6; i++) { std::vector> tmp; for (int l = 0; l < C[i]; l++) { std::vector f(6, 0); for (int x = 0; x < 6; x++) { for (int z = 0; z <= x; z++) { f[x] += F[l % C[i - 1]].eval(C[i] / C[i - 1] * z + (l / C[i - 1])); } } tmp.push_back(Lagrange({0, 1, 2, 3, 4, 5}, f)); } F = tmp; } const int T = read(); for (int t = 0; t < T; t++) { const ll M = read(); const mint x = M / C[5]; const int l = M % C[5]; std::cout << F[l].eval(x()) << std::endl; } return 0; }