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MACRO_OUT(__VA_ARGS__); #define FOUT(n, dist) std::cout<=(a);--w) #define RREP(w, n) RFOR(w, 0, n) template bool IN(S a, T x, U b) { return a <= x && x < b; } template inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; } template inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; } // test template using V = std::vector; template using VV = V>; template std::ostream& operator<<(std::ostream& os, const std::pair& p) { os << "(" << p.first << ", " << p.second << ")"; return os; } template std::ostream& operator<<(std::ostream& os, const std::vector& v) { os << "{"; for (size_t i = 0; i < v.size(); ++i) os << v[i] << ((i + 1 < v.size()) ? ", " : ""); os << "}"; return os; } template std::ostream & operator<<(std::ostream & os, const std::set & v) { os << "{"; for (auto it = v.cbegin();;) { os << *it; ++it; if (it == v.cend()) { os << "}"; break; } else { os << ", "; } } return os; } template std::ostream& operator<<(std::ostream & os, const std::map & m) { os << "{"; for (auto it = m.cbegin(); it != m.cend();) { os << it->first << ":" << it->second; ++it; os << (it == m.cend() ? "" : ", "); } os << "}"; return os; } template std::ostream& operator<<(std::ostream & os, std::queue q) { os << "<"; while (!q.empty()) { os << q.front(); q.pop(); os << (q.empty() ? "<" : ", "); } return os; } template std::ostream& operator<<(std::ostream & os, std::stack q) { os << ">"; while (!q.empty()) { os << q.top(); q.pop(); os << (q.empty() ? "]" : ", "); } return os; } namespace std { template class numeric_limits> { public: static constexpr pair max() noexcept { return { numeric_limits::max(), numeric_limits::max() }; } static constexpr pair lowest() noexcept { return { numeric_limits::lowest(), numeric_limits::lowest() }; } }; } // type/const using i64 = std::int_fast64_t; using u64 = std::uint_fast64_t; using ll = long long; using ull = unsigned long long; using ld = long double; using PAIR = std::pair; using PAIRLL = std::pair; constexpr int INFINT = (1 << 30) - 1; // 1.07x10^ 9 constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9 constexpr ll INFLL = 1LL << 60; // 1.15x10^18 constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18 constexpr double EPS = 1e-6; constexpr i64 MOD = 1000000009; constexpr double PI = 3.141592653589793238462643383279; template void FILL(T(&a)[N], const T & val) { for (auto& x : a) x = val; } template void FILL(ARY(&a)[N][M], const T & val) { for (auto& b : a) FILL(b, val); } template void FILL(std::vector & a, const T & val) { for (auto& x : a) x = val; } template void FILL(std::vector> & a, const T & val) { for (auto& b : a) FILL(b, val); } // ------------>8--------- ll powMod(ll n, ll p, ll mod) { ll res = 1; while (p) { if (p & 1) (res *= n) %= mod; (n *= n) %= mod; p >>= 1; } return res; } ll invMod(ll n, ll mod) { return powMod(n, MOD - 2, MOD); } const signed FACT_MAX_N = 1000006; signed fact[FACT_MAX_N]; signed factInv[FACT_MAX_N]; struct INIT_FACT { INIT_FACT() { fact[0] = 1; for (int i = 1; i < FACT_MAX_N; ++i) fact[i] = (long long)i * fact[i - 1] % MOD; factInv[FACT_MAX_N - 1] = powMod(fact[FACT_MAX_N - 1], MOD - 2, MOD); for (int i = FACT_MAX_N - 2; i >= 0; --i) factInv[i] = (long long)(i + 1) * factInv[i + 1] % MOD; } } init_fact; ll Combination(ll n, ll r) { if (n < r) return 0; if (n < 2 * r) r = n - r; ll ans = factInv[r]; n %= MOD; for (int i = 1; i <= r; ++i) (ans *= n - i + 1) %= MOD; if (ans < 0) ans += MOD; return ans; } class Polynomial { std::vector coef; public: Polynomial(int N) : coef(N + 1, 0) {} Polynomial(std::initializer_list a) : coef(a) {} Polynomial& operator+=(const Polynomial& r) { if (coef.size() < r.coef.size()) coef.resize(r.coef.size()); for (size_t i = 0; i < r.coef.size(); ++i) (coef[i] += r.coef[i]) %= MOD; return *this; } Polynomial & operator*=(const Polynomial & r) { // O(N^2) std::vector c(this->coef.size() + r.coef.size() - 1); REP(i, this->coef.size()) REP(j, r.coef.size()) c[i + j] += this->coef[i] * r.coef[j]; coef = c; return *this; } /*Polynomial& operator*=(const Polynomial & r) { // O(NlogN) auto c = NTT::mul(this->coef, r.coef, MOD); coef = c; return *this; }*/ Polynomial& operator^=(long long p) { Polynomial x(*this); *this = Polynomial(0); coef[0] = 1; while (p) { if (p & 1) (*this) *= x; x *= x; p >>= 1; } return *this; } int& operator[](size_t i) { return coef[i]; } std::vector getCoef() const { return coef; } }; signed main() { INIT; Polynomial P(0); P[0] = 1; { { Polynomial t(4); REP(k, 5) t[k] = 1; P *= t; } { Polynomial t(5); t[0] = t[5] = 1; REP(_, 2) P *= t; } { Polynomial t(40); REP(k, 5) t[k * 10] = 1; REP(_, 3) P *= t; } { Polynomial t(50); t[0] = t[50] = 1; REP(_, 4) P *= t; } { Polynomial t(400); REP(k, 5) t[k * 100] = 1; REP(_, 5) P *= t; } } auto Q = [&](i64 m) { if (m < 0 || m % 500) return 0ll; return Combination(m / 500 + 5, 5); }; VAR(int, T); REP(_, T) { VAR(i64, m); i64 ans = 0; for (i64 k = m / 500 * 500; k >= std::max((i64)0, m - 2334); k -= 500) (ans += P[m - k] * Q(k)) %= MOD; OUT(ans)BR; } return 0; }