#include #include /* [q^m] 1/(1-q)(1-q^5)(1-q^10)(1-q^50)(1-q^100)(1-q^500) [q^m] (1+q+q^2+q^3+q^4)/(1-q^5)^2(1-q^10)(1-q^50)(1-q^100)(1-q^500) [q^{m/5}] 1/(1-q)^2(1-q^2)(1-q^10)(1-q^20)(1-q^100) [q^m] (1+q)^2/(1-q^2)^3(1-q^10)(1-q^20)(1-q^100) If m is odd [q^{m}] 2q /(1-q^2)^3(1-q^10)(1-q^20)(1-q^100) [q^{m/2}] 2 /(1-q)^3(1-q^5)(1-q^10)(1-q^50) If m is even [q^{m}] (1+q^2) /(1-q^2)^3(1-q^10)(1-q^20)(1-q^100) [q^{m/2}] (1+q) /(1-q)^3(1-q^5)(1-q^10)(1-q^50) [q^{m}] P(q)/(1-q)^3(1-q^5)(1-q^10)(1-q^50) [q^{m}] P(q)(1+q+q^2+q^3+q^4)^3/(1-q^5)^4(1-q^10)(1-q^50) [q^{m}] P(q)/(1-q)^4(1-q^2)(1-q^10) [q^{m}] P(q)(1+q)^4/(1-q^2)^5(1-q^10) [q^{m}] P(q)/(1-q)^5(1-q^5) [q^{m}] P(q)(1+q+2^2+q^3+q^4)^5/(1-q^5)^6 [q^{m}] P(q)/(1-q)^6 binom{i+5}{5} [q^m] (1+q+...+q^499)(1+q^5+...+q^495)(1+q^10+...+q^490)(1+q^50+...+1+q^450)(1+q^100+...+q^400)/(1-q^500)^6 [q^{m}] P(q) /(1-q)^3(1-q^5)(1-q^10)(1-q^50) [q^{m}] P(q)(1+q+q^2+...+q^49)^3(1+q^5+...+q^45)(1+q^10+...+q^40) /(1-q^50)^6 */ constexpr int mod = 1000000009; void mul(std::vector &P, int a){ for(std::size_t i = a; i < P.size(); i++) P[i] += P[i-a]; } int binom5(long long int k){ return k * (k - 1) % mod * (k - 2) % mod * (k - 3) % mod * (k - 4) % mod; } void print(std::vector &P){ for(long long int x: P) printf("%lld ", x); puts(""); } int main(){ std::vector P(49*3 + 45 + 40 + 2); P[0] = 1; P[50] = mod-5; P[100] = 10; P[150] = mod-10; P[200] = 5; // P[250] = mod-1; mul(P, 1); mul(P, 1); mul(P, 1); mul(P, 5); mul(P, 10); for(long long int &x: P) x %= mod; int t; scanf("%d", &t); // print(P); while(t--){ long long int m; scanf("%lld", &m); m /= 5; long long int r = 0; if(m&1){ m /= 2; for(std::size_t i = m % 50; i < P.size() && i <= m; i+=50) r += (long long) binom5(((m-i)/50+5)%mod) * P[i]; r += r; } else { m /= 2; for(std::size_t i = m % 50; i < P.size() && i <= m; i+=50) r += (long long) binom5(((m-i)/50+5)%mod) * (P[i] + (i ? P[i-1] : 0)); } printf("%d\n", (int) (r % mod * 591666672 % mod)); } return 0; }