#include using namespace std; using ll = long long; using ld = long double; // -------------------------------------------------------- #define FOR(i,l,r) for (ll i = (l); i < (r); ++i) #define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) RFOR(i,0,n) #define ALL(c) (c).begin(), (c).end() #define RALL(c) (c).rbegin(), (c).rend() #define SORT(c) sort(ALL(c)) #define RSORT(c) sort(RALL(c)) #define MIN(c) *min_element(ALL(c)) #define MAX(c) *max_element(ALL(c)) #define SUMLL(c) accumulate(ALL(c), 0LL) #define COUNT(c,v) count(ALL(c),(v)) #define SZ(c) ((ll)(c).size()) #define BIT(b,i) (((b)>>(i)) & 1) #define PCNT(b) __builtin_popcountll(b) #define P0(i) (((i) & 1) == 0) #define P1(i) (((i) & 1) == 1) #ifdef _LOCAL #define debug_bar cerr << "--------------------\n"; #define debug(x) cerr << "l." << __LINE__ << " : " << #x << " = " << (x) << '\n' #define debug_pair(x) cerr << "l." << __LINE__ << " : " << #x << " = (" << x.first << "," << x.second << ")\n"; template void debug_line(const vector& ans, int l, int r, int L = 0) { cerr << "l." << L << " :"; for (int i = l; i < r; i++) { cerr << ' ' << ans[i]; } cerr << '\n'; } #else #define cerr if (false) cerr #define debug_bar #define debug(x) #define debug_pair(x) template void debug_line([[maybe_unused]] const vector& ans, [[maybe_unused]] int l, [[maybe_unused]] int r, [[maybe_unused]] int L = 0) {} #endif template void input(T&... a) { (cin >> ... >> a); } void print() { cout << '\n'; } template void print(const T& a) { cout << a << '\n'; } template void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void cout_line(const vector& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; } template bool chmin(T& a, const T b) { if (b < a) { a = b; return 1; } return 0; } template bool chmax(T& a, const T b) { if (a < b) { a = b; return 1; } return 0; } pair divmod(ll a, ll b) { assert(a >= 0 && b > 0); return make_pair(a / b, a % b); } ll mod(ll x, ll m) { assert(m != 0); return (x % m + m) % m; } ll llceil(ll a, ll b) { if (b < 0) { return llceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); } ll llfloor(ll a, ll b) { if (b < 0) { return llfloor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); } ll llpow(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = llpow(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; } ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); } ll digit_len(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; } ll digit_sum(ll n) { assert(n >= 0); ll sum = 0; while (n > 0) { sum += n % 10; n /= 10; } return sum; } ll digit_prod(ll n) { assert(n >= 0); if (n == 0) { return 0; } ll prod = 1; while (n > 0) { prod *= n % 10; n /= 10; } return prod; } ll xor_sum(ll x) { assert(0 <= x); switch (x % 4) { case 0: return x; case 1: return 1; case 2: return x ^ 1; case 3: return 0; } assert(false); } string toupper(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = toupper(T[i]); } return T; } string tolower(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = tolower(T[i]); } return T; } int a2i(const char& c) { assert(islower(c)); return (c - 'a'); } int A2i(const char& c) { assert(isupper(c)); return (c - 'A'); } int d2i(const char& d) { assert(isdigit(d)); return (d - '0'); } char i2a(const int& i) { assert(0 <= i && i < 26); return ('a' + i); } char i2A(const int& i) { assert(0 <= i && i < 26); return ('A' + i); } char i2d(const int& i) { assert(0 <= i && i <= 9); return ('0' + i); } using P = pair; using VP = vector

; using VVP = vector; using VS = vector; using VVS = vector; using VI = vector; using VVI = vector; using VVVI = vector; using VLL = vector; using VVLL = vector; using VVVLL = vector; using VB = vector; using VVB = vector; using VVVB = vector; using VD = vector; using VVD = vector; using VVVD = vector; using VLD = vector; using VVLD = vector; using VVVLD = vector; const ld EPS = 1e-10; const ld PI = acosl(-1.0); // constexpr ll MOD = 1000000007; constexpr ll MOD = 1000000009; // constexpr ll MOD = 998244353; constexpr int inf = (1 << 30) - 1; // 1073741824 - 1 constexpr ll INF = (1LL << 62) - 1; // 4611686018427387904 - 1 // -------------------------------------------------------- // #include // using namespace atcoder; // References: // mint: // // // // // // combination: // // struct mint { ll x; constexpr mint(ll x = 0) noexcept : x((x % MOD + MOD) % MOD) {} constexpr mint& operator+=(const mint& a) noexcept { if ((x += a.x) >= MOD) x -= MOD; return *this; } constexpr mint& operator-=(const mint& a) noexcept { if ((x += MOD - a.x) >= MOD) x -= MOD; return *this; } constexpr mint& operator*=(const mint& a) noexcept { (x *= a.x) %= MOD; return *this; } constexpr mint& operator/=(const mint& a) noexcept { return *this *= a.inv(); } constexpr mint operator-() const noexcept { return mint(-x); } constexpr mint operator+(const mint& a) const noexcept { return mint(*this) += a; } constexpr mint operator-(const mint& a) const noexcept { return mint(*this) -= a; } constexpr mint operator*(const mint& a) const noexcept { return mint(*this) *= a; } constexpr mint operator/(const mint& a) const noexcept { return mint(*this) /= a; } constexpr bool operator==(const mint& a) const noexcept { return x == a.x; } constexpr bool operator!=(const mint& a) const noexcept { return x != a.x; } constexpr mint pow(ll n) const { if (n == 0) return 1; mint res = pow(n >> 1); res *= res; if (n & 1) res *= *this; return res; } constexpr mint inv() const { return pow(MOD - 2); } friend istream& operator>>(istream& is, mint& a) noexcept { ll v; is >> v; a = mint(v); return is; } friend ostream& operator<<(ostream& os, const mint& a) noexcept { return os << a.x; } }; using VM = vector; using VVM = vector; using VVVM = vector; using VVVVM = vector; struct combination { vector fact_, ifact_, inv_; int n_; combination() {} combination(int n) : fact_(n+1,0), ifact_(n+1,0), inv_(n+1,0) { assert(n != 0); assert(n < MOD); n_ = n; fact_[0] = 1; fact_[1] = 1; ifact_[0] = 1; ifact_[1] = 1; inv_[1] = 1; for(int i = 2; i <= n; ++i) { fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); ifact_[i] = ifact_[i-1] * inv_[i]; } } mint P(const int& n, const int& k) const noexcept { if (n < 0 || k < 0 || n < k) return 0; assert(n <= n_); return fact_[n] * ifact_[n-k]; } mint C(const int& n, const int& k) const noexcept { if (n < 0 || k < 0 || n < k) return 0; assert(n <= n_); return fact_[n] * ifact_[n-k] * ifact_[k]; } mint H(const int& n, const int& k) const noexcept { if (n < 0 || k < 0) return 0; assert(n + k - 1 <= n_); return C(n + k - 1, k); } mint fact(const int& n) const noexcept { assert(n <= n_); if (n < 0) return 0; return fact_[n]; } mint ifact(const int& n) const noexcept { assert(n <= n_); if (n < 0) return 0; return ifact_[n]; } mint inv(const int& n) const noexcept { assert(n <= n_); if (n < 0) return 0; return inv_[n]; } }; /** * @brief 行列累乗 * d x d の正方行列 A に対して A^n を O(k^3 log n) で求める * * @tparam T 行列要素の型 e.g.) mint, ll * @param A 正方行列 * @param n 指数 * @return vector> A^n の計算結果 */ template vector> mat_exp(vector> A, ll n) { int d = A.size(); vector> B(d, vector(d, 0)); for (int i = 0; i < d; i++) { B[i][i] = 1; } // 単位行列で初期化 auto mat_mul = [&](const vector>& A, const vector>& B) -> vector> { vector> C(d, vector(d, 0)); for (int i = 0; i < d; i++) { for (int k = 0; k < d; k++) { for (int j = 0; j < d; j++) { C[i][j] += A[i][k] * B[k][j]; } } } return C; }; // e.g.) n = 11, B = A^(2^3) + A^(2^1) + A^(2^0) (11 = 2^3 + 2^1 + 2^0) while (n > 0) { if (n & 1) { B = mat_mul(B, A); } // 欲しいタイミングで拾う A = mat_mul(A, A); n >>= 1; } return B; }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); VI B = {1, 5, 10, 50, 100, 500}; ll N = 500, K = SZ(B); VVVM C(N+1, VVM(K, VM(K, 0))); REP(j,K) C[0][j][j] = 1; REP(x,N) REP(i,K) REP(j,K) { FOR(k,i,K) if (x + B[k] <= N) C[x+B[k]][k][j] += C[x][i][j]; } VVM dp(N+1, VM(K, 0)); REP(i,K) dp[B[i]][i] = 1; FOR(x,1,N) REP(i,K) { FOR(k,i,K) if (x + B[k] <= N) dp[x+B[k]][k] += dp[x][i]; } int T; cin >> T; while (T--) { ll M; cin >> M; VVM A(K,VM(K,0)); REP(i,K) REP(j,K) A[i][j] = C[N][i][j]; auto [q, r] = divmod(M, 500); mint ans = 0; if (q == 0) { REP(i,K) ans += dp[M][i]; } else if (r == 0) { auto An = mat_exp(A, q-1); REP(i,K) REP(j,K) ans += An[i][j] * dp[N][j]; } else { auto An = mat_exp(A, q); REP(i,K) REP(j,K) ans += An[i][j] * dp[r][j]; } print(ans); } return 0; }