結果

問題 No.42 貯金箱の溜息
ユーザー PachicobuePachicobue
提出日時 2019-07-04 16:37:40
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 24 ms / 5,000 ms
コード長 11,573 bytes
コンパイル時間 2,626 ms
コンパイル使用メモリ 220,840 KB
実行使用メモリ 4,348 KB
最終ジャッジ日時 2023-10-19 07:40:08
合計ジャッジ時間 3,761 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge15
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 19 ms
4,348 KB
testcase_01 AC 23 ms
4,348 KB
testcase_02 AC 24 ms
4,348 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#define NDEBUG
#define SHOW(...) static_cast<void>(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 <typename T>
T read()
{
    T v;
    return std::cin >> v, v;
}
template <typename T>
std::vector<T> readVec(const std::size_t l)
{
    std::vector<T> 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 <typename T>
constexpr T INF = std::numeric_limits<T>::max() / 4;
template <typename F>
constexpr F PI = static_cast<F>(3.1415926535897932385);
std::mt19937 mt{std::random_device{}()};
template <typename T>
bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template <typename T>
bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
template <typename T>
std::vector<T> Vec(const std::size_t n, T v) { return std::vector<T>(n, v); }
template <class... Args>
auto Vec(const std::size_t n, Args... args) { return std::vector<decltype(Vec(args...))>(n, Vec(args...)); }
template <typename T>
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<unsigned long long>(u);
    return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast<T>(v * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}
template <typename T>
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<unsigned long long>(u);
    return v = static_cast<unsigned long long>(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v);
#endif
}
template <typename T>
constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); }
template <typename T>
constexpr T msbp1(const T v) { return log2p1(v); }
template <typename T>
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 <typename T>
constexpr bool ispow2(const T v) { return popCount(v) == 1; }
template <typename T>
constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); }
template <typename T>
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 <typename T>
constexpr std::pair<T, T> extgcd(const T a, const T b)
{
    if (b == 0) { return std::pair<T, T>{1, 0}; }
    const auto p = extgcd(b, a % b);
    return {p.second, p.first - p.second * (a / b)};
}
template <typename T>
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 <uint mod>
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<ll>(x.v), static_cast<ll>(mod))}; }

public:
    ModInt() : v{0} {}
    ModInt(const ll val) : v{norm(uint(val % static_cast<ll>(mod) + static_cast<ll>(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<ll>(mod) + static_cast<ll>(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<uint>(static_cast<ll>(m1.v) * static_cast<ll>(m2.v) % static_cast<ll>(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<ll>(m.v) + val}; }
    friend ModInt operator-(const ModInt& m, const ll val) { return ModInt{static_cast<ll>(m.v) - val}; }
    friend ModInt operator*(const ModInt& m, const ll val) { return ModInt{static_cast<ll>(m.v) * (val % static_cast<ll>(mod))}; }
    friend ModInt operator/(const ModInt& m, const ll val) { return ModInt{static_cast<ll>(m.v) * inv(val)}; }
    friend ModInt operator+(const ll val, const ModInt& m) { return ModInt{static_cast<ll>(m.v) + val}; }
    friend ModInt operator-(const ll val, const ModInt& m) { return ModInt{static_cast<ll>(m.v) - val}; }
    friend ModInt operator*(const ll val, const ModInt& m) { return ModInt{static_cast<ll>(m.v) * (val % static_cast<ll>(mod))}; }
    friend ModInt operator/(const ll val, const ModInt& m) { return ModInt{static_cast<ll>(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<uint>(static_cast<ll>(mod) + val % static_cast<ll>(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<uint>(static_cast<ll>(mod) + val % static_cast<ll>(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<ModInt> invVec(const std::size_t N)
    {
        std::vector<ModInt> 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 <uint mod>
class Lagrange
{
    using mint = ModInt<mod>;

public:
    Lagrange(const std::vector<ll>& x, const std::vector<mint>& 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<ll>& x) { return (x.back() - x.front() + 1LL) == N; }
    std::size_t N;
    std::vector<mint> a;
    std::vector<ll> 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<MOD>;
    constexpr int C[6] = {1, 5, 10, 50, 100, 500};
    std::vector<Lagrange<MOD>> F;
    F.push_back(Lagrange<MOD>({0, 1, 2, 3, 4, 5}, {1, 1, 1, 1, 1, 1}));
    for (int i = 1; i < 6; i++) {
        std::vector<Lagrange<MOD>> tmp;
        for (int l = 0; l < C[i]; l++) {
            std::vector<mint> 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<MOD>({0, 1, 2, 3, 4, 5}, f));
        }
        F = tmp;
    }
    const int T = read<int>();
    for (int t = 0; t < T; t++) {
        const ll M = read<ll>();
        const mint x = M / C[5];
        const int l = M % C[5];
        std::cout << F[l].eval(x()) << std::endl;
    }
    return 0;
}
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