#982734 (C++17) No.2763 Macaron Gift Box

• 問題: No.2763 Macaron Gift Box
• ユーザー: Today03
• 提出日時: 2024-05-19 09:08:31
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 444 ms / 3,000 ms
• コード長: 19,503 bytes
• コンパイル時間: 2,812 ms
• コンパイル使用メモリ: 216,152 KB
• 最終ジャッジ日時: 2025-02-21 15:50:30
• ジャッジサーバーID （参考情報）: judge3 / judge5

ファイルパターン	結果
sample	AC * 2
other	AC * 15

ソースコード

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int INF = 1e9 + 10;
const ll INFL = 4e18;

template <int mod>
struct ModInt {
    int x;
    ModInt() : x(0) {}
    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    ModInt &operator+=(const ModInt &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }
    ModInt operator-() const { return ModInt(-x); }
    ModInt operator+() const { return ModInt(*this); }
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    bool operator==(const ModInt &p) const { return x == p.x; }
    bool operator!=(const ModInt &p) const { return x != p.x; }
    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }
    ModInt pow(int64_t n) const {
        ModInt ret(1), mul(x);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
    friend istream &operator>>(istream &is, ModInt &a) {
        int64_t t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }
    int get() const { return x; }
    static constexpr int get_mod() { return mod; }
};

template <typename mint>
struct NTT {
    static constexpr uint32_t get_pr() {
        uint32_t _mod = mint::get_mod();
        using u64 = uint64_t;
        u64 ds[32] = {};
        int idx = 0;
        u64 m = _mod - 1;
        for (u64 i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                ds[idx++] = i;
                while (m % i == 0) m /= i;
            }
        }
        if (m != 1) ds[idx++] = m;
        uint32_t _pr = 2;
        while (1) {
            int flg = 1;
            for (int i = 0; i < idx; ++i) {
                u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
                while (b) {
                    if (b & 1) r = r * a % _mod;
                    a = a * a % _mod;
                    b >>= 1;
                }
                if (r == 1) {
                    flg = 0;
                    break;
                }
            }
            if (flg == 1) break;
            ++_pr;
        }
        return _pr;
    };
    static constexpr uint32_t mod = mint::get_mod();
    static constexpr uint32_t pr = get_pr();
    static constexpr int level = __builtin_ctzll(mod - 1);
    mint dw[level], dy[level];
    void setwy(int k) {
        mint w[level], y[level];
        w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
        y[k - 1] = w[k - 1].inverse();
        for (int i = k - 2; i > 0; --i)
            w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
        dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
        for (int i = 3; i < k; ++i) {
            dw[i] = dw[i - 1] * y[i - 2] * w[i];
            dy[i] = dy[i - 1] * w[i - 2] * y[i];
        }
    }
    NTT() { setwy(level); }
    void fft4(vector<mint> &a, int k) {
        if ((int)a.size() <= 1) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        if (k & 1) {
            int v = 1 << (k - 1);
            for (int j = 0; j < v; ++j) {
                mint ajv = a[j + v];
                a[j + v] = a[j] - ajv;
                a[j] += ajv;
            }
        }
        int u = 1 << (2 + (k & 1));
        int v = 1 << (k - 2 - (k & 1));
        mint one = mint(1);
        mint imag = dw[1];
        while (v) {
            {
                int j0 = 0;
                int j1 = v;
                int j2 = j1 + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
                }
            }
            mint ww = one, xx = one * dw[2], wx = one;
            for (int jh = 4; jh < u;) {
                ww = xx * xx, wx = ww * xx;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
                         t3 = a[j2 + v] * wx;
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
                }
                xx *= dw[__builtin_ctzll((jh += 4))];
            }
            u <<= 2;
            v >>= 2;
        }
    }
    void ifft4(vector<mint> &a, int k) {
        if ((int)a.size() <= 1) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        int u = 1 << (k - 2);
        int v = 1;
        mint one = mint(1);
        mint imag = dy[1];
        while (u) {
            {
                int j0 = 0;
                int j1 = v;
                int j2 = v + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
                    a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
                    a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
                }
            }
            mint ww = one, xx = one * dy[2], yy = one;
            u <<= 2;
            for (int jh = 4; jh < u;) {
                ww = xx * xx, yy = xx * imag;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
                    a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
                    a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
                }
                xx *= dy[__builtin_ctzll(jh += 4)];
            }
            u >>= 4;
            v <<= 2;
        }
        if (k & 1) {
            u = 1 << (k - 1);
            for (int j = 0; j < u; ++j) {
                mint ajv = a[j] - a[j + u];
                a[j] += a[j + u];
                a[j + u] = ajv;
            }
        }
    }
    void ntt(vector<mint> &a) {
        if ((int)a.size() <= 1) return;
        fft4(a, __builtin_ctz(a.size()));
    }
    void intt(vector<mint> &a) {
        if ((int)a.size() <= 1) return;
        ifft4(a, __builtin_ctz(a.size()));
        mint iv = mint(a.size()).inverse();
        for (auto &x : a) x *= iv;
    }
    vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
        int l = a.size() + b.size() - 1;
        if (min<int>(a.size(), b.size()) <= 40) {
            vector<mint> s(l);
            for (int i = 0; i < (int)a.size(); ++i)
                for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
            return s;
        }
        int k = 2, M = 4;
        while (M < l) M <<= 1, ++k;
        setwy(k);
        vector<mint> s(M);
        for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
        fft4(s, k);
        if (a.size() == b.size() && a == b) {
            for (int i = 0; i < M; ++i) s[i] *= s[i];
        } else {
            vector<mint> t(M);
            for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
            fft4(t, k);
            for (int i = 0; i < M; ++i) s[i] *= t[i];
        }
        ifft4(s, k);
        s.resize(l);
        mint invm = mint(M).inverse();
        for (int i = 0; i < l; ++i) s[i] *= invm;
        return s;
    }
    void ntt_doubling(vector<mint> &a) {
        int M = (int)a.size();
        auto b = a;
        intt(b);
        mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
        for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
        ntt(b);
        copy(begin(b), end(b), back_inserter(a));
    }
};

template <typename mint>
struct FormalPowerSeries : vector<mint> {
    using vector<mint>::vector;
    using FPS = FormalPowerSeries;
    FPS &operator+=(const FPS &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
        return *this;
    }
    FPS &operator+=(const mint &r) {
        if (this->empty()) this->resize(1);
        (*this)[0] += r;
        return *this;
    }
    FPS &operator-=(const FPS &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
        return *this;
    }
    FPS &operator-=(const mint &r) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= r;
        return *this;
    }
    FPS &operator*=(const mint &v) {
        for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
        return *this;
    }
    FPS &operator/=(const FPS &r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = this->size() - r.size() + 1;
        if ((int)r.size() <= 64) {
            FPS f(*this), g(r);
            g.shrink();
            mint coeff = g.back().inverse();
            for (auto &x : g) x *= coeff;
            int deg = (int)f.size() - (int)g.size() + 1;
            int gs = g.size();
            FPS quo(deg);
            for (int i = deg - 1; i >= 0; i--) {
                quo[i] = f[i + gs - 1];
                for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
            }
            *this = quo * coeff;
            this->resize(n, mint(0));
            return *this;
        }
        return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
    }
    FPS &operator%=(const FPS &r) {
        *this -= *this / r * r;
        shrink();
        return *this;
    }
    FPS operator+(const FPS &r) const { return FPS(*this) += r; }
    FPS operator+(const mint &v) const { return FPS(*this) += v; }
    FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
    FPS operator-(const mint &v) const { return FPS(*this) -= v; }
    FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
    FPS operator*(const mint &v) const { return FPS(*this) *= v; }
    FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
    FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
    FPS operator-() const {
        FPS ret(this->size());
        for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
        return ret;
    }
    void shrink() {
        while (this->size() && this->back() == mint(0)) this->pop_back();
    }
    FPS rev() const {
        FPS ret(*this);
        reverse(begin(ret), end(ret));
        return ret;
    }
    FPS dot(FPS r) const {
        FPS ret(min(this->size(), r.size()));
        for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
        return ret;
    }
    FPS pre(int sz) const {
        FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));
        if ((int)ret.size() < sz) ret.resize(sz);
        return ret;
    }
    FPS operator>>(int sz) const {
        if ((int)this->size() <= sz) return {};
        FPS ret(*this);
        ret.erase(ret.begin(), ret.begin() + sz);
        return ret;
    }
    FPS operator<<(int sz) const {
        FPS ret(*this);
        ret.insert(ret.begin(), sz, mint(0));
        return ret;
    }
    FPS diff() const {
        const int n = (int)this->size();
        FPS ret(max(0, n - 1));
        mint one(1), coeff(1);
        for (int i = 1; i < n; i++) {
            ret[i - 1] = (*this)[i] * coeff;
            coeff += one;
        }
        return ret;
    }
    FPS integral() const {
        const int n = (int)this->size();
        FPS ret(n + 1);
        ret[0] = mint(0);
        if (n > 0) ret[1] = mint(1);
        auto mod = mint::get_mod();
        for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
        for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
        return ret;
    }
    mint eval(mint x) const {
        mint r = 0, w = 1;
        for (auto &v : *this) r += w * v, w *= x;
        return r;
    }
    FPS log(int deg = -1) const {
        assert(!(*this).empty() && (*this)[0] == mint(1));
        if (deg == -1) deg = (int)this->size();
        return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
    }
    FPS pow(int64_t k, int deg = -1) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (k == 0) {
            FPS ret(deg);
            if (deg) ret[0] = 1;
            return ret;
        }
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != mint(0)) {
                mint rev = mint(1) / (*this)[i];
                FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
                ret *= (*this)[i].pow(k);
                ret = (ret << (i * k)).pre(deg);
                if ((int)ret.size() < deg) ret.resize(deg, mint(0));
                return ret;
            }
            if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
        }
        return FPS(deg, mint(0));
    }
    static void *ntt_ptr;
    static void set_fft();
    FPS &operator*=(const FPS &r);
    void ntt();
    void intt();
    void ntt_doubling();
    static int ntt_pr();
    FPS inv(int deg = -1) const;
    FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;
template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
    if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}
template <typename mint>
FormalPowerSeries<mint> &FormalPowerSeries<mint>::operator*=(
    const FormalPowerSeries<mint> &r) {
    if (this->empty() || r.empty()) {
        this->clear();
        return *this;
    }
    set_fft();
    auto ret = static_cast<NTT<mint> *>(ntt_ptr)->multiply(*this, r);
    return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <typename mint>
void FormalPowerSeries<mint>::ntt() {
    set_fft();
    static_cast<NTT<mint> *>(ntt_ptr)->ntt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::intt() {
    set_fft();
    static_cast<NTT<mint> *>(ntt_ptr)->intt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
    set_fft();
    static_cast<NTT<mint> *>(ntt_ptr)->ntt_doubling(*this);
}
template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
    set_fft();
    return static_cast<NTT<mint> *>(ntt_ptr)->pr;
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
    assert((*this)[0] != mint(0));
    if (deg == -1) deg = (int)this->size();
    FormalPowerSeries<mint> res(deg);
    res[0] = {mint(1) / (*this)[0]};
    for (int d = 1; d < deg; d <<= 1) {
        FormalPowerSeries<mint> f(2 * d), g(2 * d);
        for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];
        for (int j = 0; j < d; j++) g[j] = res[j];
        f.ntt();
        g.ntt();
        for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
        f.intt();
        for (int j = 0; j < d; j++) f[j] = 0;
        f.ntt();
        for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
        f.intt();
        for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
    }
    return res.pre(deg);
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
    using fps = FormalPowerSeries<mint>;
    assert((*this).size() == 0 || (*this)[0] == mint(0));
    if (deg == -1) deg = this->size();

    fps inv;
    inv.reserve(deg + 1);
    inv.push_back(mint(0));
    inv.push_back(mint(1));

    auto inplace_integral = [&](fps &F) -> void {
        const int n = (int)F.size();
        auto mod = mint::get_mod();
        while ((int)inv.size() <= n) {
            int i = inv.size();
            inv.push_back((-inv[mod % i]) * (mod / i));
        }
        F.insert(begin(F), mint(0));
        for (int i = 1; i <= n; i++) F[i] *= inv[i];
    };

    auto inplace_diff = [](fps &F) -> void {
        if (F.empty()) return;
        F.erase(begin(F));
        mint coeff = 1, one = 1;
        for (int i = 0; i < (int)F.size(); i++) {
            F[i] *= coeff;
            coeff += one;
        }
    };

    fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
    for (int m = 2; m < deg; m *= 2) {
        auto y = b;
        y.resize(2 * m);
        y.ntt();
        z1 = z2;
        fps z(m);
        for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
        z.intt();
        fill(begin(z), begin(z) + m / 2, mint(0));
        z.ntt();
        for (int i = 0; i < m; ++i) z[i] *= -z1[i];
        z.intt();
        c.insert(end(c), begin(z) + m / 2, end(z));
        z2 = c;
        z2.resize(2 * m);
        z2.ntt();
        fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
        x.resize(m);
        inplace_diff(x);
        x.push_back(mint(0));
        x.ntt();
        for (int i = 0; i < m; ++i) x[i] *= y[i];
        x.intt();
        x -= b.diff();
        x.resize(2 * m);
        for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);
        x.ntt();
        for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
        x.intt();
        x.pop_back();
        inplace_integral(x);
        for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];
        fill(begin(x), begin(x) + m, mint(0));
        x.ntt();
        for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];
        x.intt();
        b.insert(end(b), begin(x) + m, end(x));
    }
    return fps{begin(b), begin(b) + deg};
}
using mint = ModInt<998244353>;

using mint = ModInt<998244353>;

int main() {
    int N, K;
    cin >> N >> K;
    FormalPowerSeries<mint> F(N + 1);
    // sum_{i=1}^{N} log(1-x^{(K+1)*i}) = sum_{i=1}^{N} sum_{j=1}^{inf} x^{(K+1)*i*j}/j
    for (int i = 1; i <= N; i++) {
        for (ll j = 1; j * i * (K + 1) <= N; j++) {
            F[j * i * (K + 1)] -= mint(j).inverse();
        }
    }
    // sum_{i=1}^{N} log(1-x^i) = sum_{i=1}^{N} sum_{j=1}^{inf} x^{i*j}/j
    for (int i = 1; i <= N; i++) {
        for (ll j = 1; j * i <= N; j++) {
            F[j * i] += mint(j).inverse();
        }
    }
    F = F.exp();
    for (int i = 1; i <= N; i++) {
        cout << F[i] << ' ';
    }
    cout << endl;
}