多変数形式的冪級数ライブラリ
(fps/multivariate-fps.hpp)

View this file on GitHub
Last update: 2023-08-31 20:44:07+09:00
Include: #include "fps/multivariate-fps.hpp"

Depends on

Verified with

verify/verify-yuki/yuki-1783.test.cpp

Code

#pragma once

#include <algorithm>
#include <cassert>
#include <vector>
using namespace std;

#include "../modulo/binomial.hpp"
#include "../ntt/multivariate-multiplication.hpp"
#include "formal-power-series.hpp"

// FFT mod でないと使えない
// f.size() != (base の総積) でも動くが, 二項演算は長さが等しい列同士しかダメ
// 添え字アクセスは operator() を使う
template <typename mint>
struct MultivariateFormalPowerSeries {
  using mfps = MultivariateFormalPowerSeries<mint>;
  using fps = FormalPowerSeries<mint>;

  fps f;
  vector<int> base;

  MultivariateFormalPowerSeries() = default;
  MultivariateFormalPowerSeries(const vector<int>& _base) : base(_base) {
    int n = 1;
    for (auto& x : base) n *= x;
    f.resize(n);
  }
  MultivariateFormalPowerSeries(const fps& _f, const vector<int>& _base)
      : f(_f), base(_base) {}

  friend ostream& operator<<(ostream& os, const mfps& rhs) {
    os << "[ ";
    for (int i = 0; i < (int)rhs.f.size(); i++) {
      os << rhs.f[i] << (i + 1 == (int)rhs.f.size() ? "" : ", ");
    }
    return os << " ]";
  }

  long long _id(int) { return 0; }
  template <typename Head, typename... Tail>
  long long _id(int i, Head&& head, Tail&&... tail) {
    assert(i < (int)base.size() && (int)head < base[i]);
    return head + _id(i + 1, forward<Tail>(tail)...) * base[i];
  }
  template <typename... Args>
  long long id(Args&&... args) {
    return _id(0, forward<Args>(args)...);
  }
  template <typename... Args>
  mint& operator()(Args&&... args) {
    return f[id(forward<Args>(args)...)];
  }

  mfps& operator+=(const mfps& rhs) {
    assert(base == rhs.base && f.size() == rhs.f.size());
    for (int i = 0; i < (int)f.size(); i++) f[i] += rhs.f[i];
    return *this;
  }
  mfps& operator-=(const mfps& rhs) {
    assert(base == rhs.base && f.size() == rhs.f.size());
    for (int i = 0; i < (int)f.size(); i++) f[i] -= rhs.f[i];
    return *this;
  }
  mfps& operator*=(const mfps& rhs) {
    assert(base == rhs.base && f.size() == rhs.f.size());
    f = multivariate_multiplication(f, rhs.f, base);
    return *this;
  }
  mfps& operator/=(const mfps& rhs) {
    assert(base == rhs.base);
    assert(f.size() == rhs.f.size());
    return (*this) *= rhs.inv();
  }

  mfps& operator+=(const mint& rhs) {
    assert(!f.empty());
    f[0] += rhs;
    return *this;
  }
  mfps& operator-=(const mint& rhs) {
    assert(!f.empty());
    f[0] -= rhs;
    return *this;
  }
  mfps& operator*=(const mint& rhs) {
    for (auto& x : f) x *= rhs;
    return *this;
  }
  mfps& operator/=(const mint& rhs) {
    for (auto& x : f) x /= rhs;
    return *this;
  }

  mfps operator+(const mfps& rhs) const { return mfps{*this} += rhs; }
  mfps operator-(const mfps& rhs) const { return mfps{*this} -= rhs; }
  mfps operator*(const mfps& rhs) const { return mfps{*this} *= rhs; }
  mfps operator/(const mfps& rhs) const { return mfps{*this} /= rhs; }

  mfps operator+(const mint& rhs) const { return mfps{*this} += rhs; }
  mfps operator-(const mint& rhs) const { return mfps{*this} -= rhs; }
  mfps operator*(const mint& rhs) const { return mfps{*this} *= rhs; }
  mfps operator/(const mint& rhs) const { return mfps{*this} /= rhs; }

  mfps operator+() const { return mfps{*this}; }
  mfps operator-() const { return mfps{-f, base}; }

  friend bool operator==(const mfps& lhs, const mfps& rhs) {
    return lhs.f == rhs.f && lhs.base == rhs.base;
  }
  friend bool operator!=(const mfps& lhs, const mfps& rhs) {
    return lhs.f != rhs.f || lhs.base != rhs.base;
  }

  mfps diff() const {
    mfps g{*this};
    for (int i = 0; i < (int)g.f.size(); i++) g.f[i] *= i;
    return g;
  }
  mfps integral() const {
    static Binomial<mint> binom;
    mfps g{*this};
    for (int i = 1; i < (int)g.f.size(); i++) g.f[i] *= binom.inv(i);
    return g;
  }

  mfps inv() const {
    assert(f[0] != 0);
    if (base.empty()) return mfps{fps{f[0].inverse()}, base};
    int n = f.size(), s = base.size(), W = 1;
    while (W < 2 * n) W *= 2;

    vector<int> chi(W);
    for (int i = 0; i < W; i++) {
      int x = i;
      for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]);
      chi[i] %= s;
    }
    auto hadamard_prod = [&s](vector<fps>& F, vector<fps>& G, vector<fps>& H) {
      fps a(s);
      for (int k = 0; k < (int)F[0].size(); k++) {
        fill(begin(a), end(a), typename fps::value_type());
        for (int i = 0; i < s; i++)
          for (int j = 0; j < s; j++) {
            a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k];
          }
        for (int i = 0; i < s; i++) H[i][k] = a[i];
      }
    };
    fps g(W);
    g[0] = f[0].inverse();
    for (int d = 1; d < n; d *= 2) {
      vector<fps> F(s, fps(2 * d)), G(s, fps(2 * d)), H(s, fps(2 * d));
      for (int j = 0; j < min((int)f.size(), 2 * d); j++) F[chi[j]][j] = f[j];
      for (int j = 0; j < d; j++) G[chi[j]][j] = g[j];
      for (auto& x : F) x.ntt();
      for (auto& x : G) x.ntt();
      hadamard_prod(F, G, H);
      for (auto& x : H) x.intt();
      for (auto& x : F) fill(begin(x), end(x), typename fps::value_type());
      for (int j = d; j < 2 * d; j++) F[chi[j]][j] = H[chi[j]][j];
      for (auto& x : F) x.ntt();
      hadamard_prod(F, G, H);
      for (auto& x : H) x.intt();
      for (int j = d; j < 2 * d; j++) g[j] = -H[chi[j]][j];
    }
    mfps res{*this};
    res.f = fps{begin(g), begin(g) + n};
    return res;
  }
  mfps log() const {
    assert(!f.empty() && f[0] == 1);
    return ((*this).diff() / *this).integral();
  }
  mfps exp() const {
    assert(!f.empty() && f[0] == mint{0});
    int n = f.size();
    mfps g{fps{1}, base};
    for (int d = 1; d < n; d *= 2) {
      int s = min(n, d * 2);
      g.f.resize(s, mint{0});
      g *= mfps{fps{begin(f), begin(f) + s}, base} - g.log() + 1;
    }
    return g;
  }
  mfps pow(long long e) const {
    assert(!f.empty());
    if (f[0] != 0) {
      mint f0inv = f[0].inverse(), coe = f[0].pow(e);
      return (((*this) * f0inv).log() * e).exp() * coe;
    }
    int n = f.size();
    long long base_sum = 0;
    for (auto& b : base) base_sum += b - 1;
    if (e > base_sum) return mfps{fps(n), base};
    mfps res{fps(n), base}, a{*this};
    res.f[0] = 1;
    for (; e; a *= a, e >>= 1) {
      if (e & 1) res *= a;
    }
    return res;
  }
};

/**
 * @brief 多変数形式的冪級数ライブラリ
 */

#line 2 "fps/multivariate-fps.hpp"

#include <algorithm>
#include <cassert>
#include <vector>
using namespace std;

#line 2 "modulo/binomial.hpp"

#line 4 "modulo/binomial.hpp"
#include <type_traits>
#line 6 "modulo/binomial.hpp"
using namespace std;

// コンストラクタの MAX に 「C(n, r) や fac(n) でクエリを投げる最大の n 」
// を入れると倍速くらいになる
// mod を超えて前計算して 0 割りを踏むバグは対策済み
template <typename T>
struct Binomial {
  vector<T> f, g, h;
  Binomial(int MAX = 0) {
    assert(T::get_mod() != 0 && "Binomial<mint>()");
    f.resize(1, T{1});
    g.resize(1, T{1});
    h.resize(1, T{1});
    if (MAX > 0) extend(MAX + 1);
  }

  void extend(int m = -1) {
    int n = f.size();
    if (m == -1) m = n * 2;
    m = min<int>(m, T::get_mod());
    if (n >= m) return;
    f.resize(m);
    g.resize(m);
    h.resize(m);
    for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
    g[m - 1] = f[m - 1].inverse();
    h[m - 1] = g[m - 1] * f[m - 2];
    for (int i = m - 2; i >= n; i--) {
      g[i] = g[i + 1] * T(i + 1);
      h[i] = g[i] * f[i - 1];
    }
  }

  T fac(int i) {
    if (i < 0) return T(0);
    while (i >= (int)f.size()) extend();
    return f[i];
  }

  T finv(int i) {
    if (i < 0) return T(0);
    while (i >= (int)g.size()) extend();
    return g[i];
  }

  T inv(int i) {
    if (i < 0) return -inv(-i);
    while (i >= (int)h.size()) extend();
    return h[i];
  }

  T C(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r) * finv(r);
  }

  inline T operator()(int n, int r) { return C(n, r); }

  template <typename I>
  T multinomial(const vector<I>& r) {
    static_assert(is_integral<I>::value == true);
    int n = 0;
    for (auto& x : r) {
      if (x < 0) return T(0);
      n += x;
    }
    T res = fac(n);
    for (auto& x : r) res *= finv(x);
    return res;
  }

  template <typename I>
  T operator()(const vector<I>& r) {
    return multinomial(r);
  }

  T C_naive(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    T ret = T(1);
    r = min(r, n - r);
    for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
    return ret;
  }

  T P(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r);
  }

  // [x^r] 1 / (1-x)^n
  T H(int n, int r) {
    if (n < 0 || r < 0) return T(0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
#line 2 "ntt/multivariate-multiplication.hpp"

// 長さが等しい列同士の畳み込みしかしない
template <typename fps>
fps multivariate_multiplication(const fps& f, const fps& g,
                                const vector<int>& base) {
  assert(f.size() == g.size());
  int n = f.size(), s = base.size(), W = 1;
  if (s == 0) return fps{f[0] * g[0]};
  while (W < 2 * n) W *= 2;

  vector<int> chi(n);
  for (int i = 0; i < n; i++) {
    int x = i;
    for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]);
    chi[i] %= s;
  }

  vector<fps> F(s, fps(W)), G(s, fps(W));
  for (int i = 0; i < n; i++) F[chi[i]][i] = f[i], G[chi[i]][i] = g[i];

  for (auto& x : F) x.ntt();
  for (auto& x : G) x.ntt();
  fps a(s);
  for (int k = 0; k < W; k++) {
    fill(begin(a), end(a), typename fps::value_type());
    for (int i = 0; i < s; i++)
      for (int j = 0; j < s; j++) {
        a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k];
      }
    for (int i = 0; i < s; i++) F[i][k] = a[i];
  }
  for (auto& x : F) x.intt();
  fps h(n);
  for (int i = 0; i < n; i++) h[i] = F[chi[i]][i];
  return h;
}

/**
 * @brief Multivariate Multiplication
 * @docs docs/ntt/multivariate-multiplication.md
 */
#line 2 "fps/formal-power-series.hpp"

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;
  }

  // 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
  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;

/**
 * @brief 多項式/形式的冪級数ライブラリ
 * @docs docs/fps/formal-power-series.md
 */
#line 11 "fps/multivariate-fps.hpp"

// FFT mod でないと使えない
// f.size() != (base の総積) でも動くが, 二項演算は長さが等しい列同士しかダメ
// 添え字アクセスは operator() を使う
template <typename mint>
struct MultivariateFormalPowerSeries {
  using mfps = MultivariateFormalPowerSeries<mint>;
  using fps = FormalPowerSeries<mint>;

  fps f;
  vector<int> base;

  MultivariateFormalPowerSeries() = default;
  MultivariateFormalPowerSeries(const vector<int>& _base) : base(_base) {
    int n = 1;
    for (auto& x : base) n *= x;
    f.resize(n);
  }
  MultivariateFormalPowerSeries(const fps& _f, const vector<int>& _base)
      : f(_f), base(_base) {}

  friend ostream& operator<<(ostream& os, const mfps& rhs) {
    os << "[ ";
    for (int i = 0; i < (int)rhs.f.size(); i++) {
      os << rhs.f[i] << (i + 1 == (int)rhs.f.size() ? "" : ", ");
    }
    return os << " ]";
  }

  long long _id(int) { return 0; }
  template <typename Head, typename... Tail>
  long long _id(int i, Head&& head, Tail&&... tail) {
    assert(i < (int)base.size() && (int)head < base[i]);
    return head + _id(i + 1, forward<Tail>(tail)...) * base[i];
  }
  template <typename... Args>
  long long id(Args&&... args) {
    return _id(0, forward<Args>(args)...);
  }
  template <typename... Args>
  mint& operator()(Args&&... args) {
    return f[id(forward<Args>(args)...)];
  }

  mfps& operator+=(const mfps& rhs) {
    assert(base == rhs.base && f.size() == rhs.f.size());
    for (int i = 0; i < (int)f.size(); i++) f[i] += rhs.f[i];
    return *this;
  }
  mfps& operator-=(const mfps& rhs) {
    assert(base == rhs.base && f.size() == rhs.f.size());
    for (int i = 0; i < (int)f.size(); i++) f[i] -= rhs.f[i];
    return *this;
  }
  mfps& operator*=(const mfps& rhs) {
    assert(base == rhs.base && f.size() == rhs.f.size());
    f = multivariate_multiplication(f, rhs.f, base);
    return *this;
  }
  mfps& operator/=(const mfps& rhs) {
    assert(base == rhs.base);
    assert(f.size() == rhs.f.size());
    return (*this) *= rhs.inv();
  }

  mfps& operator+=(const mint& rhs) {
    assert(!f.empty());
    f[0] += rhs;
    return *this;
  }
  mfps& operator-=(const mint& rhs) {
    assert(!f.empty());
    f[0] -= rhs;
    return *this;
  }
  mfps& operator*=(const mint& rhs) {
    for (auto& x : f) x *= rhs;
    return *this;
  }
  mfps& operator/=(const mint& rhs) {
    for (auto& x : f) x /= rhs;
    return *this;
  }

  mfps operator+(const mfps& rhs) const { return mfps{*this} += rhs; }
  mfps operator-(const mfps& rhs) const { return mfps{*this} -= rhs; }
  mfps operator*(const mfps& rhs) const { return mfps{*this} *= rhs; }
  mfps operator/(const mfps& rhs) const { return mfps{*this} /= rhs; }

  mfps operator+(const mint& rhs) const { return mfps{*this} += rhs; }
  mfps operator-(const mint& rhs) const { return mfps{*this} -= rhs; }
  mfps operator*(const mint& rhs) const { return mfps{*this} *= rhs; }
  mfps operator/(const mint& rhs) const { return mfps{*this} /= rhs; }

  mfps operator+() const { return mfps{*this}; }
  mfps operator-() const { return mfps{-f, base}; }

  friend bool operator==(const mfps& lhs, const mfps& rhs) {
    return lhs.f == rhs.f && lhs.base == rhs.base;
  }
  friend bool operator!=(const mfps& lhs, const mfps& rhs) {
    return lhs.f != rhs.f || lhs.base != rhs.base;
  }

  mfps diff() const {
    mfps g{*this};
    for (int i = 0; i < (int)g.f.size(); i++) g.f[i] *= i;
    return g;
  }
  mfps integral() const {
    static Binomial<mint> binom;
    mfps g{*this};
    for (int i = 1; i < (int)g.f.size(); i++) g.f[i] *= binom.inv(i);
    return g;
  }

  mfps inv() const {
    assert(f[0] != 0);
    if (base.empty()) return mfps{fps{f[0].inverse()}, base};
    int n = f.size(), s = base.size(), W = 1;
    while (W < 2 * n) W *= 2;

    vector<int> chi(W);
    for (int i = 0; i < W; i++) {
      int x = i;
      for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]);
      chi[i] %= s;
    }
    auto hadamard_prod = [&s](vector<fps>& F, vector<fps>& G, vector<fps>& H) {
      fps a(s);
      for (int k = 0; k < (int)F[0].size(); k++) {
        fill(begin(a), end(a), typename fps::value_type());
        for (int i = 0; i < s; i++)
          for (int j = 0; j < s; j++) {
            a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k];
          }
        for (int i = 0; i < s; i++) H[i][k] = a[i];
      }
    };
    fps g(W);
    g[0] = f[0].inverse();
    for (int d = 1; d < n; d *= 2) {
      vector<fps> F(s, fps(2 * d)), G(s, fps(2 * d)), H(s, fps(2 * d));
      for (int j = 0; j < min((int)f.size(), 2 * d); j++) F[chi[j]][j] = f[j];
      for (int j = 0; j < d; j++) G[chi[j]][j] = g[j];
      for (auto& x : F) x.ntt();
      for (auto& x : G) x.ntt();
      hadamard_prod(F, G, H);
      for (auto& x : H) x.intt();
      for (auto& x : F) fill(begin(x), end(x), typename fps::value_type());
      for (int j = d; j < 2 * d; j++) F[chi[j]][j] = H[chi[j]][j];
      for (auto& x : F) x.ntt();
      hadamard_prod(F, G, H);
      for (auto& x : H) x.intt();
      for (int j = d; j < 2 * d; j++) g[j] = -H[chi[j]][j];
    }
    mfps res{*this};
    res.f = fps{begin(g), begin(g) + n};
    return res;
  }
  mfps log() const {
    assert(!f.empty() && f[0] == 1);
    return ((*this).diff() / *this).integral();
  }
  mfps exp() const {
    assert(!f.empty() && f[0] == mint{0});
    int n = f.size();
    mfps g{fps{1}, base};
    for (int d = 1; d < n; d *= 2) {
      int s = min(n, d * 2);
      g.f.resize(s, mint{0});
      g *= mfps{fps{begin(f), begin(f) + s}, base} - g.log() + 1;
    }
    return g;
  }
  mfps pow(long long e) const {
    assert(!f.empty());
    if (f[0] != 0) {
      mint f0inv = f[0].inverse(), coe = f[0].pow(e);
      return (((*this) * f0inv).log() * e).exp() * coe;
    }
    int n = f.size();
    long long base_sum = 0;
    for (auto& b : base) base_sum += b - 1;
    if (e > base_sum) return mfps{fps(n), base};
    mfps res{fps(n), base}, a{*this};
    res.f[0] = 1;
    for (; e; a *= a, e >>= 1) {
      if (e & 1) res *= a;
    }
    return res;
  }
};

/**
 * @brief 多変数形式的冪級数ライブラリ
 */

Nyaan's Library

This documentation is automatically generated by online-judge-tools/verification-helper

多変数形式的冪級数ライブラリ
(fps/multivariate-fps.hpp)

Depends on

Verified with

Code

多変数形式的冪級数ライブラリ (fps/multivariate-fps.hpp)

Depends on

Verified with

Code

多変数形式的冪級数ライブラリ
(fps/multivariate-fps.hpp)