verify/set/LC_polynomial_composite_set_power_series.test.cpp

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• Last update: 2025-10-29 02:30:28+09:00
• Problem: https://judge.yosupo.jp/problem/polynomial_composite_set_power_series

Depends on

• modint/modint.hpp
• Polynomial Composite Set Power Series (set/composite-set-power-series.hpp)
• Subset Convolution (set/subset-convolution.hpp)
• template/debug.hpp
• template/inout.hpp
• template/macro.hpp
• template/template.hpp
• template/util.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/polynomial_composite_set_power_series"

#include "template/template.hpp"
#include "modint/modint.hpp"
using mint = ModInt<998244353>;
#include "set/composite-set-power-series.hpp"

int main() {
  int m, n;
  in(m, n);
  vector<mint> a(m), b(1 << n);
  in(a, b);
  auto c = SetPowerSeries::composite_polynomial(a, b);
  out(c);
}

#line 1 "verify/set/LC_polynomial_composite_set_power_series.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/polynomial_composite_set_power_series"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <class T, class S = T>
S SUM(const vector<T> &a) {
  return accumulate(ALL(a), S(0));
}
template <class T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

template <class T1, class T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream &operator>>(istream &is, vector<T> &a) {
  for (auto &v : a) is >> v;
  return is;
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream &operator<<(ostream &os, const set<T> &st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream &operator<<(ostream &os, const map<T1, T2> &mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int i, T name) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "modint/modint.hpp"

template <unsigned int m = 998244353>
struct ModInt {
  using mint = ModInt;
  unsigned int _v;
  static constexpr unsigned int get_mod() { return m; }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }
  ModInt() : _v(0) {}
  ModInt(int64_t v) {
    long long x = (long long)(v % (long long)(umod()));
    if (x < 0) x += umod();
    _v = (unsigned int)(x);
  }
  unsigned int val() const { return _v; }
  mint &operator++() {
    _v++;
    if (_v == umod()) _v = 0;
    return *this;
  }
  mint &operator--() {
    if (_v == 0) _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint &operator+=(const mint &rhs) {
    _v += rhs._v;
    if (_v >= umod()) _v -= umod();
    return *this;
  }
  mint &operator-=(const mint &rhs) {
    _v -= rhs._v;
    if (_v >= umod()) _v += umod();
    return *this;
  }
  mint &operator*=(const mint &rhs) {
    unsigned long long z = _v;
    z *= rhs._v;
    _v = (unsigned int)(z % umod());
    return *this;
  }
  mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1) r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    assert(_v);
    return pow(umod() - 2);
  }

  friend mint operator+(const mint &lhs, const mint &rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint &lhs, const mint &rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint &lhs, const mint &rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint &lhs, const mint &rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint &lhs, const mint &rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint &lhs, const mint &rhs) {
    return lhs._v != rhs._v;
  }
  friend istream &operator>>(istream &is, mint &x) {
    return is >> x._v;
  }
  friend ostream &operator<<(ostream &os, const mint &x) {
    return os << x.val();
  }

 private:
  static constexpr unsigned int umod() { return m; }
};
#line 5 "verify/set/LC_polynomial_composite_set_power_series.test.cpp"
using mint = ModInt<998244353>;
#line 2 "set/subset-convolution.hpp"

template <class mint, int n_>
struct SubsetConvolution {
  static constexpr int n = n_;
  using poly = array<mint, n_ + 1>;
  vector<int> pc;
  SubsetConvolution() {
    pc.assign(1 << n, 0);
    for (int i = 1; i < pc.size(); i++) pc[i] = pc[i >> 1] + (i & 1);
  }
  void poly_add(poly& p, const poly& q, int d) {
    for (int i = 0; i < d; i++) p[i] += q[i];
  }
  void poly_sub(poly& p, const poly& q, int d) {
    for (int i = d; i <= n; i++) p[i] -= q[i];
  }
  void poly_mul(poly& p, const poly& q) {
    poly r{};
    for (int i = 0; i <= n; i++)
      for (int j = 0; j <= n - i; j++)
        r[i + j] += p[i] * q[j];
    swap(p, r);
  }
  vector<poly> lift(const vector<mint>& a) {
    int n = a.size();
    assert(n == (n & -n));
    vector<poly> b(n);
    for (int i = 0; i < n; i++) {
      b[i].fill(0);
      b[i][pc[i]] = a[i];
    }
    return b;
  }
  vector<mint> unlift(const vector<poly>& b) {
    int n = b.size();
    assert(n == (n & -n));
    vector<mint> a(n);
    for (int i = 0; i < n; i++) a[i] = b[i][pc[i]];
    return a;
  }
  void ranked_zeta(vector<poly>& a) {
    int n = a.size();
    for (int i = 1; i < n; i <<= 1)
      for (int j = 0; j < n; j += i * 2)
        for (int k = 0; k < i; k++)
          poly_add(a[i + j + k], a[j + k], pc[i + j + k]);
  }
  void ranked_mobius(vector<poly>& a) {
    int n = a.size();
    for (int i = 1; i < n; i <<= 1)
      for (int j = 0; j < n; j += i * 2)
        for (int k = 0; k < i; k++)
          poly_sub(a[i + j + k], a[j + k], pc[i + j + k]);
  }
  void ranked_mul(vector<poly>& a, const vector<poly>& b) {
    for (int i = 0; i < a.size(); i++) poly_mul(a[i], b[i]);
  }
  vector<mint> multiply(const vector<mint>& a, const vector<mint>& b) {
    auto p = lift(a);
    auto q = lift(b);
    ranked_zeta(p);
    ranked_zeta(q);
    ranked_mul(p, q);
    ranked_mobius(p);
    return unlift(p);
  }
};

/**
 * @brief Subset Convolution
 * @docs docs/set/subset-convolution.md
 */
#line 3 "set/composite-set-power-series.hpp"

namespace SetPowerSeries {
template <class mint, int sz = 21>
vector<mint> composite_egf(vector<mint> f, vector<mint> a) {
  static SubsetConvolution<mint, sz> sc;
  assert(a[0] == 0);
  if (f.empty()) return vector<mint>(a.size());
  int l = __builtin_ctz(a.size());
  f.resize(l + 1);
  vector<vector<mint>> g(l + 1);
  for (int i = 0; i <= l; i++) g[i] = vector<mint>(1 << (l - i), 0);
  for (int i = 0; i <= l; i++) g[i][0] = f[i];
  for (int k = 0; k < l; k++) {
    auto p = sc.lift(vector<mint>(a.begin() + (1 << k), a.begin() + (2 << k)));
    sc.ranked_zeta(p);
    for (int i = 0; i < l - k; i++) {
      auto q = sc.lift(vector<mint>(g[i + 1].begin(), g[i + 1].begin() + (1 << k)));
      sc.ranked_zeta(q);
      sc.ranked_mul(q, p);
      sc.ranked_mobius(q);
      auto h = sc.unlift(q);
      copy(h.begin(), h.end(), g[i].begin() + (1 << k));
    }
  }
  return g[0];
}
template <class mint, int sz = 21>
vector<mint> composite_polynomial(vector<mint> p, vector<mint> a) {
  if (p.empty()) return vector<mint>(a.size());
  int l = __builtin_ctz(a.size());
  if (a[0] != 0) {
    mint c = a[0];
    a[0] = 0;
    vector<mint> p1(l + 1, 0), binom(l + 1, 0);
    binom[0] = 1;
    for (int i = 0; i < p.size(); i++) {
      mint r = i <= l ? 1 : c.pow(i - l);
      for (int j = min(i, l); j >= 0; j--, r *= c) p1[j] += p[i] * binom[j] * r;
      for (int j = l; j > 0; j--) binom[j] += binom[j - 1];
    }
    swap(p, p1);
  }
  mint r = 1;
  for (int i = 1; i <= l; i++) p[i] *= (r *= i);
  return composite_egf<mint, sz>(p, a);
}

// log(a), [x^0]a=1
// require inverse of 1,...,sz
template <class mint, int sz = 21>
vector<mint> log(vector<mint> a) {
  static SubsetConvolution<mint, sz> sc;
  assert(a[0] == 1);
  int l = __builtin_ctz(a.size());
  if (l == 0) return {0};
  vector<mint> inv(l + 1, 1);
  rep(i, 1, l + 1) inv[i] = mint(i).inv();
  auto p = sc.lift(a);
  sc.ranked_zeta(p);
  for (int k = 0; k < p.size(); k++) {
    auto q = p[k];
    p[k][0] = 0;
    for (int i = 1; i <= l; i++) {
      mint v = i * q[i];
      for (int j = 1; j < i; j++) v -= j * p[k][j] * q[i - j];
      p[k][i] = v * inv[i];
    }
  }
  sc.ranked_mobius(p);
  return sc.unlift(p);
}
// log(a), [x^0]a=1
// not require inverse of 1,...,sz
template <class mint, int sz = 21>
vector<mint> log_arbitrary(vector<mint> a) {
  assert(a[0] == 1);
  int l = __builtin_ctz(a.size());
  if (l == 0) return {0};
  a[0] = 0;
  vector<mint> f(l + 1, 0);
  f[1] = 1;
  for (int i = 2; i <= l; i++) f[i] = f[i - 1] * (1 - i);
  return composite_egf<mint, sz>(f, a);
}
// a^m, [x^0]a=1
// require inverse of 1,...,sz
template <class mint, int sz = 21>
vector<mint> pow(vector<mint> a, mint m) {
  static SubsetConvolution<mint, sz> sc;
  assert(a[0] == 1);
  int l = __builtin_ctz(a.size());
  if (l == 0) return {1};
  vector<mint> inv(l + 1, 1);
  rep(i, 1, l + 1) inv[i] = mint(i).inv();
  auto p = sc.lift(a);
  sc.ranked_zeta(p);
  for (int k = 0; k < p.size(); k++) {
    auto q = p[k];
    p[k][0] = 1;
    for (int i = 1; i <= l; i++) {
      mint v = 0;
      for (int j = 1; j < i; j++) v += (m * j - (i - j)) * p[k][i - j] * q[j];
      v *= inv[i];
      v += m * p[k][0] * q[i];
      p[k][i] = v;
    }
  }
  sc.ranked_mobius(p);
  return sc.unlift(p);
}
// a^m, [x^0]a=1
// not require inverse of 1,...,sz
template <class mint, int sz = 21>
vector<mint> pow_arbitrary(vector<mint> a, mint m) {
  assert(a[0] == 1);
  int l = __builtin_ctz(a.size());
  if (l == 0) return {1};
  a[0] = 0;
  vector<mint> f(l + 1, 0);
  f[0] = 1;
  for (int i = 1; i <= l; i++) {
    f[i] = f[i - 1] * m;
    m -= 1;
  }
  return composite_egf<mint, sz>(f, a);
}
};  // namespace SetPowerSeries
/**
 * @brief Polynomial Composite Set Power Series
 * @docs docs/set/composite-set-power-series.md
 */
#line 7 "verify/set/LC_polynomial_composite_set_power_series.test.cpp"

int main() {
  int m, n;
  in(m, n);
  vector<mint> a(m), b(1 << n);
  in(a, b);
  auto c = SetPowerSeries::composite_polynomial(a, b);
  out(c);
}

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