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#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_and_convolution" #include "../../modint.hpp" #include "../multidim_index.hpp" #include <iostream> #include <vector> using namespace std; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int N; cin >> N; multidim_index mi(std::vector<int>(N, 2)); vector<ModInt<998244353>> A(1 << N), B(1 << N); for (auto &x : A) cin >> x; for (auto &x : B) cin >> x; mi.superset_sum(A); mi.superset_sum(B); for (int i = 0; i < 1 << N; ++i) A.at(i) *= B.at(i); mi.superset_sum_inv(A); for (auto x : A) cout << x << ' '; }
#line 1 "utilities/test/multidim_index.zeta.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/bitwise_and_convolution" #line 2 "modint.hpp" #include <cassert> #include <iostream> #include <set> #include <vector> template <int md> struct ModInt { using lint = long long; constexpr static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set<int> fac; int v = md - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val_; int val() const noexcept { return val_; } constexpr ModInt() : val_(0) {} constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; } constexpr ModInt(lint v) { _setval(v % md + md); } constexpr explicit operator bool() const { return val_ != 0; } constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val_ + x.val_); } constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val_ - x.val_ + md); } constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.val_ % md); } constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.inv().val() % md); } constexpr ModInt operator-() const { return ModInt()._setval(md - val_); } constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; } constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; } constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; } constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; } friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; } friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; } friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; } constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; } constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; } constexpr bool operator<(const ModInt &x) const { return val_ < x.val_; } // To use std::map<ModInt, T> friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val_; } constexpr ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static constexpr int cache_limit = std::min(md, 1 << 21); static std::vector<ModInt> facs, facinvs, invs; constexpr static void _precalculation(int N) { const int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } constexpr ModInt inv() const { if (this->val_ < cache_limit) { if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0}; while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val_]; } else { return this->pow(md - 2); } } constexpr ModInt fac() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val_]; } constexpr ModInt facinv() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val_]; } constexpr ModInt doublefac() const { lint k = (this->val_ + 1) / 2; return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } constexpr ModInt nCr(int r) const { if (r < 0 or this->val_ < r) return ModInt(0); return this->fac() * (*this - r).facinv() * ModInt(r).facinv(); } constexpr ModInt nPr(int r) const { if (r < 0 or this->val_ < r) return ModInt(0); return this->fac() * (*this - r).facinv(); } static ModInt binom(int n, int r) { static long long bruteforce_times = 0; if (r < 0 or n < r) return ModInt(0); if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r); r = std::min(r, n - r); ModInt ret = ModInt(r).facinv(); for (int i = 0; i < r; ++i) ret *= n - i; bruteforce_times += r; return ret; } // Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!) // Complexity: O(sum(ks)) template <class Vec> static ModInt multinomial(const Vec &ks) { ModInt ret{1}; int sum = 0; for (int k : ks) { assert(k >= 0); ret *= ModInt(k).facinv(), sum += k; } return ret * ModInt(sum).fac(); } // Catalan number, C_n = binom(2n, n) / (n + 1) // C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ... // https://oeis.org/A000108 // Complexity: O(n) static ModInt catalan(int n) { if (n < 0) return ModInt(0); return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv(); } ModInt sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val_, md - x.val_)); } }; template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1}; template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1}; template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0}; using ModInt998244353 = ModInt<998244353>; // using mint = ModInt<998244353>; // using mint = ModInt<1000000007>; #line 3 "utilities/multidim_index.hpp" // n-dimentional index <-> 1-dimentional index converter // [a_0, ..., a_{dim - 1}] <-> a_0 + a_1 * size_0 + ... + a_{dim - 1} * (size_0 * ... * size_{dim - 2}) template <class T = int> struct multidim_index { int dim = 0; T _size = 1; std::vector<T> sizes; std::vector<T> weights; multidim_index() = default; explicit multidim_index(const std::vector<T> &sizes) : dim(sizes.size()), sizes(sizes), weights(dim, T(1)) { for (int d = 0; d < (int)sizes.size(); ++d) { assert(sizes.at(d) > 0); _size *= sizes.at(d); if (d >= 1) weights.at(d) = weights.at(d - 1) * sizes.at(d - 1); } } T size() const { return _size; } T flat_index(const std::vector<T> &encoded_vec) const { assert((int)encoded_vec.size() == (int)sizes.size()); T ret = 0; for (int d = 0; d < (int)sizes.size(); ++d) { assert(0 <= encoded_vec.at(d) and encoded_vec.at(d) < sizes.at(d)); ret += encoded_vec.at(d) * weights.at(d); } return ret; } std::vector<T> encode(T flat_index) const { assert(0 <= flat_index and flat_index < size()); std::vector<T> ret(sizes.size()); for (int d = (int)sizes.size() - 1; d >= 0; --d) { ret.at(d) = flat_index / weights.at(d); flat_index %= weights.at(d); } return ret; } template <class F> void lo_to_hi(F f) { for (int d = 0; d < (int)sizes.size(); ++d) { if (sizes.at(d) == 1) continue; T i = 0; std::vector<T> ivec(sizes.size()); int cur = sizes.size(); while (true) { f(i, i + weights.at(d)); --cur; while (cur >= 0 and ivec.at(cur) + 1 == sizes.at(cur) - (cur == d)) { i -= ivec.at(cur) * weights.at(cur); ivec.at(cur--) = 0; } if (cur < 0) break; ++ivec.at(cur); i += weights.at(cur); cur = sizes.size(); } } } // Subset sum (fast zeta transform) template <class U> void subset_sum(std::vector<U> &vec) { assert((T)vec.size() == size()); lo_to_hi([&](T lo, T hi) { vec.at(hi) += vec.at(lo); }); } // Inverse of subset sum (fast moebius transform) template <class U> void subset_sum_inv(std::vector<U> &vec) { assert((T)vec.size() == size()); const T s = size() - 1; lo_to_hi([&](T dummylo, T dummyhi) { vec.at(s - dummylo) -= vec.at(s - dummyhi); }); } // Superset sum (fast zeta transform) template <class U> void superset_sum(std::vector<U> &vec) { assert((T)vec.size() == size()); const T s = size() - 1; lo_to_hi([&](T dummylo, T dummyhi) { vec.at(s - dummyhi) += vec.at(s - dummylo); }); } // Inverse of superset sum (fast moebius transform) template <class U> void superset_sum_inv(std::vector<U> &vec) { assert((T)vec.size() == size()); lo_to_hi([&](T lo, T hi) { vec.at(lo) -= vec.at(hi); }); } }; #line 4 "utilities/test/multidim_index.zeta.test.cpp" #line 7 "utilities/test/multidim_index.zeta.test.cpp" using namespace std; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int N; cin >> N; multidim_index mi(std::vector<int>(N, 2)); vector<ModInt<998244353>> A(1 << N), B(1 << N); for (auto &x : A) cin >> x; for (auto &x : B) cin >> x; mi.superset_sum(A); mi.superset_sum(B); for (int i = 0; i < 1 << N; ++i) A.at(i) *= B.at(i); mi.superset_sum_inv(A); for (auto x : A) cout << x << ' '; }