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#define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution" #include "../../convolution/lcm_convolution.hpp" #include <iostream> #include <vector> #include "../../modint/modint.hpp" using mint = ebi::modint998244353; int main() { int n; std::cin >> n; std::vector<mint> a(n + 1), b(n + 1); for (int i = 1; i <= n; i++) { std::cin >> a[i]; } for (int i = 1; i <= n; i++) { std::cin >> b[i]; } auto c = ebi::lcm_convolution(a, b); for (int i = 1; i <= n; i++) { std::cout << c[i].val() << " \n"[i == n]; } }
#line 1 "test/convolution/Lcm_Convolution.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution" #line 2 "convolution/lcm_convolution.hpp" #line 2 "math/divisor_transform.hpp" #include <vector> #line 2 "math/eratosthenes_sieve.hpp" #include <cassert> #include <cstdint> #line 6 "math/eratosthenes_sieve.hpp" /* reference: https://37zigen.com/sieve-eratosthenes/ */ namespace ebi { struct eratosthenes_sieve { private: using i64 = std::int_fast64_t; int n; std::vector<bool> table; public: eratosthenes_sieve(int _n) : n(_n), table(std::vector<bool>(n + 1, true)) { table[1] = false; for (i64 i = 2; i * i <= n; i++) { if (!table[i]) continue; for (i64 j = i; i * j <= n; j++) { table[i * j] = false; } } } bool is_prime(int p) { return table[p]; } std::vector<int> prime_table(int m = -1) { if (m < 0) m = n; std::vector<int> prime; for (int i = 2; i <= m; i++) { if (table[i]) prime.emplace_back(i); } return prime; } }; } // namespace ebi #line 6 "math/divisor_transform.hpp" namespace ebi { struct divisor_transform { divisor_transform() = default; template <class mint> static std::vector<mint> zeta_transform(const std::vector<mint> &f) { int n = f.size() - 1; auto F = f; if (m < n) { while (m < n) m <<= 1; eratosthenes_sieve sieve(m); primes = sieve.prime_table(); } for (const auto &p : primes) { if (n < p) break; for (int i = 1; i * p <= n; i++) F[p * i] += F[i]; } return F; } template <class mint> static std::vector<mint> mobius_transform(const std::vector<mint> &F) { int n = F.size() - 1; auto f = F; if (m < n) { while (m < n) m <<= 1; eratosthenes_sieve sieve(m); primes = sieve.prime_table(); } for (const auto &p : primes) { if (n < p) break; for (int i = n / p; i > 0; i--) f[p * i] -= f[i]; } return f; } private: static int m; static std::vector<int> primes; }; int divisor_transform::m = 4; std::vector<int> divisor_transform::primes = {2, 3}; } // namespace ebi #line 4 "convolution/lcm_convolution.hpp" namespace ebi { template <class mint> std::vector<mint> lcm_convolution(const std::vector<mint> &a, const std::vector<mint> &b) { int n = a.size(); assert(a.size() == b.size()); auto ra = divisor_transform::zeta_transform(a); auto rb = divisor_transform::zeta_transform(b); for (int i = 0; i < n; i++) { ra[i] *= rb[i]; } return divisor_transform::mobius_transform(ra); } } // namespace ebi #line 4 "test/convolution/Lcm_Convolution.test.cpp" #include <iostream> #line 7 "test/convolution/Lcm_Convolution.test.cpp" #line 2 "modint/modint.hpp" #line 5 "modint/modint.hpp" #line 2 "modint/base.hpp" #include <concepts> #line 5 "modint/base.hpp" #include <utility> namespace ebi { template <class T> concept Modint = requires(T a, T b) { a + b; a - b; a * b; a / b; a.inv(); a.val(); a.pow(std::declval<long long>()); T::mod(); }; template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) { long long x; os >> x; a = x; return os; } template <Modint mint> std::ostream &operator<<(std::ostream &os, const mint &a) { return os << a.val(); } } // namespace ebi #line 7 "modint/modint.hpp" namespace ebi { template <int m> struct static_modint { private: using modint = static_modint; public: static constexpr int mod() { return m; } static constexpr modint raw(int v) { modint x; x._v = v; return x; } constexpr static_modint() : _v(0) {} constexpr static_modint(long long v) { v %= (long long)umod(); if (v < 0) v += (long long)umod(); _v = (unsigned int)v; } constexpr unsigned int val() const { return _v; } constexpr unsigned int value() const { return val(); } constexpr modint &operator++() { _v++; if (_v == umod()) _v = 0; return *this; } constexpr modint &operator--() { if (_v == 0) _v = umod(); _v--; return *this; } constexpr modint operator++(int) { modint res = *this; ++*this; return res; } constexpr modint operator--(int) { modint res = *this; --*this; return res; } constexpr modint &operator+=(const modint &rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } constexpr modint &operator-=(const modint &rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } constexpr modint &operator*=(const modint &rhs) { unsigned long long x = _v; x *= rhs._v; _v = (unsigned int)(x % (unsigned long long)umod()); return *this; } constexpr modint &operator/=(const modint &rhs) { return *this = *this * rhs.inv(); } constexpr modint operator+() const { return *this; } constexpr modint operator-() const { return modint() - *this; } constexpr modint pow(long long n) const { assert(0 <= n); modint x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } constexpr modint inv() const { assert(_v); return pow(umod() - 2); } friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += rhs; } friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= rhs; } friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= rhs; } friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= rhs; } friend bool operator==(const modint &lhs, const modint &rhs) { return lhs.val() == rhs.val(); } friend bool operator!=(const modint &lhs, const modint &rhs) { return !(lhs == rhs); } private: unsigned int _v = 0; static constexpr unsigned int umod() { return m; } }; using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; } // namespace ebi #line 9 "test/convolution/Lcm_Convolution.test.cpp" using mint = ebi::modint998244353; int main() { int n; std::cin >> n; std::vector<mint> a(n + 1), b(n + 1); for (int i = 1; i <= n; i++) { std::cin >> a[i]; } for (int i = 1; i <= n; i++) { std::cin >> b[i]; } auto c = ebi::lcm_convolution(a, b); for (int i = 1; i <= n; i++) { std::cout << c[i].val() << " \n"[i == n]; } }