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#define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution" #include "../../math/modint.hpp" #include "../../convolution/gcd_lcm_convolution.hpp" #include <bits/stdc++.h> using namespace std; using ll = long long; using mint = Modint<998244353>; int main() { int N; cin >> N; vector<mint> a(N+1), b(N+1); for (int i = 1; i <= N; ++i) cin >> a[i]; for (int i = 1; i <= N; ++i) cin >> b[i]; auto c = lcm_convolution(a, b); for (int i = 1; i <= N; ++i) cout << c[i] << (i < N ? " " : "\n"); }
#line 1 "test/yosupo/lcm_convolution.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution" #line 2 "math/modint.hpp" #include <algorithm> #include <iostream> /** * @brief Mod int */ template <int m> class Modint { using mint = Modint; static_assert(m > 0, "Modulus must be positive"); public: static constexpr int mod() { return m; } constexpr Modint(long long y = 0) : x(y >= 0 ? y % m : (y % m + m) % m) {} constexpr int val() const { return x; } constexpr mint& operator+=(const mint& r) { if ((x += r.x) >= m) x -= m; return *this; } constexpr mint& operator-=(const mint& r) { if ((x += m - r.x) >= m) x -= m; return *this; } constexpr mint& operator*=(const mint& r) { x = static_cast<int>(1LL * x * r.x % m); return *this; } constexpr mint& operator/=(const mint& r) { return *this *= r.inv(); } constexpr bool operator==(const mint& r) const { return x == r.x; } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return mint(-x); } constexpr friend mint operator+(const mint& l, const mint& r) { return mint(l) += r; } constexpr friend mint operator-(const mint& l, const mint& r) { return mint(l) -= r; } constexpr friend mint operator*(const mint& l, const mint& r) { return mint(l) *= r; } constexpr friend mint operator/(const mint& l, const mint& r) { return mint(l) /= r; } constexpr mint inv() const { int a = x, b = m, u = 1, v = 0; while (b > 0) { int t = a / b; std::swap(a -= t * b, b); std::swap(u -= t * v, v); } return mint(u); } constexpr mint pow(long long n) const { mint ret(1), mul(x); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend std::ostream& operator<<(std::ostream& os, const mint& r) { return os << r.x; } friend std::istream& operator>>(std::istream& is, mint& r) { long long t; is >> t; r = mint(t); return is; } private: int x; }; #line 2 "convolution/gcd_lcm_convolution.hpp" #include <vector> #line 3 "convolution/divisor_zeta_moebius_transform.hpp" template <typename T> void divisor_fzt(std::vector<T>& a) { const int n = a.size(); std::vector<bool> sieve(n, true); for (int p = 2; p < n; ++p) { if (!sieve[p]) continue; for (int k = 1; k * p < n; ++k) { sieve[k * p] = false; a[k * p] += a[k]; } } } template <typename T> void divisor_fmt(std::vector<T>& a) { const int n = a.size(); std::vector<bool> sieve(n, true); for (int p = 2; p < n; ++p) { if (!sieve[p]) continue; for (int k = (n - 1) / p; k > 0; --k) { sieve[k * p] = false; a[k * p] -= a[k]; } } } template <typename T> void multiple_fzt(std::vector<T>& a) { const int n = a.size(); std::vector<bool> sieve(n, true); for (int p = 2; p < n; ++p) { if (!sieve[p]) continue; for (int k = (n - 1) / p; k > 0; --k) { sieve[k * p] = false; a[k] += a[k * p]; } } } template <typename T> void multiple_fmt(std::vector<T>& a) { const int n = a.size(); std::vector<bool> sieve(n, true); for (int p = 2; p < n; ++p) { if (!sieve[p]) continue; for (int k = 1; k * p < n; ++k) { sieve[k * p] = false; a[k] -= a[k * p]; } } } #line 5 "convolution/gcd_lcm_convolution.hpp" /** * @brief GCD/LCM Convolution */ template <typename T> std::vector<T> gcd_convolution(std::vector<T> a, std::vector<T> b) { const int n = std::max(a.size(), b.size()); a.resize(n); b.resize(n); multiple_fzt(a); multiple_fzt(b); for (int i = 0; i < n; ++i) a[i] *= b[i]; multiple_fmt(a); return a; } template <typename T> std::vector<T> lcm_convolution(std::vector<T> a, std::vector<T> b) { const int n = std::max(a.size(), b.size()); a.resize(n); b.resize(n); divisor_fzt(a); divisor_fzt(b); for (int i = 0; i < n; ++i) a[i] *= b[i]; divisor_fmt(a); return a; } #line 5 "test/yosupo/lcm_convolution.test.cpp" #include <bits/stdc++.h> using namespace std; using ll = long long; using mint = Modint<998244353>; int main() { int N; cin >> N; vector<mint> a(N+1), b(N+1); for (int i = 1; i <= N; ++i) cin >> a[i]; for (int i = 1; i <= N; ++i) cin >> b[i]; auto c = lcm_convolution(a, b); for (int i = 1; i <= N; ++i) cout << c[i] << (i < N ? " " : "\n"); }