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#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_and_convolution" #include "../../template/template.hpp" #include "../../math/fft/bitwise-and-convolution.hpp" #include "../../math/combinatorics/mod-int.hpp" #include "../../other/scanner.hpp" #include "../../other/printer.hpp" const int MOD = 998244353; using mint = ModInt< MOD >; int main() { Scanner in(stdin); Printer out(stdout); int N; in.read(N); vector< mint > a(1 << N), b(1 << N); for(auto &x : a) { int p; in.read(p); x = p; } for(auto &x : b) { int p; in.read(p); x = p; } auto c = bitwise_and_convolution(a, b); for(int i = 0; i < (1 << N); i++) { if(i) out.write(' '); out.write(c[i].x); } out.writeln(); }
#line 1 "test/verify/yosupo-bitwise-and-convolution.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/bitwise_and_convolution" #line 1 "template/template.hpp" #include<bits/stdc++.h> using namespace std; using int64 = long long; const int mod = 1e9 + 7; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 >& p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { explicit FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 4 "test/verify/yosupo-bitwise-and-convolution.test.cpp" #line 1 "math/fft/superset-zeta-moebius-transform.hpp" /** * @brief Superset Zeta/Moebius Transform (上位集合のゼータ/メビウス変換) */ template< typename T > void superset_zeta_transform(vector< T > &f) { const int n = (int) f.size(); assert((n & (n - 1)) == 0); for(int i = 1; i < n; i <<= 1) { for(int j = 0; j < n; j += i << 1) { for(int k = 0; k < i; k++) { f[j + k] += f[j + k + i]; } } } } template< typename T > void superset_moebius_transform(vector< T > &f) { const int n = (int) f.size(); assert((n & (n - 1)) == 0); for(int i = 1; i < n; i <<= 1) { for(int j = 0; j < n; j += i << 1) { for(int k = 0; k < i; k++) { f[j + k] -= f[j + k + i]; } } } } #line 2 "math/fft/bitwise-and-convolution.hpp" /** * @brief Bitwise And Convolution (Bitwise-AND畳み込み) */ template< typename T > vector< T > bitwise_and_convolution(vector< T > f, vector< T > g) { const int n = (int) f.size(); assert(f.size() == g.size()); assert((n & (n - 1)) == 0); superset_zeta_transform(f); superset_zeta_transform(g); for(int i = 0; i < n; i++) f[i] *= g[i]; superset_moebius_transform(f); return f; } #line 1 "math/combinatorics/mod-int.hpp" template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; #line 7 "test/verify/yosupo-bitwise-and-convolution.test.cpp" #line 1 "other/scanner.hpp" /** * @brief Scanner(高速入力) */ struct Scanner { public: explicit Scanner(FILE *fp) : fp(fp) {} template< typename T, typename... E > void read(T &t, E &... e) { read_single(t); read(e...); } private: static constexpr size_t line_size = 1 << 16; static constexpr size_t int_digits = 20; char line[line_size + 1] = {}; FILE *fp = nullptr; char *st = line; char *ed = line; void read() {} static inline bool is_space(char c) { return c <= ' '; } void reread() { ptrdiff_t len = ed - st; memmove(line, st, len); char *tmp = line + len; ed = tmp + fread(tmp, 1, line_size - len, fp); *ed = 0; st = line; } void skip_space() { while(true) { if(st == ed) reread(); while(*st && is_space(*st)) ++st; if(st != ed) return; } } template< typename T, enable_if_t< is_integral< T >::value, int > = 0 > void read_single(T &s) { skip_space(); if(st + int_digits >= ed) reread(); bool neg = false; if(is_signed< T >::value && *st == '-') { neg = true; ++st; } typename make_unsigned< T >::type y = *st++ - '0'; while(*st >= '0') { y = 10 * y + *st++ - '0'; } s = (neg ? -y : y); } template< typename T, enable_if_t< is_same< T, string >::value, int > = 0 > void read_single(T &s) { s = ""; skip_space(); while(true) { char *base = st; while(*st && !is_space(*st)) ++st; s += string(base, st); if(st != ed) return; reread(); } } template< typename T > void read_single(vector< T > &s) { for(auto &d : s) read(d); } }; #line 1 "other/printer.hpp" /** * @brief Printer(高速出力) */ struct Printer { public: explicit Printer(FILE *fp) : fp(fp) {} ~Printer() { flush(); } template< bool f = false, typename T, typename... E > void write(const T &t, const E &... e) { if(f) write_single(' '); write_single(t); write< true >(e...); } template< typename... T > void writeln(const T &...t) { write(t...); write_single('\n'); } void flush() { fwrite(line, 1, st - line, fp); st = line; } private: FILE *fp = nullptr; static constexpr size_t line_size = 1 << 16; static constexpr size_t int_digits = 20; char line[line_size + 1] = {}; char *st = line; template< bool f = false > void write() {} void write_single(const char &t) { if(st + 1 >= line + line_size) flush(); *st++ = t; } template< typename T, enable_if_t< is_integral< T >::value, int > = 0 > void write_single(T s) { if(st + int_digits >= line + line_size) flush(); st += to_chars(st, st + int_digits, s).ptr - st; } void write_single(const string &s) { for(auto &c: s) write_single(c); } void write_single(const char *s) { while(*s != 0) write_single(*s++); } template< typename T > void write_single(const vector< T > &s) { for(size_t i = 0; i < s.size(); i++) { if(i) write_single(' '); write_single(s[i]); } } }; #line 10 "test/verify/yosupo-bitwise-and-convolution.test.cpp" const int MOD = 998244353; using mint = ModInt< MOD >; int main() { Scanner in(stdin); Printer out(stdout); int N; in.read(N); vector< mint > a(1 << N), b(1 << N); for(auto &x : a) { int p; in.read(p); x = p; } for(auto &x : b) { int p; in.read(p); x = p; } auto c = bitwise_and_convolution(a, b); for(int i = 0; i < (1 << N); i++) { if(i) out.write(' '); out.write(c[i].x); } out.writeln(); }