This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/subset_convolution"
#include "../../template/template.hpp"
#include "../../math/fft/subset-convolution.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"
#include "../../other/scanner.hpp"
#include "../../other/printer.hpp"
const int MOD = 998244353;
using mint = MontgomeryModInt< MOD, true >;
int main() {
Scanner in(stdin);
Printer out(stdout);
int N;
in.read(N);
vector< mint > f(1 << N), g(1 << N);
for(auto &a : f) {
int x;
in.read(x);
a = x;
}
for(auto &a : g) {
int x;
in.read(x);
a = x;
}
auto h = SubsetConvolution< mint, 20 >::multiply(f, g);
for(auto &a : h) {
out.write(a.get());
out.write(' ');
}
out.writeln();
}
#line 1 "test/verify/yosupo-subset-convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/subset_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-subset-convolution.test.cpp"
#line 1 "math/fft/subset-convolution.hpp"
/**
* @brief Subset Convolution
*/
template< typename Mint, int _s >
struct SubsetConvolution {
using fps = array< Mint, _s + 1 >;
static array< int, (1 << _s) > pop_count;
static constexpr int s = _s;
SubsetConvolution() = default;
static void init() {
if(pop_count.back() == 0) {
pop_count[0] = 0;
for(int i = 1; i < (1 << s); i++) {
pop_count[i] = pop_count[i - (i & -i)] + 1;
}
}
}
static inline void add(fps &f, const fps &g, int d) {
for(int i = 0; i < d; i++) {
f[i] += g[i];
}
}
static inline void sub(fps &f, const fps &g, int d) {
for(int i = d; i <= s; i++) {
f[i] -= g[i];
}
}
static void zeta_transform(vector< fps > &F) {
const int n = (int) F.size();
assert((n & (n - 1)) == 0);
init();
for(int i = 1; i < n; i <<= 1) {
for(int j = 0; j < n; j += i << 1) {
for(int k = 0; k < i; k++) {
add(F[j + k + i], F[j + k], pop_count[j + k + i]);
}
}
}
}
static void moebius_transform(vector< fps > &F) {
const int n = (int) F.size();
assert((n & (n - 1)) == 0);
init();
for(int i = 1; i < n; i <<= 1) {
for(int j = 0; j < n; j += i << 1) {
for(int k = 0; k < i; k++) {
sub(F[j + k + i], F[j + k], pop_count[j + k + i]);
}
}
}
}
static vector< fps > lift(const vector< Mint > &f) {
const int n = (int) f.size();
init();
vector< fps > F(n);
for(int i = 0; i < n; i++) {
fill(begin(F[i]), end(F[i]), Mint());
F[i][pop_count[i]] = f[i];
}
return F;
}
static vector< Mint > unlift(const vector< fps > &F) {
const int n = (int) F.size();
init();
vector< Mint > f(n);
for(int i = 0; i < (int) F.size(); i++) {
f[i] = F[i][pop_count[i]];
}
return f;
}
static void prod(vector< fps > &F, const vector< fps > &G) {
int n = (int) F.size();
int d = __builtin_ctz(n);
for(int i = 0; i < n; i++) {
fps h{};
for(int j = 0; j <= d; j++) {
for(int k = 0; k <= d - j; k++) {
h[j + k] += F[i][j] * G[i][k];
}
}
F[i] = move(h);
}
}
static vector< Mint > multiply(const vector< Mint > &f, const vector< Mint > &g) {
auto F = lift(f), G = lift(g);
zeta_transform(F);
zeta_transform(G);
prod(F, G);
moebius_transform(F);
return unlift(F);
}
};
template< typename Mint, int s >
array< int, (1 << s) > SubsetConvolution< Mint, s >::pop_count;
#line 6 "test/verify/yosupo-subset-convolution.test.cpp"
#line 1 "math/combinatorics/montgomery-mod-int.hpp"
/**
* @brief Montgomery ModInt
*/
template< uint32_t mod, bool fast = false >
struct MontgomeryModInt {
using mint = MontgomeryModInt;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for(i32 i = 0; i < 4; i++) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(r * mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 x;
MontgomeryModInt() : x{} {}
MontgomeryModInt(const i64 &a)
: x(reduce(u64(fast ? a : (a % mod + mod)) * n2)) {}
static constexpr u32 reduce(const u64 &b) {
return u32(b >> 32) + mod - u32((u64(u32(b) * r) * mod) >> 32);
}
mint &operator+=(const mint &p) {
if(i32(x += p.x - 2 * mod) < 0) x += 2 * mod;
return *this;
}
mint &operator-=(const mint &p) {
if(i32(x -= p.x) < 0) x += 2 * mod;
return *this;
}
mint &operator*=(const mint &p) {
x = reduce(u64(x) * p.x);
return *this;
}
mint &operator/=(const mint &p) {
*this *= p.inverse();
return *this;
}
mint operator-() const { return mint() - *this; }
mint operator+(const mint &p) const { return mint(*this) += p; }
mint operator-(const mint &p) const { return mint(*this) -= p; }
mint operator*(const mint &p) const { return mint(*this) *= p; }
mint operator/(const mint &p) const { return mint(*this) /= p; }
bool operator==(const mint &p) const { return (x >= mod ? x - mod : x) == (p.x >= mod ? p.x - mod : p.x); }
bool operator!=(const mint &p) const { return (x >= mod ? x - mod : x) != (p.x >= mod ? p.x - mod : p.x); }
u32 get() const {
u32 ret = reduce(x);
return ret >= mod ? ret - mod : ret;
}
mint pow(u64 n) const {
mint ret(1), mul(*this);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
mint inverse() const {
return pow(mod - 2);
}
friend ostream &operator<<(ostream &os, const mint &p) {
return os << p.get();
}
friend istream &operator>>(istream &is, mint &a) {
i64 t;
is >> t;
a = mint(t);
return is;
}
static u32 get_mod() { return mod; }
};
using modint = MontgomeryModInt< mod >;
#line 8 "test/verify/yosupo-subset-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 11 "test/verify/yosupo-subset-convolution.test.cpp"
const int MOD = 998244353;
using mint = MontgomeryModInt< MOD, true >;
int main() {
Scanner in(stdin);
Printer out(stdout);
int N;
in.read(N);
vector< mint > f(1 << N), g(1 << N);
for(auto &a : f) {
int x;
in.read(x);
a = x;
}
for(auto &a : g) {
int x;
in.read(x);
a = x;
}
auto h = SubsetConvolution< mint, 20 >::multiply(f, g);
for(auto &a : h) {
out.write(a.get());
out.write(' ');
}
out.writeln();
}