This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#include "../../template/template.hpp"
#include "../../math/fft/bitwise-xor-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_xor_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-xor-convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_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-xor-convolution.test.cpp"
#line 1 "math/fft/fast-walsh-hadamard-transform.hpp"
/**
* @brief Fast Walsh Hadamard Transform (高速ウォルシュアダマール変換)
*/
template< typename T >
void fast_walsh_hadamard_transform(vector< T > &f, bool inv = false) {
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++) {
T s = f[j + k], t = f[j + k + i];
f[j + k] = s + t;
f[j + k + i] = s - t;
}
}
}
if(inv) {
T inv_n = T(1) / n;
for(auto &x : f) x *= inv_n;
}
}
#line 2 "math/fft/bitwise-xor-convolution.hpp"
/**
* @brief Bitwise Xor Convolution (Bitwise-XOR畳み込み)
*/
template< typename T >
vector< T > bitwise_xor_convolution(vector< T > f, vector< T > g) {
const int n = (int) f.size();
assert(f.size() == g.size());
assert((n & (n - 1)) == 0);
fast_walsh_hadamard_transform(f, false);
fast_walsh_hadamard_transform(g, false);
for(int i = 0; i < n; i++) f[i] *= g[i];
fast_walsh_hadamard_transform(f, true);
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-xor-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-xor-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_xor_convolution(a, b);
for(int i = 0; i < (1 << N); i++) {
if(i) out.write(' ');
out.write(c[i].x);
}
out.writeln();
}