This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#include "../../../src/template/template.hpp"
#include "../../../src/template/static_modint.hpp"
#include "../../../src/convolution/xor_convolution.hpp"
using mint = modint998244353;
int main(void) {
int n;
cin >> n;
vector<mint> a(1 << n), b(1 << n);
rep(i, 0, 1 << n) cin >> a[i];
rep(i, 0, 1 << n) cin >> b[i];
vector<mint> c = xor_convolution(a, b);
rep(i, 0, 1 << n) cout << c[i] << " \n"[i + 1 == (1 << n)];
}
#line 1 "verify/library_checker/convolution/bitwise_xor_convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
SetupIO() {
ios::sync_with_stdio(0);
cin.tie(0);
cout << fixed << setprecision(30);
}
} setup_io;
#line 3 "src/template/static_modint.hpp"
template <uint32_t m>
struct StaticModint {
using mint = StaticModint;
static constexpr uint32_t mod() {
return m;
}
static constexpr mint raw(const uint32_t v) {
mint a;
a._v = v;
return a;
}
constexpr StaticModint()
: _v(0) {}
template <class T>
constexpr StaticModint(const T& v) {
static_assert(is_integral_v<T>);
if constexpr(is_signed_v<T>) {
int64_t x = int64_t(v % int64_t(m));
if(x < 0) x += m;
_v = uint32_t(x);
} else _v = uint32_t(v % m);
}
constexpr uint32_t val() const {
return _v;
}
constexpr mint& operator++() {
return *this += 1;
}
constexpr mint& operator--() {
return *this -= 1;
}
constexpr mint operator++(int) {
mint res = *this;
++*this;
return res;
}
constexpr mint operator--(int) {
mint res = *this;
--*this;
return res;
}
constexpr mint& operator+=(mint rhs) {
if(_v >= m - rhs._v) _v -= m;
_v += rhs._v;
return *this;
}
constexpr mint& operator-=(mint rhs) {
if(_v < rhs._v) _v += m;
_v -= rhs._v;
return *this;
}
constexpr mint& operator*=(mint rhs) {
return *this = *this * rhs;
}
constexpr mint& operator/=(mint rhs) {
return *this *= rhs.inv();
}
constexpr mint operator+() const {
return *this;
}
constexpr mint operator-() const {
return mint{} - *this;
}
constexpr mint pow(long long n) const {
assert(0 <= n);
if(n == 0) return 1;
mint x = *this, r = 1;
while(1) {
if(n & 1) r *= x;
n >>= 1;
if(n == 0) return r;
x *= x;
}
}
constexpr mint inv() const {
if constexpr(prime) {
assert(_v);
return pow(m - 2);
} else {
const auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(mint lhs, mint rhs) {
return lhs += rhs;
}
friend constexpr mint operator-(mint lhs, mint rhs) {
return lhs -= rhs;
}
friend constexpr mint operator*(mint lhs, mint rhs) {
return uint64_t(lhs._v) * rhs._v;
}
friend constexpr mint operator/(mint lhs, mint rhs) {
return lhs /= rhs;
}
friend constexpr bool operator==(mint lhs, mint rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(mint lhs, mint rhs) {
return lhs._v != rhs._v;
}
friend istream& operator>>(istream& in, mint& x) {
long long a;
in >> a;
x = a;
return in;
}
friend ostream& operator<<(ostream& out, const mint& x) {
return out << x.val();
}
private:
uint32_t _v = 0;
static constexpr bool prime = []() -> bool {
if(m == 1) return 0;
if(m == 2 or m == 7 or m == 61) return 1;
if(m % 2 == 0) return 0;
uint32_t d = m - 1;
while(d % 2 == 0) d /= 2;
for(uint32_t a : {2, 7, 61}) {
uint32_t t = d;
mint y = mint(a).pow(t);
while(t != m - 1 && y != 1 && y != m - 1) {
y *= y;
t <<= 1;
}
if(y != m - 1 && t % 2 == 0) return 0;
}
return 1;
}();
static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
if(a == 0) return {b, 0};
int32_t s = b, t = a, m0 = 0, m1 = 1;
while(t) {
const int32_t u = s / t;
s -= t * u;
m0 -= m1 * u;
swap(s, t);
swap(m0, m1);
}
if(m0 < 0) m0 += b / s;
return {s, m0};
}
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;
#line 3 "src/math/walsh_hadamard_transform.hpp"
template <typename T>
void walsh_hadamard_transform(vector<T>& f, const bool inv = false) {
const int n = f.size();
assert((n & (n - 1)) == 0);
for(int i = 1; i < n; i <<= 1) {
for(int j = 0; j < n; ++j) {
if((j & i) == 0) {
const T x = f[j], y = f[j | i];
f[j] = x + y, f[j | i] = x - y;
}
}
}
if(inv) {
if constexpr(is_integral<T>::value) {
for(auto& x : f) x /= n;
} else {
const T invn = T(1) / T(f.size());
for(auto& x : f) x *= invn;
}
}
}
#line 4 "src/convolution/xor_convolution.hpp"
template <typename T>
vector<T> xor_convolution(vector<T> a, vector<T> b) {
const int n = (int)a.size(), m = (int)b.size();
assert(n == m and (n & (n - 1)) == 0);
walsh_hadamard_transform(a);
walsh_hadamard_transform(b);
for(int i = 0; i < (int)a.size(); ++i) a[i] *= b[i];
walsh_hadamard_transform(a, true);
return a;
}
#line 5 "verify/library_checker/convolution/bitwise_xor_convolution.test.cpp"
using mint = modint998244353;
int main(void) {
int n;
cin >> n;
vector<mint> a(1 << n), b(1 << n);
rep(i, 0, 1 << n) cin >> a[i];
rep(i, 0, 1 << n) cin >> b[i];
vector<mint> c = xor_convolution(a, b);
rep(i, 0, 1 << n) cout << c[i] << " \n"[i + 1 == (1 << n)];
}