This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#include <iostream>
#include <vector>
#include "../../convolution/xor_convolution.hpp"
#include "../../modint/modint.hpp"
using mint = ebi::modint998244353;
int main() {
int n;
std::cin >> n;
std::vector<mint> a(1 << n), b(1 << n);
for (int i = 0; i < (1 << n); i++) {
int val;
std::cin >> val;
a[i] = val;
}
for (int i = 0; i < (1 << n); i++) {
int val;
std::cin >> val;
b[i] = val;
}
auto c = ebi::xor_convolution(a, b);
for (int i = 0; i < (1 << n); i++) {
std::cout << c[i].val() << " \n"[i == (1 << n) - 1];
}
}
#line 1 "test/convolution/Bitwise_Xor_Convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#include <iostream>
#include <vector>
#line 2 "convolution/xor_convolution.hpp"
#include <cassert>
#line 5 "convolution/xor_convolution.hpp"
#line 2 "set_function/hadamard_transform.hpp"
#line 4 "set_function/hadamard_transform.hpp"
namespace ebi {
template <class T>
std::vector<T> hadamard_transform(std::vector<T> f, bool inverse = false) {
int n = f.size();
for (int i = 1; i < n; i <<= 1) {
for (int j = 0; j < n; j++) {
if ((i & j) == 0) {
T x = f[j], y = f[j | i];
f[j] = x + y;
f[j | i] = x - y;
}
}
}
if (inverse) {
for (auto& x : f) {
x /= T(n);
}
}
return f;
}
} // namespace ebi
#line 7 "convolution/xor_convolution.hpp"
namespace ebi {
template <class T>
std::vector<T> xor_convolution(const std::vector<T> &a,
const std::vector<T> &b) {
assert(a.size() == b.size());
auto ta = hadamard_transform(a);
auto tb = hadamard_transform(b);
for (int i = 0; i < (int)a.size(); i++) {
ta[i] *= tb[i];
}
return hadamard_transform(ta, true);
}
} // namespace ebi
#line 2 "modint/modint.hpp"
#line 5 "modint/modint.hpp"
#line 2 "modint/base.hpp"
#include <concepts>
#line 5 "modint/base.hpp"
#include <utility>
namespace ebi {
template <class T>
concept Modint = requires(T a, T b) {
a + b;
a - b;
a * b;
a / b;
a.inv();
a.val();
a.pow(std::declval<long long>());
T::mod();
};
template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
long long x;
os >> x;
a = x;
return os;
}
template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
return os << a.val();
}
} // namespace ebi
#line 7 "modint/modint.hpp"
namespace ebi {
template <int m> struct static_modint {
private:
using modint = static_modint;
public:
static constexpr int mod() {
return m;
}
static constexpr modint raw(int v) {
modint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template <std::signed_integral T> constexpr static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <std::unsigned_integral T> constexpr static_modint(T v) {
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const {
return _v;
}
constexpr unsigned int value() const {
return val();
}
constexpr modint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr modint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr modint operator++(int) {
modint res = *this;
++*this;
return res;
}
constexpr modint operator--(int) {
modint res = *this;
--*this;
return res;
}
constexpr modint &operator+=(const modint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr modint &operator-=(const modint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr modint &operator*=(const modint &rhs) {
unsigned long long x = _v;
x *= rhs._v;
_v = (unsigned int)(x % (unsigned long long)umod());
return *this;
}
constexpr modint &operator/=(const modint &rhs) {
return *this = *this * rhs.inv();
}
constexpr modint operator+() const {
return *this;
}
constexpr modint operator-() const {
return modint() - *this;
}
constexpr modint pow(long long n) const {
assert(0 <= n);
modint x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
constexpr modint inv() const {
assert(_v);
return pow(umod() - 2);
}
friend modint operator+(const modint &lhs, const modint &rhs) {
return modint(lhs) += rhs;
}
friend modint operator-(const modint &lhs, const modint &rhs) {
return modint(lhs) -= rhs;
}
friend modint operator*(const modint &lhs, const modint &rhs) {
return modint(lhs) *= rhs;
}
friend modint operator/(const modint &lhs, const modint &rhs) {
return modint(lhs) /= rhs;
}
friend bool operator==(const modint &lhs, const modint &rhs) {
return lhs.val() == rhs.val();
}
friend bool operator!=(const modint &lhs, const modint &rhs) {
return !(lhs == rhs);
}
private:
unsigned int _v = 0;
static constexpr unsigned int umod() {
return m;
}
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
} // namespace ebi
#line 8 "test/convolution/Bitwise_Xor_Convolution.test.cpp"
using mint = ebi::modint998244353;
int main() {
int n;
std::cin >> n;
std::vector<mint> a(1 << n), b(1 << n);
for (int i = 0; i < (1 << n); i++) {
int val;
std::cin >> val;
a[i] = val;
}
for (int i = 0; i < (1 << n); i++) {
int val;
std::cin >> val;
b[i] = val;
}
auto c = ebi::xor_convolution(a, b);
for (int i = 0; i < (1 << n); i++) {
std::cout << c[i].val() << " \n"[i == (1 << n) - 1];
}
}