This documentation is automatically generated by online-judge-tools/verification-helper
// verification-helper: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution
#include "src/math/convolution/bitwise-xor-convolution.hpp"
#include "src/math/modular-arithmetic/static-modint.hpp"
#include <iostream>
#include <vector>
namespace luz {
void main_() {
usize n;
std::cin >> n;
using mint = modint998244353;
std::vector< mint > as(1 << n);
for (mint &a: as) {
i32 v;
std::cin >> v;
a = mint(v);
}
std::vector< mint > bs(1 << n);
for (mint &b: bs) {
i32 v;
std::cin >> v;
b = mint(v);
}
auto cs = bitwise_xor_convolution(as, bs);
for (usize i: rep(0, 1 << n)) {
std::cout << cs[i].val()
<< (i + 1 == (usize(1) << n) ? "\n" : " ");
}
}
} // namespace luz
int main() {
luz::main_();
}
#line 1 "test/library-checker/bitwise_xor_convolution.test.cpp"
// verification-helper: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution
#line 2 "src/math/convolution/bitwise-xor-convolution.hpp"
#line 2 "src/cpp-template/header/rep.hpp"
#line 2 "src/cpp-template/header/size-alias.hpp"
#include <cstddef>
namespace luz {
using isize = std::ptrdiff_t;
using usize = std::size_t;
} // namespace luz
#line 4 "src/cpp-template/header/rep.hpp"
#include <algorithm>
namespace luz {
struct rep {
struct itr {
usize i;
constexpr itr(const usize i) noexcept: i(i) {}
void operator++() noexcept {
++i;
}
constexpr usize operator*() const noexcept {
return i;
}
constexpr bool operator!=(const itr x) const noexcept {
return i != x.i;
}
};
const itr f, l;
constexpr rep(const usize f, const usize l) noexcept
: f(std::min(f, l)),
l(l) {}
constexpr auto begin() const noexcept {
return f;
}
constexpr auto end() const noexcept {
return l;
}
};
struct rrep {
struct itr {
usize i;
constexpr itr(const usize i) noexcept: i(i) {}
void operator++() noexcept {
--i;
}
constexpr usize operator*() const noexcept {
return i;
}
constexpr bool operator!=(const itr x) const noexcept {
return i != x.i;
}
};
const itr f, l;
constexpr rrep(const usize f, const usize l) noexcept
: f(l - 1),
l(std::min(f, l) - 1) {}
constexpr auto begin() const noexcept {
return f;
}
constexpr auto end() const noexcept {
return l;
}
};
} // namespace luz
#line 2 "src/math/convolution/fast-walsh-hadamard-transform.hpp"
#line 5 "src/math/convolution/fast-walsh-hadamard-transform.hpp"
#include <cassert>
#include <vector>
namespace luz {
template < typename T, typename F >
void fast_walsh_hadamard_transform(std::vector< T > &f, F op) {
const usize n = f.size();
assert((n & (n - 1)) == 0);
usize i = 1;
while (i < n) {
usize j = 0;
while (j < n) {
for (usize k: rep(0, i)) {
op(f[j + k], f[j + k + i]);
}
j += i << 1;
}
i <<= 1;
}
}
} // namespace luz
#line 6 "src/math/convolution/bitwise-xor-convolution.hpp"
#line 9 "src/math/convolution/bitwise-xor-convolution.hpp"
namespace luz {
template < typename T >
std::vector< T > bitwise_xor_convolution(std::vector< T > f,
std::vector< T > g) {
assert(f.size() == g.size());
T inv2 = T(1) / T(2);
auto zeta = [](T &lo, T &hi) {
T x = lo + hi;
T y = lo - hi;
lo = x;
hi = y;
};
auto mobius = [inv2](T &lo, T &hi) {
T x = lo + hi;
T y = lo - hi;
lo = x * inv2;
hi = y * inv2;
};
fast_walsh_hadamard_transform(f, zeta);
fast_walsh_hadamard_transform(g, zeta);
for (usize i: rep(0, f.size())) {
f[i] *= g[i];
}
fast_walsh_hadamard_transform(f, mobius);
return f;
}
} // namespace luz
#line 2 "src/math/modular-arithmetic/static-modint.hpp"
#line 2 "src/cpp-template/header/int-alias.hpp"
#include <cstdint>
namespace luz {
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using u128 = __uint128_t;
} // namespace luz
#line 4 "src/math/modular-arithmetic/static-modint.hpp"
#line 6 "src/math/modular-arithmetic/static-modint.hpp"
#include <iostream>
namespace luz {
template < u32 mod >
class StaticPrimeModInt {
using modint = StaticPrimeModInt;
u32 v;
public:
StaticPrimeModInt(): v(0) {}
template < typename T >
StaticPrimeModInt(T v_) {
i64 x = (i64)(v_ % (i64)mod);
if (x < 0) x += mod;
v = (u32)x;
}
u32 val() const {
return v;
}
modint &operator+=(const modint &rhs) {
v += rhs.v;
if (v >= mod) v -= mod;
return *this;
}
modint &operator-=(const modint &rhs) {
v += mod - rhs.v;
if (v >= mod) v -= mod;
return *this;
}
modint &operator*=(const modint &rhs) {
v = (u32)(u64(1) * v * rhs.v % mod);
return *this;
}
modint &operator/=(const modint &rhs) {
*this *= rhs.inverse();
return *this;
}
modint operator+() const {
return *this;
}
modint operator-() const {
return modint() - *this;
}
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.v == rhs.v;
}
friend bool operator!=(const modint &lhs, const modint &rhs) {
return lhs.v != rhs.v;
}
modint pow(i64 n) const {
assert(0 <= n);
modint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
modint inverse() const {
assert(v != 0);
return pow(mod - 2);
}
static constexpr u32 get_mod() {
return mod;
}
friend std::ostream &operator<<(std::ostream &os,
const modint &m) {
os << m.val();
return os;
}
};
using modint998244353 = StaticPrimeModInt< 998244353 >;
using modint1000000007 = StaticPrimeModInt< 1000000007 >;
} // namespace luz
#line 5 "test/library-checker/bitwise_xor_convolution.test.cpp"
#line 8 "test/library-checker/bitwise_xor_convolution.test.cpp"
namespace luz {
void main_() {
usize n;
std::cin >> n;
using mint = modint998244353;
std::vector< mint > as(1 << n);
for (mint &a: as) {
i32 v;
std::cin >> v;
a = mint(v);
}
std::vector< mint > bs(1 << n);
for (mint &b: bs) {
i32 v;
std::cin >> v;
b = mint(v);
}
auto cs = bitwise_xor_convolution(as, bs);
for (usize i: rep(0, 1 << n)) {
std::cout << cs[i].val()
<< (i + 1 == (usize(1) << n) ? "\n" : " ");
}
}
} // namespace luz
int main() {
luz::main_();
}