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#define PROBLEM "https://judge.yosupo.jp/problem/subset_convolution"
#include "../algorithm/subset_convolution.cpp"
#include "../math/static_modint.cpp"
#include "../traits/num_ring.cpp"
#include <iostream>
#include <vector>
using Fp = Modint998244353;
int main() {
int N;
std::cin >> N;
N = 1 << N;
std::vector<Fp> A(N), B(N);
for (auto& x : A) {
u32 t;
std::cin >> t;
x = t;
}
for (auto& x : B) {
u32 t;
std::cin >> t;
x = t;
}
const auto C = subset_convolution<NumRing<Fp>>(A, B);
for (const int i : rep(N)) {
std::cout << C[i] << " \n"[i + 1 == N];
}
}
#line 1 "test/subset_convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/subset_convolution"
#line 2 "algorithm/subset_convolution.cpp"
#include <cassert>
#include <vector>
#line 2 "internal/enable_avx2.cpp"
#ifdef ENABLE_AVX2
#define TARGET_AVX2 __attribute__((target("avx2")))
#else
#define TARGET_AVX2
#endif
#line 2 "utility/int_alias.cpp"
#include <cstdint>
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
#line 4 "utility/countl_zero.cpp"
TARGET_AVX2 constexpr int countl_zero(u64 x) {
#ifdef __GNUC__
return x == 0 ? 64 : __builtin_clzll(x);
#else
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
x |= x >> 32;
return 64 - countr_zero(~x);
#endif
}
#line 4 "utility/bit_width.cpp"
TARGET_AVX2 constexpr int bit_width(const u64 x) { return 64 - countl_zero(x); }
#line 2 "utility/rep.cpp"
#include <algorithm>
class Range {
struct Iter {
int itr;
constexpr Iter(const int pos) noexcept : itr(pos) {}
constexpr void operator++() noexcept { ++itr; }
constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
constexpr int operator*() const noexcept { return itr; }
};
const Iter first, last;
public:
explicit constexpr Range(const int first, const int last) noexcept : first(first), last(std::max(first, last)) {}
constexpr Iter begin() const noexcept { return first; }
constexpr Iter end() const noexcept { return last; }
};
constexpr Range rep(const int l, const int r) noexcept { return Range(l, r); }
constexpr Range rep(const int n) noexcept { return Range(0, n); }
#line 4 "utility/popcount.cpp"
TARGET_AVX2 constexpr int popcount(u64 x) {
#ifdef __GNUC__
return __builtin_popcountll(x);
#else
x -= x >> 1 & 0x5555555555555555;
x = (x & 0x3333333333333333) + (x >> 2 & 0x3333333333333333);
x = (x + (x >> 4)) & 0x0F0F0F0F0F0F0F0F;
return x * 0x0101010101010101 >> 56 & 0x7f;
#endif
}
#line 7 "algorithm/ranked_subset_mobius_transform.cpp"
template <class G>
std::vector<typename G::Type> ranked_subset_mobius_transform(std::vector<std::vector<typename G::Type>> f) {
const int n = f.size();
assert((n & (n - 1)) == 0);
const int logn = bit_width(n);
for (int i = n; i >>= 1;) {
for (const int j : rep(n)) {
if (j & i) {
auto& a = f[j];
const auto& b = f[j & ~i];
for (const int k : rep(logn)) a[k] = G::operation(G::inverse(b[k]), a[k]);
}
}
}
std::vector<typename G::Type> g(n, G::identity());
for (const int i : rep(n)) g[i] = f[i][popcount(i)];
return g;
}
#line 7 "algorithm/ranked_subset_zeta_transform.cpp"
template <class S>
std::vector<std::vector<typename S::Type>> ranked_subset_zeta_transform(const std::vector<typename S::Type>& f) {
const int n = f.size();
assert((n & (n - 1)) == 0);
const int logn = bit_width(n);
std::vector<std::vector<typename S::Type>> g(n, std::vector<typename S::Type>(logn, S::identity()));
for (const int i : rep(n)) g[i][popcount(i)] = f[i];
for (int i = 1; i < n; i <<= 1) {
for (const int j : rep(n)) {
if (j & i) {
auto& a = g[j];
const auto& b = g[j & ~i];
for (const int k : rep(logn)) a[k] = S::operation(b[k], a[k]);
}
}
}
return g;
}
#line 8 "algorithm/subset_convolution.cpp"
template <class R>
std::vector<typename R::Type> subset_convolution(const std::vector<typename R::Type>& a,
const std::vector<typename R::Type>& b) {
assert(a.size() == b.size());
const auto f = ranked_subset_zeta_transform<typename R::Sum>(a);
const auto g = ranked_subset_zeta_transform<typename R::Sum>(b);
const int n = a.size();
const int logn = bit_width(n);
std::vector<std::vector<typename R::Type>> h(n, std::vector<typename R::Type>(logn, R::Sum::identity()));
for (const int i : rep(n))
for (const int j : rep(logn))
for (const int k : rep(logn - j))
h[i][j + k] = R::Sum::operation(h[i][j + k], R::Product::operation(f[i][j], g[i][k]));
return ranked_subset_mobius_transform<typename R::Sum>(std::move(h));
}
#line 2 "math/static_modint.cpp"
#include <ostream>
#include <type_traits>
#line 3 "math/rem_euclid.cpp"
template <class T> constexpr T rem_euclid(T value, const T& mod) {
assert(mod > 0);
return (value %= mod) >= 0 ? value : value + mod;
}
#line 2 "math/totient.cpp"
template <class T> constexpr T totient(T x) {
T ret = x;
for (T i = 2; i * i <= x; ++i) {
if (x % i == 0) {
ret /= i;
ret *= i - 1;
while (x % i == 0) x /= i;
}
}
if (x > 1) {
ret /= x;
ret *= x - 1;
}
return ret;
}
#line 7 "math/static_modint.cpp"
template <u32 MOD, std::enable_if_t<((u32)1 <= MOD and MOD <= ((u32)1 << 31))>* = nullptr> class StaticModint {
using Self = StaticModint;
static inline constexpr u32 PHI = totient(MOD);
u32 v;
public:
static constexpr u32 mod() noexcept { return MOD; }
template <class T, std::enable_if_t<std::is_integral_v<T>>* = nullptr>
static constexpr T normalize(const T& x) noexcept {
return rem_euclid<std::common_type_t<T, i64>>(x, MOD);
}
constexpr StaticModint() noexcept : v(0) {}
template <class T> constexpr StaticModint(const T& x) noexcept : v(normalize(x)) {}
template <class T> static constexpr Self raw(const T& x) noexcept {
Self ret;
ret.v = x;
return ret;
}
constexpr u32 val() const noexcept { return v; }
constexpr Self neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
constexpr Self inv() const noexcept { return pow(PHI - 1); }
constexpr Self pow(u64 exp) const noexcept {
Self ret(1), mult(*this);
for (; exp > 0; exp >>= 1) {
if (exp & 1) ret *= mult;
mult *= mult;
}
return ret;
}
constexpr Self operator-() const noexcept { return neg(); }
constexpr Self operator~() const noexcept { return inv(); }
constexpr Self operator+(const Self& rhs) const noexcept { return Self(*this) += rhs; }
constexpr Self& operator+=(const Self& rhs) noexcept {
if ((v += rhs.v) >= MOD) v -= MOD;
return *this;
}
constexpr Self operator-(const Self& rhs) const noexcept { return Self(*this) -= rhs; }
constexpr Self& operator-=(const Self& rhs) noexcept {
if (v < rhs.v) v += MOD;
v -= rhs.v;
return *this;
}
constexpr Self operator*(const Self& rhs) const noexcept { return Self(*this) *= rhs; }
constexpr Self& operator*=(const Self& rhs) noexcept {
v = (u64)v * rhs.v % MOD;
return *this;
}
constexpr Self operator/(const Self& rhs) const noexcept { return Self(*this) /= rhs; }
constexpr Self& operator/=(const Self& rhs) noexcept { return *this *= rhs.inv(); }
constexpr bool operator==(const Self& rhs) const noexcept { return v == rhs.v; }
constexpr bool operator!=(const Self& rhs) const noexcept { return v != rhs.v; }
friend std::ostream& operator<<(std::ostream& stream, const Self& rhs) { return stream << rhs.v; }
};
using Modint1000000007 = StaticModint<1000000007>;
using Modint998244353 = StaticModint<998244353>;
#line 2 "traits/sum_group.cpp"
template <class T> struct SumGroup {
using Type = T;
static constexpr T identity() { return T(0); }
static constexpr T operation(const T& l, const T& r) { return l + r; }
static constexpr T inverse(const T& x) { return -x; }
};
#line 2 "traits/product_monoid.cpp"
template <class T> struct ProductMonoid {
using Type = T;
static constexpr T identity() { return T(1); }
static constexpr T operation(const T& l, const T& r) { return l * r; }
};
#line 4 "traits/num_ring.cpp"
template <class T> struct NumRing {
using Type = T;
using Sum = SumGroup<T>;
using Product = ProductMonoid<T>;
};
#line 5 "test/subset_convolution.test.cpp"
#include <iostream>
#line 7 "test/subset_convolution.test.cpp"
using Fp = Modint998244353;
int main() {
int N;
std::cin >> N;
N = 1 << N;
std::vector<Fp> A(N), B(N);
for (auto& x : A) {
u32 t;
std::cin >> t;
x = t;
}
for (auto& x : B) {
u32 t;
std::cin >> t;
x = t;
}
const auto C = subset_convolution<NumRing<Fp>>(A, B);
for (const int i : rep(N)) {
std::cout << C[i] << " \n"[i + 1 == N];
}
}