#line 1 "verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/subset_convolution"
//
#include <immintrin.h>
//
#include <algorithm>
#include <cassert>
#include <chrono>
#include <cstdint>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <random>
#include <type_traits>
#include <utility>
#include <vector>
using namespace std;
#line 2 "misc/fastio.hpp"
#line 5 "misc/fastio.hpp"
#include <string>
#line 8 "misc/fastio.hpp"
using namespace std;
#line 2 "internal/internal-type-traits.hpp"
#line 4 "internal/internal-type-traits.hpp"
using namespace std;
namespace internal {
template <typename T>
using is_broadly_integral =
typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
is_same_v<T, __uint128_t>,
true_type, false_type>::type;
template <typename T>
using is_broadly_signed =
typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
true_type, false_type>::type;
template <typename T>
using is_broadly_unsigned =
typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
true_type, false_type>::type;
#define ENABLE_VALUE(x) \
template <typename T> \
constexpr bool x##_v = x<T>::value;
ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE
#define ENABLE_HAS_TYPE(var) \
template <class, class = void> \
struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<typename T::var>> : true_type {}; \
template <class T> \
constexpr auto has_##var##_v = has_##var<T>::value;
#define ENABLE_HAS_VAR(var) \
template <class, class = void> \
struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
template <class T> \
constexpr auto has_##var##_v = has_##var<T>::value;
} // namespace internal
#line 12 "misc/fastio.hpp"
namespace fastio {
static constexpr int SZ = 1 << 17;
static constexpr int offset = 64;
char inbuf[SZ], outbuf[SZ];
int in_left = 0, in_right = 0, out_right = 0;
struct Pre {
char num[40000];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i * 4 + j] = n % 10 + '0';
n /= 10;
}
}
}
} constexpr pre;
void load() {
int len = in_right - in_left;
memmove(inbuf, inbuf + in_left, len);
in_right = len + fread(inbuf + len, 1, SZ - len, stdin);
in_left = 0;
}
void flush() {
fwrite(outbuf, 1, out_right, stdout);
out_right = 0;
}
void skip_space() {
if (in_left + offset > in_right) load();
while (inbuf[in_left] <= ' ') in_left++;
}
void single_read(char& c) {
if (in_left + offset > in_right) load();
skip_space();
c = inbuf[in_left++];
}
void single_read(string& S) {
skip_space();
while (true) {
if (in_left == in_right) load();
int i = in_left;
for (; i != in_right; i++) {
if (inbuf[i] <= ' ') break;
}
copy(inbuf + in_left, inbuf + i, back_inserter(S));
in_left = i;
if (i != in_right) break;
}
}
template <typename T,
enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr>
void single_read(T& x) {
if (in_left + offset > in_right) load();
skip_space();
char c = inbuf[in_left++];
[[maybe_unused]] bool minus = false;
if constexpr (internal::is_broadly_signed_v<T>) {
if (c == '-') minus = true, c = inbuf[in_left++];
}
x = 0;
while (c >= '0') {
x = x * 10 + (c & 15);
c = inbuf[in_left++];
}
if constexpr (internal::is_broadly_signed_v<T>) {
if (minus) x = -x;
}
}
void rd() {}
template <typename Head, typename... Tail>
void rd(Head& head, Tail&... tail) {
single_read(head);
rd(tail...);
}
void single_write(const char& c) {
if (out_right > SZ - offset) flush();
outbuf[out_right++] = c;
}
void single_write(const bool& b) {
if (out_right > SZ - offset) flush();
outbuf[out_right++] = b ? '1' : '0';
}
void single_write(const string& S) {
flush(), fwrite(S.data(), 1, S.size(), stdout);
}
void single_write(const char* p) { flush(), fwrite(p, 1, strlen(p), stdout); }
template <typename T,
enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr>
void single_write(const T& _x) {
if (out_right > SZ - offset) flush();
if (_x == 0) {
outbuf[out_right++] = '0';
return;
}
T x = _x;
if constexpr (internal::is_broadly_signed_v<T>) {
if (x < 0) outbuf[out_right++] = '-', x = -x;
}
constexpr int buffer_size = sizeof(T) * 10 / 4;
char buf[buffer_size];
int i = buffer_size;
while (x >= 10000) {
i -= 4;
memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
x /= 10000;
}
if (x < 100) {
if (x < 10) {
outbuf[out_right] = '0' + x;
++out_right;
} else {
uint32_t q = (uint32_t(x) * 205) >> 11;
uint32_t r = uint32_t(x) - q * 10;
outbuf[out_right] = '0' + q;
outbuf[out_right + 1] = '0' + r;
out_right += 2;
}
} else {
if (x < 1000) {
memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3);
out_right += 3;
} else {
memcpy(outbuf + out_right, pre.num + (x << 2), 4);
out_right += 4;
}
}
memcpy(outbuf + out_right, buf + i, buffer_size - i);
out_right += buffer_size - i;
}
void wt() {}
template <typename Head, typename... Tail>
void wt(const Head& head, const Tail&... tail) {
single_write(head);
wt(std::forward<const Tail>(tail)...);
}
template <typename... Args>
void wtn(const Args&... x) {
wt(std::forward<const Args>(x)...);
wt('\n');
}
struct Dummy {
Dummy() { atexit(flush); }
} dummy;
} // namespace fastio
using fastio::rd;
using fastio::skip_space;
using fastio::wt;
using fastio::wtn;
#line 20 "verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp"
//
#line 2 "math-fast/subset-convolution.hpp"
#line 5 "math-fast/subset-convolution.hpp"
using namespace std;
#line 2 "modint/vectorize-modint.hpp"
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#line 8 "modint/vectorize-modint.hpp"
using namespace std;
using m256 = __m256i;
struct alignas(32) mmint {
m256 x;
static mmint R, M0, M1, M2, N2;
mmint() : x() {}
inline mmint(const m256& _x) : x(_x) {}
inline mmint(unsigned int a) : x(_mm256_set1_epi32(a)) {}
inline mmint(unsigned int a0, unsigned int a1, unsigned int a2,
unsigned int a3, unsigned int a4, unsigned int a5,
unsigned int a6, unsigned int a7)
: x(_mm256_set_epi32(a7, a6, a5, a4, a3, a2, a1, a0)) {}
inline operator m256&() { return x; }
inline operator const m256&() const { return x; }
inline int& operator[](int i) { return *(reinterpret_cast<int*>(&x) + i); }
inline const int& operator[](int i) const {
return *(reinterpret_cast<const int*>(&x) + i);
}
friend ostream& operator<<(ostream& os, const mmint& m) {
unsigned r = R[0], mod = M1[0];
auto reduce1 = [&](const uint64_t& b) {
unsigned res = (b + uint64_t(unsigned(b) * unsigned(-r)) * mod) >> 32;
return res >= mod ? res - mod : res;
};
for (int i = 0; i < 8; i++) {
os << reduce1(m[i]) << (i == 7 ? "" : " ");
}
return os;
}
template <typename mint>
static void set_mod() {
R = _mm256_set1_epi32(mint::r);
M0 = _mm256_setzero_si256();
M1 = _mm256_set1_epi32(mint::get_mod());
M2 = _mm256_set1_epi32(mint::get_mod() * 2);
N2 = _mm256_set1_epi32(mint::n2);
}
static inline mmint reduce(const mmint& prod02, const mmint& prod13) {
m256 unpalo = _mm256_unpacklo_epi32(prod02, prod13);
m256 unpahi = _mm256_unpackhi_epi32(prod02, prod13);
m256 prodlo = _mm256_unpacklo_epi64(unpalo, unpahi);
m256 prodhi = _mm256_unpackhi_epi64(unpalo, unpahi);
m256 hiplm1 = _mm256_add_epi32(prodhi, M1);
m256 prodlohi = _mm256_shuffle_epi32(prodlo, 0xF5);
m256 lmlr02 = _mm256_mul_epu32(prodlo, R);
m256 lmlr13 = _mm256_mul_epu32(prodlohi, R);
m256 prod02_ = _mm256_mul_epu32(lmlr02, M1);
m256 prod13_ = _mm256_mul_epu32(lmlr13, M1);
m256 unpalo_ = _mm256_unpacklo_epi32(prod02_, prod13_);
m256 unpahi_ = _mm256_unpackhi_epi32(prod02_, prod13_);
m256 prod = _mm256_unpackhi_epi64(unpalo_, unpahi_);
return _mm256_sub_epi32(hiplm1, prod);
}
static inline mmint itom(const mmint& A) { return A * N2; }
static inline mmint mtoi(const mmint& A) {
m256 A13 = _mm256_shuffle_epi32(A, 0xF5);
m256 lmlr02 = _mm256_mul_epu32(A, R);
m256 lmlr13 = _mm256_mul_epu32(A13, R);
m256 prod02_ = _mm256_mul_epu32(lmlr02, M1);
m256 prod13_ = _mm256_mul_epu32(lmlr13, M1);
m256 unpalo_ = _mm256_unpacklo_epi32(prod02_, prod13_);
m256 unpahi_ = _mm256_unpackhi_epi32(prod02_, prod13_);
m256 prod = _mm256_unpackhi_epi64(unpalo_, unpahi_);
m256 cmp = _mm256_cmpgt_epi32(prod, M0);
m256 dif = _mm256_and_si256(cmp, M1);
return _mm256_sub_epi32(dif, prod);
}
friend inline mmint operator+(const mmint& A, const mmint& B) {
m256 apb = _mm256_add_epi32(A, B);
m256 ret = _mm256_sub_epi32(apb, M2);
m256 cmp = _mm256_cmpgt_epi32(M0, ret);
m256 add = _mm256_and_si256(cmp, M2);
return _mm256_add_epi32(add, ret);
}
friend inline mmint operator-(const mmint& A, const mmint& B) {
m256 ret = _mm256_sub_epi32(A, B);
m256 cmp = _mm256_cmpgt_epi32(M0, ret);
m256 add = _mm256_and_si256(cmp, M2);
return _mm256_add_epi32(add, ret);
}
friend inline mmint operator*(const mmint& A, const mmint& B) {
m256 a13 = _mm256_shuffle_epi32(A, 0xF5);
m256 b13 = _mm256_shuffle_epi32(B, 0xF5);
m256 prod02 = _mm256_mul_epu32(A, B);
m256 prod13 = _mm256_mul_epu32(a13, b13);
return reduce(prod02, prod13);
}
inline mmint& operator+=(const mmint& A) { return (*this) = (*this) + A; }
inline mmint& operator-=(const mmint& A) { return (*this) = (*this) - A; }
inline mmint& operator*=(const mmint& A) { return (*this) = (*this) * A; }
bool operator==(const mmint& A) {
m256 sub = _mm256_sub_epi32(x, A.x);
return _mm256_testz_si256(sub, sub) == 1;
}
bool operator!=(const mmint& A) { return !((*this) == A); }
};
__attribute__((aligned(32))) mmint mmint::R;
__attribute__((aligned(32))) mmint mmint::M0, mmint::M1, mmint::M2, mmint::N2;
/**
* @brief vectorize modint
*/
#line 8 "math-fast/subset-convolution.hpp"
template <typename mint>
vector<mint> fast_multiply(const vector<mint>& a, const vector<mint>& b) {
int n = a.size();
int d = __builtin_ctz(n);
assert(d <= 23);
mmint* a1 = new mmint[max(n, 8) * 3];
mmint* a2 = new mmint[max(n, 8) * 3];
memset((void*)a1, 0, max(n, 8) * 3 * sizeof(mmint));
memset((void*)a2, 0, max(n, 8) * 3 * sizeof(mmint));
mmint b1[24], b2[24], b3[24];
for (int i = 0; i < n; i++) {
unsigned int pc = __builtin_popcount(i);
a1[i * 3 + pc / 8][pc % 8] = a[i].a;
a2[i * 3 + pc / 8][pc % 8] = b[i].a;
}
for (int j = 2; j <= n; j += 2) {
unsigned int pc = __builtin_popcount(j);
unsigned int ctz = __builtin_ctz(j);
for (int h = 0; h < d; h++) {
if (j & (1 << h)) break;
int li = j - 2 * (1 << h), ri = j - (1 << h);
if (pc + ctz <= 16) {
for (int i = 0; i < 3 * (1 << h); i += 3) {
a1[ri * 3 + i + 0] += a1[li * 3 + i + 0];
a2[ri * 3 + i + 0] += a2[li * 3 + i + 0];
a1[ri * 3 + i + 1] += a1[li * 3 + i + 1];
a2[ri * 3 + i + 1] += a2[li * 3 + i + 1];
}
} else {
for (int i = 0; i < 3 * (1 << h); i++) {
a1[ri * 3 + i] += a1[li * 3 + i];
a2[ri * 3 + i] += a2[li * 3 + i];
}
}
}
}
mmint th = _mm256_set1_epi64x(4LL * mmint::M1[0] * mmint::M1[0]);
for (int is = 0; is < n; is += 8) {
int mpc = d;
for (int i = is; i < is + 8; i++) {
int pc = __builtin_popcount(i);
mpc = min(mpc, pc);
for (int j = 0; j <= d; j++) {
b1[j][i - is] = a1[i * 3 + j / 8][j % 8];
b2[j][i - is] = a2[i * 3 + j / 8][j % 8];
b3[j][i - is] = 0;
}
}
for (int j = 0; j <= d; j++) {
m256 cmpB1 = _mm256_cmpgt_epi32(mmint::M1, b1[j]);
m256 cmpB2 = _mm256_cmpgt_epi32(mmint::M1, b2[j]);
m256 difB1 = _mm256_andnot_si256(cmpB1, mmint::M1);
m256 difB2 = _mm256_andnot_si256(cmpB2, mmint::M1);
b1[j] = _mm256_sub_epi32(b1[j], difB1);
b2[j] = _mm256_sub_epi32(b2[j], difB2);
}
#define PROD(k) \
m256 A13##k = _mm256_shuffle_epi32(b1[j + k], 0xF5); \
m256 B13##k = _mm256_shuffle_epi32(b2[l - j - k], 0xF5); \
m256 p02##k = _mm256_mul_epi32(b1[j + k], b2[l - j - k]); \
m256 p13##k = _mm256_mul_epi32(A13##k, B13##k); \
prod02 = _mm256_add_epi64(prod02, p02##k); \
prod13 = _mm256_add_epi64(prod13, p13##k)
#define COMP() \
do { \
m256 cmp02 = _mm256_cmpgt_epi64(prod02, th); \
m256 cmp13 = _mm256_cmpgt_epi64(prod13, th); \
m256 dif02 = _mm256_and_si256(cmp02, th); \
m256 dif13 = _mm256_and_si256(cmp13, th); \
prod02 = _mm256_sub_epi64(prod02, dif02); \
prod13 = _mm256_sub_epi64(prod13, dif13); \
} while (0)
for (int l = mpc; l <= d; l++) {
int j = 0;
mmint prod02 = mmint::M0, prod13 = mmint::M0;
for (; j <= l - 3; j += 4) {
PROD(0);
PROD(1);
PROD(2);
PROD(3);
COMP();
}
for (; j <= l; j++) {
PROD(0);
}
COMP();
b3[l] = mmint::reduce(prod02, prod13);
}
#undef PROD
#undef COMP
for (int i = is; i < is + 8; i++) {
for (unsigned j = mpc; j <= unsigned(d); j++) {
a1[i * 3 + j / 8][j % 8] = b3[j][i - is];
}
}
}
for (int j = 2; j <= n; j += 2) {
for (int h = 0; h < d; h++) {
if (j & (1 << h)) break;
int li = j - 2 * (1 << h), ri = j - (1 << h);
for (int i = 0; i < 3 * (1 << h); i++) {
a1[ri * 3 + i] -= a1[li * 3 + i];
}
}
}
vector<mint> c(n);
for (int i = 0; i < n; i++) {
unsigned int pc = __builtin_popcount(i);
c[i].a = a1[i * 3 + pc / 8][pc % 8];
}
delete[] (a1);
delete[] (a2);
return c;
}
#line 22 "verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp"
//
#line 2 "modint/montgomery-modint.hpp"
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
#line 24 "verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp"
int main() {
using mint = LazyMontgomeryModInt<998244353>;
using vm = vector<mint>;
mmint::set_mod<mint>();
int N;
rd(N);
using vm = vector<mint>;
vm a(1 << N), b(1 << N);
unsigned int n;
for (int i = 0; i < 1 << N; i++) {
rd(n);
a[i].a = mint::reduce(uint64_t(n) * mint::n2);
}
for (int i = 0; i < 1 << N; i++) {
rd(n);
b[i].a = mint::reduce(uint64_t(n) * mint::n2);
}
auto c = fast_multiply(a, b);
for (int i = 0; i < 1 << N; i++) {
if (i) wt(' ');
wt(c[i].get());
}
wt('\n');
}
verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp