#line 2 "fps/formal-power-series.hpp"
template <typename mint>
struct FormalPowerSeries : vector<mint> {
using vector<mint>::vector;
using FPS = FormalPowerSeries;
FPS &operator+=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
return *this;
}
FPS &operator+=(const mint &r) {
if (this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
FPS &operator-=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
return *this;
}
FPS &operator-=(const mint &r) {
if (this->empty()) this->resize(1);
(*this)[0] -= r;
return *this;
}
FPS &operator*=(const mint &v) {
for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
return *this;
}
FPS &operator/=(const FPS &r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
if ((int)r.size() <= 64) {
FPS f(*this), g(r);
g.shrink();
mint coeff = g.back().inverse();
for (auto &x : g) x *= coeff;
int deg = (int)f.size() - (int)g.size() + 1;
int gs = g.size();
FPS quo(deg);
for (int i = deg - 1; i >= 0; i--) {
quo[i] = f[i + gs - 1];
for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
}
*this = quo * coeff;
this->resize(n, mint(0));
return *this;
}
return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
}
FPS &operator%=(const FPS &r) {
*this -= *this / r * r;
shrink();
return *this;
}
FPS operator+(const FPS &r) const { return FPS(*this) += r; }
FPS operator+(const mint &v) const { return FPS(*this) += v; }
FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
FPS operator-(const mint &v) const { return FPS(*this) -= v; }
FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
FPS operator*(const mint &v) const { return FPS(*this) *= v; }
FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
FPS operator-() const {
FPS ret(this->size());
for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
void shrink() {
while (this->size() && this->back() == mint(0)) this->pop_back();
}
FPS rev() const {
FPS ret(*this);
reverse(begin(ret), end(ret));
return ret;
}
FPS dot(FPS r) const {
FPS ret(min(this->size(), r.size()));
for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
// 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
FPS pre(int sz) const {
FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));
if ((int)ret.size() < sz) ret.resize(sz);
return ret;
}
FPS operator>>(int sz) const {
if ((int)this->size() <= sz) return {};
FPS ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
FPS operator<<(int sz) const {
FPS ret(*this);
ret.insert(ret.begin(), sz, mint(0));
return ret;
}
FPS diff() const {
const int n = (int)this->size();
FPS ret(max(0, n - 1));
mint one(1), coeff(1);
for (int i = 1; i < n; i++) {
ret[i - 1] = (*this)[i] * coeff;
coeff += one;
}
return ret;
}
FPS integral() const {
const int n = (int)this->size();
FPS ret(n + 1);
ret[0] = mint(0);
if (n > 0) ret[1] = mint(1);
auto mod = mint::get_mod();
for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
return ret;
}
mint eval(mint x) const {
mint r = 0, w = 1;
for (auto &v : *this) r += w * v, w *= x;
return r;
}
FPS log(int deg = -1) const {
assert(!(*this).empty() && (*this)[0] == mint(1));
if (deg == -1) deg = (int)this->size();
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
FPS pow(int64_t k, int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
if (k == 0) {
FPS ret(deg);
if (deg) ret[0] = 1;
return ret;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != mint(0)) {
mint rev = mint(1) / (*this)[i];
FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
ret *= (*this)[i].pow(k);
ret = (ret << (i * k)).pre(deg);
if ((int)ret.size() < deg) ret.resize(deg, mint(0));
return ret;
}
if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
}
return FPS(deg, mint(0));
}
static void *ntt_ptr;
static void set_fft();
FPS &operator*=(const FPS &r);
void ntt();
void intt();
void ntt_doubling();
static int ntt_pr();
FPS inv(int deg = -1) const;
FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;
/**
* @brief 多項式/形式的冪級数ライブラリ
* @docs docs/fps/formal-power-series.md
*/
#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 2 "modulo/strassen.hpp"
#include <immintrin.h>
//
#line 2 "modint/simd-montgomery.hpp"
#line 4 "modint/simd-montgomery.hpp"
__attribute__((target("sse4.2"))) inline __m128i my128_mullo_epu32(
const __m128i &a, const __m128i &b) {
return _mm_mullo_epi32(a, b);
}
__attribute__((target("sse4.2"))) inline __m128i my128_mulhi_epu32(
const __m128i &a, const __m128i &b) {
__m128i a13 = _mm_shuffle_epi32(a, 0xF5);
__m128i b13 = _mm_shuffle_epi32(b, 0xF5);
__m128i prod02 = _mm_mul_epu32(a, b);
__m128i prod13 = _mm_mul_epu32(a13, b13);
__m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13),
_mm_unpackhi_epi32(prod02, prod13));
return prod;
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_mul_128(
const __m128i &a, const __m128i &b, const __m128i &r, const __m128i &m1) {
return _mm_sub_epi32(
_mm_add_epi32(my128_mulhi_epu32(a, b), m1),
my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1));
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_add_128(
const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
__m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2);
return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_sub_128(
const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
__m128i ret = _mm_sub_epi32(a, b);
return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("avx2"))) inline __m256i my256_mullo_epu32(
const __m256i &a, const __m256i &b) {
return _mm256_mullo_epi32(a, b);
}
__attribute__((target("avx2"))) inline __m256i my256_mulhi_epu32(
const __m256i &a, const __m256i &b) {
__m256i a13 = _mm256_shuffle_epi32(a, 0xF5);
__m256i b13 = _mm256_shuffle_epi32(b, 0xF5);
__m256i prod02 = _mm256_mul_epu32(a, b);
__m256i prod13 = _mm256_mul_epu32(a13, b13);
__m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13),
_mm256_unpackhi_epi32(prod02, prod13));
return prod;
}
__attribute__((target("avx2"))) inline __m256i montgomery_mul_256(
const __m256i &a, const __m256i &b, const __m256i &r, const __m256i &m1) {
return _mm256_sub_epi32(
_mm256_add_epi32(my256_mulhi_epu32(a, b), m1),
my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1));
}
__attribute__((target("avx2"))) inline __m256i montgomery_add_256(
const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
__m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2);
return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
ret);
}
__attribute__((target("avx2"))) inline __m256i montgomery_sub_256(
const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
__m256i ret = _mm256_sub_epi32(a, b);
return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
ret);
}
#line 7 "modulo/strassen.hpp"
namespace FastMatProd {
using mint = LazyMontgomeryModInt<998244353>;
using u32 = uint32_t;
using i32 = int32_t;
using u64 = uint64_t;
using m256 = __m256i;
constexpr u32 SHIFT_ = 6;
u32 a[1 << (SHIFT_ * 2)] __attribute__((aligned(64)));
u32 b[1 << (SHIFT_ * 2)] __attribute__((aligned(64)));
u32 c[1 << (SHIFT_ * 2)] __attribute__((aligned(64)));
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
normalize_m256(const m256& x, const m256& M1) {
m256 CMP = _mm256_cmpgt_epi32(x, M1);
return _mm256_sub_epi32(x, _mm256_and_si256(CMP, M1));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
simd_mulhi(const m256& _a, const m256& _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);
m256 unpalo = _mm256_unpacklo_epi32(prod02, prod13);
m256 unpahi = _mm256_unpackhi_epi32(prod02, prod13);
m256 prod = _mm256_unpackhi_epi64(unpalo, unpahi);
return prod;
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
simd_reduct(const m256& prod02, const m256& prod13, const m256& R,
const m256& M1) {
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 lomulr = _mm256_mullo_epi32(prodlo, R);
m256 lomulrmulm1 = simd_mulhi(lomulr, M1);
return _mm256_sub_epi32(hiplm1, lomulrmulm1);
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
mul4(const m256& A00, const m256& A01, const m256& A02, const m256& A03,
const m256& B00, const m256& B10, const m256& B20, const m256& B30,
const m256& R, const m256& M1) {
const m256 A00n = normalize_m256(A00, M1);
const m256 A01n = normalize_m256(A01, M1);
const m256 A02n = normalize_m256(A02, M1);
const m256 A03n = normalize_m256(A03, M1);
const m256 B00n = normalize_m256(B00, M1);
const m256 B10n = normalize_m256(B10, M1);
const m256 B20n = normalize_m256(B20, M1);
const m256 B30n = normalize_m256(B30, M1);
m256 a013 = _mm256_shuffle_epi32(A00n, 0xF5);
m256 b013 = _mm256_shuffle_epi32(B00n, 0xF5);
m256 a113 = _mm256_shuffle_epi32(A01n, 0xF5);
m256 b113 = _mm256_shuffle_epi32(B10n, 0xF5);
m256 a213 = _mm256_shuffle_epi32(A02n, 0xF5);
m256 b213 = _mm256_shuffle_epi32(B20n, 0xF5);
m256 a313 = _mm256_shuffle_epi32(A03n, 0xF5);
m256 b313 = _mm256_shuffle_epi32(B30n, 0xF5);
m256 p0_02 = _mm256_mul_epu32(A00n, B00n);
m256 p0_13 = _mm256_mul_epu32(a013, b013);
m256 p1_02 = _mm256_mul_epu32(A01n, B10n);
m256 p1_13 = _mm256_mul_epu32(a113, b113);
m256 p2_02 = _mm256_mul_epu32(A02n, B20n);
m256 p2_13 = _mm256_mul_epu32(a213, b213);
m256 p3_02 = _mm256_mul_epu32(A03n, B30n);
m256 p3_13 = _mm256_mul_epu32(a313, b313);
m256 p02_02 = _mm256_add_epi64(p0_02, p2_02);
m256 p13_02 = _mm256_add_epi64(p1_02, p3_02);
m256 prod02 = _mm256_add_epi64(p02_02, p13_02);
m256 p02_13 = _mm256_add_epi64(p0_13, p2_13);
m256 p13_13 = _mm256_add_epi64(p1_13, p3_13);
m256 prod13 = _mm256_add_epi64(p02_13, p13_13);
return simd_reduct(prod02, prod13, R, M1);
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
inner_simd_mul(u32 n, u32 m, u32 p) {
memset(c, 0, sizeof(c));
const m256 R = _mm256_set1_epi32(mint::r);
const m256 M0 = _mm256_set1_epi32(0);
const m256 M1 = _mm256_set1_epi32(mint::get_mod());
const m256 M2 = _mm256_set1_epi32(mint::get_mod() << 1);
u32 k0 = 0;
for (; i32(k0) < i32(p) - 3; k0 += 4) {
const u32 k1 = k0 + 1;
const u32 k2 = k0 + 2;
const u32 k3 = k0 + 3;
u32 j0 = 0;
for (; i32(j0) < i32(m) - 7; j0 += 8) {
const m256 B00 = _mm256_load_si256((m256*)(b + (k0 << SHIFT_) + j0));
const m256 B10 = _mm256_load_si256((m256*)(b + (k1 << SHIFT_) + j0));
const m256 B20 = _mm256_load_si256((m256*)(b + (k2 << SHIFT_) + j0));
const m256 B30 = _mm256_load_si256((m256*)(b + (k3 << SHIFT_) + j0));
for (u32 i0 = 0; i0 < n; ++i0) {
const m256 A00 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k0]);
const m256 A01 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k1]);
const m256 A02 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k2]);
const m256 A03 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k3]);
const u32* pc00 = c + (i0 << SHIFT_) + j0;
const m256 C00 = _mm256_load_si256((m256*)pc00);
const m256 C00_ad = mul4(A00, A01, A02, A03, B00, B10, B20, B30, R, M1);
const m256 C00sum = montgomery_add_256(C00, C00_ad, M2, M0);
_mm256_store_si256((m256*)pc00, C00sum);
}
}
for (; j0 < m; j0++) {
for (u32 i0 = 0; i0 < n; ++i0) {
u32 ab0 =
mint::reduce(u64(a[(i0 << SHIFT_) | k0]) * b[(k0 << SHIFT_) | j0]);
u32 ab1 =
mint::reduce(u64(a[(i0 << SHIFT_) | k1]) * b[(k1 << SHIFT_) | j0]);
u32 ab2 =
mint::reduce(u64(a[(i0 << SHIFT_) | k2]) * b[(k2 << SHIFT_) | j0]);
u32 ab3 =
mint::reduce(u64(a[(i0 << SHIFT_) | k3]) * b[(k3 << SHIFT_) | j0]);
if ((ab0 += ab1) >= 2 * mint::get_mod()) ab0 -= 2 * mint::get_mod();
if ((ab2 += ab3) >= 2 * mint::get_mod()) ab2 -= 2 * mint::get_mod();
if ((ab0 += ab2) >= 2 * mint::get_mod()) ab0 -= 2 * mint::get_mod();
if ((c[(i0 << SHIFT_) | j0] += ab0) >= 2 * mint::get_mod())
c[(i0 << SHIFT_) | j0] -= 2 * mint::get_mod();
}
}
}
for (; k0 < p; k0++) {
u32 j0 = 0;
for (; i32(j0) < i32(m) - 7; j0 += 8) {
const m256 B00 = _mm256_load_si256((m256*)(b + (k0 << SHIFT_) + j0));
for (u32 i0 = 0; i0 < n; ++i0) {
const m256 A00 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k0]);
const m256 A00B00 = montgomery_mul_256(A00, B00, R, M1);
const u32* pc00 = c + (i0 << SHIFT_) + j0;
const m256 C00 = _mm256_load_si256((m256*)pc00);
const m256 C00_ad = montgomery_add_256(C00, A00B00, M2, M0);
_mm256_store_si256((m256*)pc00, C00_ad);
}
}
for (; j0 < m; j0++) {
for (u32 i0 = 0; i0 < n; ++i0) {
u32 ab0 =
mint::reduce(u64(a[(i0 << SHIFT_) | k0]) * b[(k0 << SHIFT_) | j0]);
if ((c[(i0 << SHIFT_) | j0] += ab0) >= 2 * mint::get_mod())
c[(i0 << SHIFT_) | j0] -= 2 * mint::get_mod();
}
}
}
}
struct Mat {
int H, W, HM, WM;
mint* a;
Mat(int H_, int W_, mint* a_) : H(H_), W(W_), a(a_) {
HM = (H >> 1) + (H & 1);
WM = (W >> 1) + (W & 1);
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
range_add(mint* _b, int as, int ae, int bs) const {
const m256 M0 = _mm256_set1_epi32(0);
const m256 M2 = _mm256_set1_epi32(mint::get_mod() * 2);
for (; as < ae - 31; as += 32, bs += 32) {
int a0 = as;
int a1 = as + 8;
int a2 = as + 16;
int a3 = as + 24;
int b0 = bs;
int b1 = bs + 8;
int b2 = bs + 16;
int b3 = bs + 24;
const m256 A0 = _mm256_loadu_si256((m256*)(a + a0));
const m256 A1 = _mm256_loadu_si256((m256*)(a + a1));
const m256 A2 = _mm256_loadu_si256((m256*)(a + a2));
const m256 A3 = _mm256_loadu_si256((m256*)(a + a3));
const m256 B0 = _mm256_loadu_si256((m256*)(_b + b0));
const m256 B1 = _mm256_loadu_si256((m256*)(_b + b1));
const m256 B2 = _mm256_loadu_si256((m256*)(_b + b2));
const m256 B3 = _mm256_loadu_si256((m256*)(_b + b3));
const m256 BA0 = montgomery_add_256(B0, A0, M2, M0);
const m256 BA1 = montgomery_add_256(B1, A1, M2, M0);
const m256 BA2 = montgomery_add_256(B2, A2, M2, M0);
const m256 BA3 = montgomery_add_256(B3, A3, M2, M0);
_mm256_storeu_si256((m256*)(_b + b0), BA0);
_mm256_storeu_si256((m256*)(_b + b1), BA1);
_mm256_storeu_si256((m256*)(_b + b2), BA2);
_mm256_storeu_si256((m256*)(_b + b3), BA3);
}
for (; as < ae; ++as, ++bs) _b[bs] += a[as];
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
range_sub(mint* _b, int as, int ae, int bs) const {
const m256 M0 = _mm256_set1_epi32(0);
const m256 M2 = _mm256_set1_epi32(mint::get_mod() * 2);
for (; as < ae - 31; as += 32, bs += 32) {
int a0 = as;
int a1 = as + 8;
int a2 = as + 16;
int a3 = as + 24;
int b0 = bs;
int b1 = bs + 8;
int b2 = bs + 16;
int b3 = bs + 24;
const m256 A0 = _mm256_loadu_si256((m256*)(a + a0));
const m256 A1 = _mm256_loadu_si256((m256*)(a + a1));
const m256 A2 = _mm256_loadu_si256((m256*)(a + a2));
const m256 A3 = _mm256_loadu_si256((m256*)(a + a3));
const m256 B0 = _mm256_loadu_si256((m256*)(_b + b0));
const m256 B1 = _mm256_loadu_si256((m256*)(_b + b1));
const m256 B2 = _mm256_loadu_si256((m256*)(_b + b2));
const m256 B3 = _mm256_loadu_si256((m256*)(_b + b3));
const m256 BA0 = montgomery_sub_256(B0, A0, M2, M0);
const m256 BA1 = montgomery_sub_256(B1, A1, M2, M0);
const m256 BA2 = montgomery_sub_256(B2, A2, M2, M0);
const m256 BA3 = montgomery_sub_256(B3, A3, M2, M0);
_mm256_storeu_si256((m256*)(_b + b0), BA0);
_mm256_storeu_si256((m256*)(_b + b1), BA1);
_mm256_storeu_si256((m256*)(_b + b2), BA2);
_mm256_storeu_si256((m256*)(_b + b3), BA3);
}
for (; as < ae; ++as, ++bs) _b[bs] -= a[as];
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
op_range_add(mint* _b, int as, int ae, int bs) const {
const m256 M0 = _mm256_set1_epi32(0);
const m256 M2 = _mm256_set1_epi32(mint::get_mod() * 2);
for (; as < ae - 31; as += 32, bs += 32) {
int a0 = as;
int a1 = as + 8;
int a2 = as + 16;
int a3 = as + 24;
int b0 = bs;
int b1 = bs + 8;
int b2 = bs + 16;
int b3 = bs + 24;
const m256 A0 = _mm256_loadu_si256((m256*)(a + a0));
const m256 A1 = _mm256_loadu_si256((m256*)(a + a1));
const m256 A2 = _mm256_loadu_si256((m256*)(a + a2));
const m256 A3 = _mm256_loadu_si256((m256*)(a + a3));
const m256 B0 = _mm256_loadu_si256((m256*)(_b + b0));
const m256 B1 = _mm256_loadu_si256((m256*)(_b + b1));
const m256 B2 = _mm256_loadu_si256((m256*)(_b + b2));
const m256 B3 = _mm256_loadu_si256((m256*)(_b + b3));
const m256 BA0 = montgomery_add_256(B0, A0, M2, M0);
const m256 BA1 = montgomery_add_256(B1, A1, M2, M0);
const m256 BA2 = montgomery_add_256(B2, A2, M2, M0);
const m256 BA3 = montgomery_add_256(B3, A3, M2, M0);
_mm256_storeu_si256((m256*)(a + a0), BA0);
_mm256_storeu_si256((m256*)(a + a1), BA1);
_mm256_storeu_si256((m256*)(a + a2), BA2);
_mm256_storeu_si256((m256*)(a + a3), BA3);
}
for (; as < ae; ++as, ++bs) a[as] += _b[bs];
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
op_range_sub(mint* _b, int as, int ae, int bs) const {
const m256 M0 = _mm256_set1_epi32(0);
const m256 M2 = _mm256_set1_epi32(mint::get_mod() * 2);
for (; as < ae - 31; as += 32, bs += 32) {
int a0 = as;
int a1 = as + 8;
int a2 = as + 16;
int a3 = as + 24;
int b0 = bs;
int b1 = bs + 8;
int b2 = bs + 16;
int b3 = bs + 24;
const m256 A0 = _mm256_loadu_si256((m256*)(a + a0));
const m256 A1 = _mm256_loadu_si256((m256*)(a + a1));
const m256 A2 = _mm256_loadu_si256((m256*)(a + a2));
const m256 A3 = _mm256_loadu_si256((m256*)(a + a3));
const m256 B0 = _mm256_loadu_si256((m256*)(_b + b0));
const m256 B1 = _mm256_loadu_si256((m256*)(_b + b1));
const m256 B2 = _mm256_loadu_si256((m256*)(_b + b2));
const m256 B3 = _mm256_loadu_si256((m256*)(_b + b3));
const m256 BA0 = montgomery_sub_256(A0, B0, M2, M0);
const m256 BA1 = montgomery_sub_256(A1, B1, M2, M0);
const m256 BA2 = montgomery_sub_256(A2, B2, M2, M0);
const m256 BA3 = montgomery_sub_256(A3, B3, M2, M0);
_mm256_storeu_si256((m256*)(a + a0), BA0);
_mm256_storeu_si256((m256*)(a + a1), BA1);
_mm256_storeu_si256((m256*)(a + a2), BA2);
_mm256_storeu_si256((m256*)(a + a3), BA3);
}
for (; as < ae; ++as, ++bs) a[as] -= _b[bs];
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
A11(mint* _b) const {
for (int i = 0; i < HM; i++)
memcpy(_b + i * WM, a + i * W, WM * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
A12(mint* _b) const {
for (int i = 0; i < HM; i++)
memcpy(_b + i * WM, a + i * W + WM, (W - WM) * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
A21(mint* _b) const {
for (int i = 0; i < H - HM; i++)
memcpy(_b + i * WM, a + (i + HM) * W, WM * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
A22(mint* _b) const {
for (int i = 0; i < H - HM; i++)
memcpy(_b + i * WM, a + (i + HM) * W + WM, (W - WM) * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
subA11(mint* _b) const {
for (int i = 0; i < HM; i++) {
int as = i * W;
int ae = i * W + WM;
int bs = i * WM;
range_sub(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
addA12(mint* _b) const {
for (int i = 0; i < HM; i++) {
int as = i * W + WM;
int ae = i * W + W;
int bs = i * WM;
range_add(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
addA22(mint* _b) const {
for (int i = 0; i < H - HM; i++) {
int as = (i + HM) * W + WM;
int ae = as + W - WM;
int bs = i * WM;
range_add(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
subA22(mint* _b) const {
for (int i = 0; i < H - HM; i++) {
int as = (i + HM) * W + WM;
int ae = as + W - WM;
int bs = i * WM;
range_sub(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
updA11(mint* _b) const {
for (int i = 0; i < HM; i++)
memcpy(a + i * W, _b + i * WM, WM * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
updA12(mint* _b) const {
for (int i = 0; i < HM; i++)
memcpy(a + i * W + WM, _b + i * WM, (W - WM) * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
updA21(mint* _b) const {
for (int i = 0; i < H - HM; i++)
memcpy(a + (i + HM) * W, _b + i * WM, WM * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
updA22(mint* _b) const {
for (int i = 0; i < H - HM; i++)
memcpy(a + (i + HM) * W + WM, _b + i * WM, (W - WM) * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
opaddA11(mint* _b) const {
for (int i = 0; i < HM; i++) {
int as = i * W;
int ae = i * W + WM;
int bs = i * WM;
op_range_add(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
opaddA12(mint* _b) const {
for (int i = 0; i < HM; i++) {
int as = i * W + WM;
int ae = i * W + W;
int bs = i * WM;
op_range_add(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
opaddA21(mint* _b) const {
for (int i = 0; i < H - HM; i++) {
int as = (i + HM) * W;
int ae = (i + HM) * W + WM;
int bs = i * WM;
op_range_add(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
opaddA22(mint* _b) const {
for (int i = 0; i < H - HM; i++) {
int as = (i + HM) * W + WM;
int ae = (i + HM) * W + W;
int bs = i * WM;
op_range_add(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
opsubA11(mint* _b) const {
for (int i = 0; i < HM; i++) {
int as = i * W;
int ae = i * W + WM;
int bs = i * WM;
op_range_sub(_b, as, ae, bs);
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
opsubA22(mint* _b) const {
for (int i = 0; i < H - HM; i++) {
int as = (i + HM) * W + WM;
int ae = (i + HM) * W + W;
int bs = i * WM;
op_range_sub(_b, as, ae, bs);
}
}
void dump() const {
cerr << "[ " << endl << " ";
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++)
cerr << a[i * W + j] << (j == W - 1 ? ",\n " : " ");
cerr << "] " << endl;
}
};
#ifndef BUFFER_SIZE
#define BUFFER_SIZE (1 << 23)
#endif
mint A[BUFFER_SIZE] __attribute__((aligned(64)));
mint B[BUFFER_SIZE] __attribute__((aligned(64)));
mint C[BUFFER_SIZE] __attribute__((aligned(64)));
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
inner_fast_mul(const Mat* s, const Mat* t, const Mat* u) {
int n = s->H, m = t->W, p = s->W;
for (int i = 0; i < n; i++)
memcpy((mint*)(a + (i << SHIFT_)), s->a + i * p, p * sizeof(int));
for (int i = 0; i < p; i++)
memcpy((mint*)(b + (i << SHIFT_)), t->a + i * m, m * sizeof(int));
inner_simd_mul(n, m, p);
for (int i = 0; i < n; i++)
memcpy(u->a + i * m, (mint*)(c + (i << SHIFT_)), m * sizeof(int));
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
inner_block_dec_mul(const Mat* s, const Mat* t, const Mat* u) {
int n = s->H, m = t->W, p = s->W;
memset((int*)(u->a), 0, n * m * sizeof(int));
for (int is = 0; is < n; is += (1 << SHIFT_))
for (int ks = 0; ks < p; ks += (1 << SHIFT_))
for (int js = 0; js < m; js += (1 << SHIFT_)) {
int ie = min(is + (1 << SHIFT_), n);
int je = min(js + (1 << SHIFT_), m);
int ke = min(ks + (1 << SHIFT_), p);
for (int l = is; l < ie; l++)
memcpy((mint*)(a + ((l - is) << SHIFT_)), s->a + l * p + ks,
(ke - ks) * sizeof(int));
for (int l = ks; l < ke; l++)
memcpy((mint*)(b + ((l - ks) << SHIFT_)), t->a + l * m + js,
(je - js) * sizeof(int));
inner_simd_mul(ie - is, je - js, ke - ks);
for (int l = is; l < ie; l++) {
for (int ll = js; ll < je; ll++) {
u->a[l * m + ll] +=
*reinterpret_cast<mint*>(c + ((l - is) << SHIFT_) + (ll - js));
}
}
}
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
inner_strassen(const Mat* _a, const Mat* _b, const Mat* _c) {
int n = _a->H, m = _b->W, p = _a->W;
if (max({n, m, p}) <= (1 << SHIFT_)) {
inner_fast_mul(_a, _b, _c);
return;
}
if (min({n, m, p}) <= (1 << (SHIFT_ - 2))) {
inner_block_dec_mul(_a, _b, _c);
return;
}
int nm = n / 2 + (n & 1);
int mm = m / 2 + (m & 1);
int pm = p / 2 + (p & 1);
Mat s(nm, pm, _a->a + n * p);
Mat t(pm, mm, _b->a + p * m);
Mat u(nm, mm, _c->a + n * m);
// P1 = (A11 + A22) * (B11 + B22)
_a->A11(s.a);
_a->addA22(s.a);
_b->A11(t.a);
_b->addA22(t.a);
inner_strassen(&s, &t, &u);
_c->updA11(u.a);
_c->updA22(u.a);
// P2 = (A21 + A22) * B11
memset((int*)s.a, 0, nm * pm * sizeof(int));
_a->A21(s.a);
_a->addA22(s.a);
_b->A11(t.a);
inner_strassen(&s, &t, &u);
_c->updA21(u.a);
_c->opsubA22(u.a);
// P3 = A11 (B12 - B22)
_a->A11(s.a);
memset((int*)t.a, 0, pm * mm * sizeof(int));
_b->A12(t.a);
_b->subA22(t.a);
inner_strassen(&s, &t, &u);
_c->updA12(u.a);
_c->opaddA22(u.a);
// P4 = A22 (B21 - B11)
memset((int*)s.a, 0, nm * pm * sizeof(int));
_a->A22(s.a);
memset((int*)t.a + (pm - 1) * mm, 0, mm * sizeof(int));
_b->A21(t.a);
_b->subA11(t.a);
inner_strassen(&s, &t, &u);
_c->opaddA11(u.a);
_c->opaddA21(u.a);
// P5 = (A11 + A12) B22
memset((int*)t.a, 0, pm * mm * sizeof(int));
_a->A11(s.a);
_a->addA12(s.a);
_b->A22(t.a);
inner_strassen(&s, &t, &u);
_c->opsubA11(u.a);
_c->opaddA12(u.a);
// P6 = (A21 - A11) (B11 + B12)
memset((int*)s.a + (nm - 1) * pm, 0, pm * sizeof(int));
_a->A21(s.a);
_a->subA11(s.a);
_b->A11(t.a);
_b->addA12(t.a);
inner_strassen(&s, &t, &u);
_c->opaddA22(u.a);
// P7 = (A12 - A22) (B21 + B22)
memset((int*)s.a, 0, nm * pm * sizeof(int));
_a->A12(s.a);
_a->subA22(s.a);
memset((int*)t.a + (pm - 1) * mm, 0, mm * sizeof(int));
_b->A21(t.a);
_b->addA22(t.a);
inner_strassen(&s, &t, &u);
_c->opaddA11(u.a);
}
template <typename fps>
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) vector<fps>
block_dec(const vector<fps>& s, const vector<fps>& t) {
int n = s.size(), p = s[0].size(), m = t[0].size();
assert(int(n * p * 1.4) <= BUFFER_SIZE);
assert(int(p * m * 1.4) <= BUFFER_SIZE);
assert(int(n * m * 1.4) <= BUFFER_SIZE);
memset(A, 0, int(n * p * 1.4) * sizeof(int));
memset(B, 0, int(p * m * 1.4) * sizeof(int));
memset(C, 0, int(m * n * 1.4) * sizeof(int));
for (int i = 0; i < n; i++) memcpy(A + i * p, s[i].data(), p * sizeof(int));
for (int i = 0; i < p; i++) memcpy(B + i * m, t[i].data(), m * sizeof(int));
Mat S(n, p, A), T(p, m, B), U(n, m, C);
inner_block_dec_mul(&S, &T, &U);
vector<fps> u(n, fps(m));
for (int i = 0; i < n; i++) memcpy(u[i].data(), C + i * m, m * sizeof(int));
return std::move(u);
}
template <typename fps>
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) vector<fps>
strassen(const vector<fps>& s, const vector<fps>& t) {
int n = s.size(), p = s[0].size(), m = t[0].size();
assert(int(n * p * 1.4) <= BUFFER_SIZE);
assert(int(p * m * 1.4) <= BUFFER_SIZE);
assert(int(n * m * 1.4) <= BUFFER_SIZE);
memset(A, 0, int(n * p * 1.4) * sizeof(int));
memset(B, 0, int(p * m * 1.4) * sizeof(int));
memset(C, 0, int(m * n * 1.4) * sizeof(int));
for (int i = 0; i < n; i++) memcpy(A + i * p, s[i].data(), p * sizeof(int));
for (int i = 0; i < p; i++) memcpy(B + i * m, t[i].data(), m * sizeof(int));
Mat S(n, p, A), T(p, m, B), U(n, m, C);
inner_strassen(&S, &T, &U);
vector<fps> u(n, fps(m));
for (int i = 0; i < n; i++) memcpy(u[i].data(), C + i * m, m * sizeof(int));
return std::move(u);
}
#ifdef BUFFER_SIZE
#undef BUFFER_SIZE
#endif
} // namespace FastMatProd
#line 5 "fps/fps-composition-fast-old.hpp"
using mint = LazyMontgomeryModInt<998244353>;
using fps = FormalPowerSeries<mint>;
// Q(P(x))
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) fps Composition(
fps P, fps Q, int deg = -1) {
int N = (deg == -1) ? min(P.size(), Q.size()) : deg;
if (N == 0) return fps{};
P.shrink();
if (P.size() == 0) {
fps R(N, mint(0));
R[0] = Q.empty() ? mint(0) : Q[0];
return R;
}
if (N == 1) return fps{Q.eval(P[0])};
P.resize(N);
int K = max<int>(ceil(sqrt(N)), 2);
assert(N <= K * K);
vector<fps> PS(K + 1);
{
// step 1
PS[0].resize(N, mint());
PS[0][0] = 1;
PS[1] = P;
fps::set_fft();
if (fps::ntt_ptr == nullptr) {
for (int i = 2; i <= K; i++) PS[i] = (PS[i - 1] * P).pre(N);
} else {
int len = 1 << (32 - __builtin_clz(2 * N - 2));
fps Pomega = P;
Pomega.resize(len);
Pomega.ntt();
for (int i = 2; i <= K; i++) {
PS[i].resize(len);
for (int j = 0; j < N; j++) PS[i][j] = PS[i - 1][j];
PS[i].ntt();
for (int j = 0; j < len; j++) PS[i][j] *= Pomega[j];
PS[i].intt();
PS[i].resize(N);
PS[i].shrink_to_fit();
}
}
}
vector<fps> TS(K);
{
// step 2
TS[0].resize(N, mint());
TS[0][0] = 1;
TS[1] = PS[K];
if (fps::ntt_ptr == nullptr) {
for (int i = 2; i < K; i++) TS[i] = (TS[i - 1] * TS[1]).pre(N);
} else {
int len = 1 << (32 - __builtin_clz(2 * N - 2));
fps Tomega = TS[1];
Tomega.resize(len);
Tomega.ntt();
for (int i = 2; i < K; i++) {
TS[i].resize(len);
for (int j = 0; j < N; j++) TS[i][j] = TS[i - 1][j];
TS[i].ntt();
for (int j = 0; j < len; j++) TS[i][j] *= Tomega[j];
TS[i].intt();
TS[i].resize(N);
TS[i].shrink_to_fit();
}
}
}
// step 3
vector<fps> QP;
{
PS.pop_back();
vector<fps> QS(K, fps(K, mint()));
for (int i = 0; i < K; i++)
for (int j = 0; j < K; j++) {
QS[i][j] = (i * K + j) < (int)Q.size() ? Q[i * K + j] : mint();
}
QP = FastMatProd::strassen(QS, PS);
}
fps ans(N, mint());
{
// step 4,5
for (int i = 0; i < K; i++) ans += (QP[i] * TS[i]).pre(N);
}
return ans;
}
/**
* @brief 関数の合成( $\mathrm{O}(N^2)$ )
*/
関数の合成( $\mathrm{O}(N^2)$ )