#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod" #include <immintrin.h> // #include "../../template/template.hpp" #include "../../misc/fastio.hpp" #include "../../modint/montgomery-modint.hpp" #include "../../ntt/ntt-avx2.hpp" NTT<LazyMontgomeryModInt<998244353>> ntt; using namespace Nyaan; void Nyaan::solve() { using namespace ntt_inner; int N, M; rd(N, M); for (int i = 0; i < N; i++) { int n; rd(n); _buf1[i] = n; } for (int i = 0; i < M; i++) { int n; rd(n); _buf2[i] = n; } ntt.inplace_multiply(N, M, false); int len = N + M - 1; for (int i = 0; i < len; i++) { if (i) wt(' '); wt(_buf1[i]); } wt('\n'); }
#line 1 "verify/verify-yosupo-ntt/yosupo-inliner-multiply.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod" #include <immintrin.h> // #line 2 "template/template.hpp" using namespace std; // intrinstic #line 6 "template/template.hpp" #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template <typename S> P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T> int sz(const T &t) { return t.size(); } template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), 0LL); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(vector<T> &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } } // namespace Nyaan #line 58 "template/template.hpp" // bit operation #line 1 "template/bitop.hpp" namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan #line 61 "template/template.hpp" // inout #line 1 "template/inout.hpp" namespace Nyaan { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template <typename T, class... U> void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" // debug #line 1 "template/debug.hpp" namespace DebugImpl { template <typename U, typename = void> struct is_specialize : false_type {}; template <typename U> struct is_specialize< U, typename conditional<false, typename U::iterator, void>::type> : true_type {}; template <typename U> struct is_specialize< U, typename conditional<false, decltype(U::first), void>::type> : true_type {}; template <typename U> struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template <typename U, enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template <typename T> void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template <typename T, typename U> void dump(const pair<T, U>&); template <typename T> void dump(const pair<T*, int>&); template <typename T> void dump(const T& t, enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template <typename T, typename U> void dump(const pair<T, U>& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template <typename T> void dump(const pair<T*, int>& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template <typename Head, typename... Tail> void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward<Tail>(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" // macro #line 1 "template/macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) #line 70 "template/template.hpp" namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } #line 2 "misc/fastio.hpp" #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(forward<const Tail>(tail)...); } template <typename... Args> void wtn(const Args&... x) { wt(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 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 "ntt/ntt-avx2.hpp" #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 4 "ntt/ntt-avx2.hpp" namespace ntt_inner { using u64 = uint64_t; constexpr uint32_t get_pr(uint32_t mod) { if (mod == 2) return 1; u64 ds[32] = {}; int idx = 0; u64 m = mod - 1; for (u64 i = 2; i * i <= m; ++i) { if (m % i == 0) { ds[idx++] = i; while (m % i == 0) m /= i; } } if (m != 1) ds[idx++] = m; uint32_t pr = 2; while (1) { int flg = 1; for (int i = 0; i < idx; ++i) { u64 a = pr, b = (mod - 1) / ds[i], r = 1; while (b) { if (b & 1) r = r * a % mod; a = a * a % mod; b >>= 1; } if (r == 1) { flg = 0; break; } } if (flg == 1) break; ++pr; } return pr; } constexpr int SZ_FFT_BUF = 1 << 23; uint32_t _buf1[SZ_FFT_BUF] __attribute__((aligned(64))); uint32_t _buf2[SZ_FFT_BUF] __attribute__((aligned(64))); } // namespace ntt_inner template <typename mint> struct NTT { static constexpr uint32_t mod = mint::get_mod(); static constexpr uint32_t pr = ntt_inner::get_pr(mint::get_mod()); static constexpr int level = __builtin_ctzll(mod - 1); mint dw[level], dy[level]; mint *buf1, *buf2; constexpr NTT() { setwy(level); union raw_cast { mint dat; uint32_t _; }; buf1 = &(((raw_cast *)(ntt_inner::_buf1))->dat); buf2 = &(((raw_cast *)(ntt_inner::_buf2))->dat); } constexpr void setwy(int k) { mint w[level], y[level]; w[k - 1] = mint(pr).pow((mod - 1) / (1 << k)); y[k - 1] = w[k - 1].inverse(); for (int i = k - 2; i > 0; --i) w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1]; dw[0] = dy[0] = w[1] * w[1]; dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2]; for (int i = 3; i < k; ++i) { dw[i] = dw[i - 1] * y[i - 2] * w[i]; dy[i] = dy[i - 1] * w[i - 2] * y[i]; } } __attribute__((target("avx2"))) void ntt(mint *a, int n) { int k = n ? __builtin_ctz(n) : 0; if (k == 0) return; if (k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } if (k & 1) { int v = 1 << (k - 1); if (v < 8) { for (int j = 0; j < v; ++j) { mint ajv = a[j + v]; a[j + v] = a[j] - ajv; a[j] += ajv; } } else { const __m256i m0 = _mm256_set1_epi32(0); const __m256i m2 = _mm256_set1_epi32(mod + mod); int j0 = 0; int j1 = v; for (; j0 < v; j0 += 8, j1 += 8) { __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0)); __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1)); __m256i naj = montgomery_add_256(T0, T1, m2, m0); __m256i najv = montgomery_sub_256(T0, T1, m2, m0); _mm256_storeu_si256((__m256i *)(a + j0), naj); _mm256_storeu_si256((__m256i *)(a + j1), najv); } } } int u = 1 << (2 + (k & 1)); int v = 1 << (k - 2 - (k & 1)); mint one = mint(1); mint imag = dw[1]; while (v) { if (v == 1) { mint ww = one, xx = one, wx = one; for (int jh = 0; jh < u;) { ww = xx * xx, wx = ww * xx; mint t0 = a[jh + 0], t1 = a[jh + 1] * xx; mint t2 = a[jh + 2] * ww, t3 = a[jh + 3] * wx; mint t0p2 = t0 + t2, t1p3 = t1 + t3; mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag; a[jh + 0] = t0p2 + t1p3, a[jh + 1] = t0p2 - t1p3; a[jh + 2] = t0m2 + t1m3, a[jh + 3] = t0m2 - t1m3; xx *= dw[__builtin_ctz((jh += 4))]; } } else if (v == 4) { const __m128i m0 = _mm_set1_epi32(0); const __m128i m1 = _mm_set1_epi32(mod); const __m128i m2 = _mm_set1_epi32(mod + mod); const __m128i r = _mm_set1_epi32(mint::r); const __m128i Imag = _mm_set1_epi32(imag.a); mint ww = one, xx = one, wx = one; for (int jh = 0; jh < u;) { if (jh == 0) { int j0 = 0; int j1 = v; int j2 = j1 + v; int j3 = j2 + v; int je = v; for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) { const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0)); const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1)); const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2)); const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3)); const __m128i T0P2 = montgomery_add_128(T0, T2, m2, m0); const __m128i T1P3 = montgomery_add_128(T1, T3, m2, m0); const __m128i T0M2 = montgomery_sub_128(T0, T2, m2, m0); const __m128i T1M3 = montgomery_mul_128( montgomery_sub_128(T1, T3, m2, m0), Imag, r, m1); _mm_storeu_si128((__m128i *)(a + j0), montgomery_add_128(T0P2, T1P3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j1), montgomery_sub_128(T0P2, T1P3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j2), montgomery_add_128(T0M2, T1M3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j3), montgomery_sub_128(T0M2, T1M3, m2, m0)); } } else { ww = xx * xx, wx = ww * xx; const __m128i WW = _mm_set1_epi32(ww.a); const __m128i WX = _mm_set1_epi32(wx.a); const __m128i XX = _mm_set1_epi32(xx.a); int j0 = jh * v; int j1 = j0 + v; int j2 = j1 + v; int j3 = j2 + v; int je = j1; for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) { const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0)); const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1)); const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2)); const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3)); const __m128i MT1 = montgomery_mul_128(T1, XX, r, m1); const __m128i MT2 = montgomery_mul_128(T2, WW, r, m1); const __m128i MT3 = montgomery_mul_128(T3, WX, r, m1); const __m128i T0P2 = montgomery_add_128(T0, MT2, m2, m0); const __m128i T1P3 = montgomery_add_128(MT1, MT3, m2, m0); const __m128i T0M2 = montgomery_sub_128(T0, MT2, m2, m0); const __m128i T1M3 = montgomery_mul_128( montgomery_sub_128(MT1, MT3, m2, m0), Imag, r, m1); _mm_storeu_si128((__m128i *)(a + j0), montgomery_add_128(T0P2, T1P3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j1), montgomery_sub_128(T0P2, T1P3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j2), montgomery_add_128(T0M2, T1M3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j3), montgomery_sub_128(T0M2, T1M3, m2, m0)); } } xx *= dw[__builtin_ctz((jh += 4))]; } } else { const __m256i m0 = _mm256_set1_epi32(0); const __m256i m1 = _mm256_set1_epi32(mod); const __m256i m2 = _mm256_set1_epi32(mod + mod); const __m256i r = _mm256_set1_epi32(mint::r); const __m256i Imag = _mm256_set1_epi32(imag.a); mint ww = one, xx = one, wx = one; for (int jh = 0; jh < u;) { if (jh == 0) { int j0 = 0; int j1 = v; int j2 = j1 + v; int j3 = j2 + v; int je = v; for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1)); const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2)); const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3)); const __m256i T0P2 = montgomery_add_256(T0, T2, m2, m0); const __m256i T1P3 = montgomery_add_256(T1, T3, m2, m0); const __m256i T0M2 = montgomery_sub_256(T0, T2, m2, m0); const __m256i T1M3 = montgomery_mul_256( montgomery_sub_256(T1, T3, m2, m0), Imag, r, m1); _mm256_storeu_si256((__m256i *)(a + j0), montgomery_add_256(T0P2, T1P3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j1), montgomery_sub_256(T0P2, T1P3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j2), montgomery_add_256(T0M2, T1M3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j3), montgomery_sub_256(T0M2, T1M3, m2, m0)); } } else { ww = xx * xx, wx = ww * xx; const __m256i WW = _mm256_set1_epi32(ww.a); const __m256i WX = _mm256_set1_epi32(wx.a); const __m256i XX = _mm256_set1_epi32(xx.a); int j0 = jh * v; int j1 = j0 + v; int j2 = j1 + v; int j3 = j2 + v; int je = j1; for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1)); const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2)); const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3)); const __m256i MT1 = montgomery_mul_256(T1, XX, r, m1); const __m256i MT2 = montgomery_mul_256(T2, WW, r, m1); const __m256i MT3 = montgomery_mul_256(T3, WX, r, m1); const __m256i T0P2 = montgomery_add_256(T0, MT2, m2, m0); const __m256i T1P3 = montgomery_add_256(MT1, MT3, m2, m0); const __m256i T0M2 = montgomery_sub_256(T0, MT2, m2, m0); const __m256i T1M3 = montgomery_mul_256( montgomery_sub_256(MT1, MT3, m2, m0), Imag, r, m1); _mm256_storeu_si256((__m256i *)(a + j0), montgomery_add_256(T0P2, T1P3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j1), montgomery_sub_256(T0P2, T1P3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j2), montgomery_add_256(T0M2, T1M3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j3), montgomery_sub_256(T0M2, T1M3, m2, m0)); } } xx *= dw[__builtin_ctz((jh += 4))]; } } u <<= 2; v >>= 2; } } __attribute__((target("avx2"))) void intt(mint *a, int n, int normalize = true) { int k = n ? __builtin_ctz(n) : 0; if (k == 0) return; if (k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; if (normalize) { a[0] *= mint(2).inverse(); a[1] *= mint(2).inverse(); } return; } int u = 1 << (k - 2); int v = 1; mint one = mint(1); mint imag = dy[1]; while (u) { if (v == 1) { mint ww = one, xx = one, yy = one; u <<= 2; for (int jh = 0; jh < u;) { ww = xx * xx, yy = xx * imag; mint t0 = a[jh + 0], t1 = a[jh + 1]; mint t2 = a[jh + 2], t3 = a[jh + 3]; mint t0p1 = t0 + t1, t2p3 = t2 + t3; mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy; a[jh + 0] = t0p1 + t2p3, a[jh + 2] = (t0p1 - t2p3) * ww; a[jh + 1] = t0m1 + t2m3, a[jh + 3] = (t0m1 - t2m3) * ww; xx *= dy[__builtin_ctz(jh += 4)]; } } else if (v == 4) { const __m128i m0 = _mm_set1_epi32(0); const __m128i m1 = _mm_set1_epi32(mod); const __m128i m2 = _mm_set1_epi32(mod + mod); const __m128i r = _mm_set1_epi32(mint::r); const __m128i Imag = _mm_set1_epi32(imag.a); mint ww = one, xx = one, yy = one; u <<= 2; for (int jh = 0; jh < u;) { if (jh == 0) { int j0 = 0; int j1 = v; int j2 = v + v; int j3 = j2 + v; for (; j0 < v; j0 += 4, j1 += 4, j2 += 4, j3 += 4) { const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0)); const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1)); const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2)); const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3)); const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0); const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0); const __m128i T0M1 = montgomery_sub_128(T0, T1, m2, m0); const __m128i T2M3 = montgomery_mul_128( montgomery_sub_128(T2, T3, m2, m0), Imag, r, m1); _mm_storeu_si128((__m128i *)(a + j0), montgomery_add_128(T0P1, T2P3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j2), montgomery_sub_128(T0P1, T2P3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j1), montgomery_add_128(T0M1, T2M3, m2, m0)); _mm_storeu_si128((__m128i *)(a + j3), montgomery_sub_128(T0M1, T2M3, m2, m0)); } } else { ww = xx * xx, yy = xx * imag; const __m128i WW = _mm_set1_epi32(ww.a); const __m128i XX = _mm_set1_epi32(xx.a); const __m128i YY = _mm_set1_epi32(yy.a); int j0 = jh * v; int j1 = j0 + v; int j2 = j1 + v; int j3 = j2 + v; int je = j1; for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) { const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0)); const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1)); const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2)); const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3)); const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0); const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0); const __m128i T0M1 = montgomery_mul_128( montgomery_sub_128(T0, T1, m2, m0), XX, r, m1); __m128i T2M3 = montgomery_mul_128( montgomery_sub_128(T2, T3, m2, m0), YY, r, m1); _mm_storeu_si128((__m128i *)(a + j0), montgomery_add_128(T0P1, T2P3, m2, m0)); _mm_storeu_si128( (__m128i *)(a + j2), montgomery_mul_128(montgomery_sub_128(T0P1, T2P3, m2, m0), WW, r, m1)); _mm_storeu_si128((__m128i *)(a + j1), montgomery_add_128(T0M1, T2M3, m2, m0)); _mm_storeu_si128( (__m128i *)(a + j3), montgomery_mul_128(montgomery_sub_128(T0M1, T2M3, m2, m0), WW, r, m1)); } } xx *= dy[__builtin_ctz(jh += 4)]; } } else { const __m256i m0 = _mm256_set1_epi32(0); const __m256i m1 = _mm256_set1_epi32(mod); const __m256i m2 = _mm256_set1_epi32(mod + mod); const __m256i r = _mm256_set1_epi32(mint::r); const __m256i Imag = _mm256_set1_epi32(imag.a); mint ww = one, xx = one, yy = one; u <<= 2; for (int jh = 0; jh < u;) { if (jh == 0) { int j0 = 0; int j1 = v; int j2 = v + v; int j3 = j2 + v; for (; j0 < v; j0 += 8, j1 += 8, j2 += 8, j3 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1)); const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2)); const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3)); const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0); const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0); const __m256i T0M1 = montgomery_sub_256(T0, T1, m2, m0); const __m256i T2M3 = montgomery_mul_256( montgomery_sub_256(T2, T3, m2, m0), Imag, r, m1); _mm256_storeu_si256((__m256i *)(a + j0), montgomery_add_256(T0P1, T2P3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j2), montgomery_sub_256(T0P1, T2P3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j1), montgomery_add_256(T0M1, T2M3, m2, m0)); _mm256_storeu_si256((__m256i *)(a + j3), montgomery_sub_256(T0M1, T2M3, m2, m0)); } } else { ww = xx * xx, yy = xx * imag; const __m256i WW = _mm256_set1_epi32(ww.a); const __m256i XX = _mm256_set1_epi32(xx.a); const __m256i YY = _mm256_set1_epi32(yy.a); int j0 = jh * v; int j1 = j0 + v; int j2 = j1 + v; int j3 = j2 + v; int je = j1; for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1)); const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2)); const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3)); const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0); const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0); const __m256i T0M1 = montgomery_mul_256( montgomery_sub_256(T0, T1, m2, m0), XX, r, m1); const __m256i T2M3 = montgomery_mul_256( montgomery_sub_256(T2, T3, m2, m0), YY, r, m1); _mm256_storeu_si256((__m256i *)(a + j0), montgomery_add_256(T0P1, T2P3, m2, m0)); _mm256_storeu_si256( (__m256i *)(a + j2), montgomery_mul_256(montgomery_sub_256(T0P1, T2P3, m2, m0), WW, r, m1)); _mm256_storeu_si256((__m256i *)(a + j1), montgomery_add_256(T0M1, T2M3, m2, m0)); _mm256_storeu_si256( (__m256i *)(a + j3), montgomery_mul_256(montgomery_sub_256(T0M1, T2M3, m2, m0), WW, r, m1)); } } xx *= dy[__builtin_ctz(jh += 4)]; } } u >>= 4; v <<= 2; } if (k & 1) { v = 1 << (k - 1); if (v < 8) { for (int j = 0; j < v; ++j) { mint ajv = a[j] - a[j + v]; a[j] += a[j + v]; a[j + v] = ajv; } } else { const __m256i m0 = _mm256_set1_epi32(0); const __m256i m2 = _mm256_set1_epi32(mod + mod); int j0 = 0; int j1 = v; for (; j0 < v; j0 += 8, j1 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1)); __m256i naj = montgomery_add_256(T0, T1, m2, m0); __m256i najv = montgomery_sub_256(T0, T1, m2, m0); _mm256_storeu_si256((__m256i *)(a + j0), naj); _mm256_storeu_si256((__m256i *)(a + j1), najv); } } } if (normalize) { mint invn = mint(n).inverse(); for (int i = 0; i < n; i++) a[i] *= invn; } } __attribute__((target("avx2"))) void inplace_multiply( int l1, int l2, int zero_padding = true) { int l = l1 + l2 - 1; int M = 4; while (M < l) M <<= 1; if (zero_padding) { for (int i = l1; i < M; i++) ntt_inner::_buf1[i] = 0; for (int i = l2; i < M; i++) ntt_inner::_buf2[i] = 0; } const __m256i m0 = _mm256_set1_epi32(0); const __m256i m1 = _mm256_set1_epi32(mod); const __m256i r = _mm256_set1_epi32(mint::r); const __m256i N2 = _mm256_set1_epi32(mint::n2); for (int i = 0; i < l1; i += 8) { __m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i)); __m256i b = montgomery_mul_256(a, N2, r, m1); _mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), b); } for (int i = 0; i < l2; i += 8) { __m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i)); __m256i b = montgomery_mul_256(a, N2, r, m1); _mm256_storeu_si256((__m256i *)(ntt_inner::_buf2 + i), b); } ntt(buf1, M); ntt(buf2, M); for (int i = 0; i < M; i += 8) { __m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i)); __m256i b = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i)); __m256i c = montgomery_mul_256(a, b, r, m1); _mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), c); } intt(buf1, M, false); const __m256i INVM = _mm256_set1_epi32((mint(M).inverse()).a); for (int i = 0; i < l; i += 8) { __m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i)); __m256i b = montgomery_mul_256(a, INVM, r, m1); __m256i c = my256_mulhi_epu32(my256_mullo_epu32(b, r), m1); __m256i d = _mm256_and_si256(_mm256_cmpgt_epi32(c, m0), m1); __m256i e = _mm256_sub_epi32(d, c); _mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), e); } } void ntt(vector<mint> &a) { int M = (int)a.size(); for (int i = 0; i < M; i++) buf1[i].a = a[i].a; ntt(buf1, M); for (int i = 0; i < M; i++) a[i].a = buf1[i].a; } void intt(vector<mint> &a) { int M = (int)a.size(); for (int i = 0; i < M; i++) buf1[i].a = a[i].a; intt(buf1, M, true); for (int i = 0; i < M; i++) a[i].a = buf1[i].a; } vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) { if (a.size() == 0 && b.size() == 0) return vector<mint>{}; int l = a.size() + b.size() - 1; if (min<int>(a.size(), b.size()) <= 40) { vector<mint> s(l); for (int i = 0; i < (int)a.size(); ++i) for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j]; return s; } assert(l <= ntt_inner::SZ_FFT_BUF); int M = 4; while (M < l) M <<= 1; for (int i = 0; i < (int)a.size(); ++i) buf1[i].a = a[i].a; for (int i = (int)a.size(); i < M; ++i) buf1[i].a = 0; for (int i = 0; i < (int)b.size(); ++i) buf2[i].a = b[i].a; for (int i = (int)b.size(); i < M; ++i) buf2[i].a = 0; ntt(buf1, M); ntt(buf2, M); for (int i = 0; i < M; ++i) buf1[i].a = mint::reduce(uint64_t(buf1[i].a) * buf2[i].a); intt(buf1, M, false); vector<mint> s(l); mint invm = mint(M).inverse(); for (int i = 0; i < l; ++i) s[i] = buf1[i] * invm; return s; } void ntt_doubling(vector<mint> &a) { int M = (int)a.size(); for (int i = 0; i < M; i++) buf1[i].a = a[i].a; intt(buf1, M); mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1)); for (int i = 0; i < M; i++) buf1[i] *= r, r *= zeta; ntt(buf1, M); a.resize(2 * M); for (int i = 0; i < M; i++) a[M + i].a = buf1[i].a; } }; #line 9 "verify/verify-yosupo-ntt/yosupo-inliner-multiply.test.cpp" NTT<LazyMontgomeryModInt<998244353>> ntt; using namespace Nyaan; void Nyaan::solve() { using namespace ntt_inner; int N, M; rd(N, M); for (int i = 0; i < N; i++) { int n; rd(n); _buf1[i] = n; } for (int i = 0; i < M; i++) { int n; rd(n); _buf2[i] = n; } ntt.inplace_multiply(N, M, false); int len = N + M - 1; for (int i = 0; i < len; i++) { if (i) wt(' '); wt(_buf1[i]); } wt('\n'); }