結果
| 問題 | No.1771 A DELETEQ |
| ユーザー |
👑  SPD_9X2
|
| 提出日時 | 2021-11-30 17:23:29 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 23 ms / 3,500 ms |
| コード長 | 45,556 bytes |
| コンパイル時間 | 5,271 ms |
| コンパイル使用メモリ | 394,552 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-07-03 21:25:30 |
| 合計ジャッジ時間 | 10,677 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 38 |
コンパイルメッセージ
main.cpp:481:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
481 | montgomery_sub_256(const __m256i &a, const __m256i &b, const __m256i &m2,
| ^~~~~~~~~~~~~~~~~~
main.cpp:473:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
473 | montgomery_add_256(const __m256i &a, const __m256i &b, const __m256i &m2,
| ^~~~~~~~~~~~~~~~~~
main.cpp:465:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
465 | montgomery_mul_256(const __m256i &a, const __m256i &b, const __m256i &r,
| ^~~~~~~~~~~~~~~~~~
main.cpp:454:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
454 | my256_mulhi_epu32(const __m256i &a, const __m256i &b) {
| ^~~~~~~~~~~~~~~~~
main.cpp:449:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
449 | my256_mullo_epu32(const __m256i &a, const __m256i &b) {
| ^~~~~~~~~~~~~~~~~
main.cpp:442:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
442 | montgomery_sub_128(const __m128i &a, const __m128i &b, const __m128i &m2,
| ^~~~~~~~~~~~~~~~~~
main.cpp:435:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
435 | montgomery_add_128(const __m128i &a, const __m128i &b, const __m128i &m2,
| ^~~~~~~~~~~~~~~~~~
main.cpp:427:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
427 | montgomery_mul_128(const __m128i &a, const __m128i &b, const __m128i &r,
| ^~~~~~~~~~~~~~~~~~
main.cpp:416:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
416 | my128_mulhi_epu32(const __m128i &a, const __m128i &b) {
| ^~~~~~~~~~~~~~~~~
main.cpp:411:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
411 | my128_mullo_epu32(const __m128i &a, const __m128i &b) {
| ^~~~~~~~~~~~~~~~~
ソースコード
/*制約チェックバージョンNyaanさんのこちらのライブラリ・実装を引用、改変しています。https://atcoder.jp/contests/s8pc-3/submissions/15526069https://nyaannyaan.github.io/library/fps/kitamasa.hpp.html*/#include <cassert>#pragma region kyopro_template#define Nyaan_template#include <immintrin.h>#include <bits/stdc++.h>#define pb push_back#define eb emplace_back#define fi first#define se second#define each(x, v) for (auto &x : v)#define all(v) (v).begin(), (v).end()#define sz(v) ((int)(v).size())#define mem(a, val) memset(a, val, sizeof(a))#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 inc(...) \char __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 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 die(...) \do { \out(__VA_ARGS__); \return; \} while (0)using namespace std;using ll = long long;template <class T>using V = vector<T>;using vi = vector<int>;using vl = vector<long long>;using vvi = vector<vector<int>>;using vd = V<double>;using vs = V<string>;using vvl = vector<vector<long long>>;using P = pair<long long, long long>;using vp = vector<P>;using pii = pair<int, int>;using vpi = vector<pair<int, int>>;constexpr int inf = 1001001001;constexpr long long infLL = (1LL << 61) - 1;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, 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;}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>void out(const T &t, const U &... u) {cout << t;if (sizeof...(u)) cout << " ";out(u...);}#ifdef NyaanDebug#define trc(...) \do { \cerr << #__VA_ARGS__ << " = "; \dbg_out(__VA_ARGS__); \} while (0)#define trca(v, N) \do { \cerr << #v << " = "; \array_out(v, N); \} while (0)#define trcc(v) \do { \cerr << #v << " = {"; \each(x, v) { cerr << " " << x << ","; } \cerr << "}" << endl; \} while (0)template <typename T>void _cout(const T &c) {cerr << c;}void _cout(const int &c) {if (c == 1001001001)cerr << "inf";else if (c == -1001001001)cerr << "-inf";elsecerr << c;}void _cout(const unsigned int &c) {if (c == 1001001001)cerr << "inf";elsecerr << c;}void _cout(const long long &c) {if (c == 1001001001 || c == (1LL << 61) - 1)cerr << "inf";else if (c == -1001001001 || c == -((1LL << 61) - 1))cerr << "-inf";elsecerr << c;}void _cout(const unsigned long long &c) {if (c == 1001001001 || c == (1LL << 61) - 1)cerr << "inf";elsecerr << c;}template <typename T, typename U>void _cout(const pair<T, U> &p) {cerr << "{ ";_cout(p.fi);cerr << ", ";_cout(p.se);cerr << " } ";}template <typename T>void _cout(const vector<T> &v) {int s = v.size();cerr << "{ ";for (int i = 0; i < s; i++) {cerr << (i ? ", " : "");_cout(v[i]);}cerr << " } ";}template <typename T>void _cout(const vector<vector<T>> &v) {cerr << "[ ";for (const auto &x : v) {cerr << endl;_cout(x);cerr << ", ";}cerr << endl << " ] ";}void dbg_out() { cerr << endl; }template <typename T, class... U>void dbg_out(const T &t, const U &... u) {_cout(t);if (sizeof...(u)) cerr << ", ";dbg_out(u...);}template <typename T>void array_out(const T &v, int s) {cerr << "{ ";for (int i = 0; i < s; i++) {cerr << (i ? ", " : "");_cout(v[i]);}cerr << " } " << endl;}template <typename T>void array_out(const T &v, int H, int W) {cerr << "[ ";for (int i = 0; i < H; i++) {cerr << (i ? ", " : "");array_out(v[i], W);}cerr << " ] " << endl;}#else#define trc(...)#define trca(...)#define trcc(...)#endifinline int popcnt(unsigned long long a) { return __builtin_popcountll(a); }inline int lsb(unsigned long long a) { return __builtin_ctzll(a); }inline int msb(unsigned long long a) { return 63 - __builtin_clzll(a); }template <typename T>inline int getbit(T a, int i) {return (a >> i) & 1;}template <typename T>inline void setbit(T &a, int i) {a |= (1LL << i);}template <typename T>inline void delbit(T &a, int i) {a &= ~(1LL << i);}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);}template <typename T>int btw(T a, T x, T b) {return a <= x && x < b;}template <typename T, typename U>T ceil(T a, U b) {return (a + b - 1) / b;}constexpr long long TEN(int n) {long long ret = 1, x = 10;while (n) {if (n & 1) ret *= x;x *= x;n >>= 1;}return ret;}template <typename T>vector<T> mkrui(const vector<T> &v) {vector<T> ret(v.size() + 1);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 = int>vector<T> mkiota(int N) {vector<T> ret(N);iota(begin(ret), end(ret), 0);return ret;}template <typename T>vector<int> mkinv(vector<T> &v) {vector<int> inv(v.size());for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;return inv;}struct IoSetupNya {IoSetupNya() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetupnya;void solve();int main() { solve(); }#pragma endregionusing namespace std;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(r * mod == 1, "invalid, r * mod != 1");static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");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 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 { return pow(mod - 2); }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; }};using namespace std;using namespace std;using namespace std;__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128imy128_mullo_epu32(const __m128i &a, const __m128i &b) {return _mm_mullo_epi32(a, b);}__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128imy128_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"))) __attribute__((always_inline)) __m128imontgomery_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"))) __attribute__((always_inline)) __m128imontgomery_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"))) __attribute__((always_inline)) __m128imontgomery_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"))) __attribute__((always_inline)) __m256imy256_mullo_epu32(const __m256i &a, const __m256i &b) {return _mm256_mullo_epi32(a, b);}__attribute__((target("avx2"))) __attribute__((always_inline)) __m256imy256_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"))) __attribute__((always_inline)) __m256imontgomery_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"))) __attribute__((always_inline)) __m256imontgomery_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"))) __attribute__((always_inline)) __m256imontgomery_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);}constexpr int SZ = 1 << 19;uint32_t buf1_[SZ * 2] __attribute__((aligned(64)));uint32_t buf2_[SZ * 2] __attribute__((aligned(64)));template <typename mint>struct NTT {static constexpr uint32_t get_pr() {uint32_t mod = mint::get_mod();using u64 = uint64_t;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;};static constexpr uint32_t mod = mint::get_mod();static constexpr uint32_t pr = get_pr();static constexpr int level = __builtin_ctzll(mod - 1);mint dw[level], dy[level];mint *buf1, *buf2;constexpr NTT() {setwy(level);buf1 = reinterpret_cast<mint *>(::buf1_);buf2 = reinterpret_cast<mint *>(::buf2_);}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++) buf1_[i] = 0;for (int i = l2; i < M; i++) 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 *)(buf1_ + i));__m256i b = montgomery_mul_256(a, N2, r, m1);_mm256_storeu_si256((__m256i *)(buf1_ + i), b);}for (int i = 0; i < l2; i += 8) {__m256i a = _mm256_loadu_si256((__m256i *)(buf2_ + i));__m256i b = montgomery_mul_256(a, N2, r, m1);_mm256_storeu_si256((__m256i *)(buf2_ + i), b);}ntt(buf1, M);ntt(buf2, M);for (int i = 0; i < M; i += 8) {__m256i a = _mm256_loadu_si256((__m256i *)(buf1_ + i));__m256i b = _mm256_loadu_si256((__m256i *)(buf2_ + i));__m256i c = montgomery_mul_256(a, b, r, m1);_mm256_storeu_si256((__m256i *)(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 *)(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 *)(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) {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;}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;}};using namespace std;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;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;}int size2() {return this->size();}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;}FPS pre(int sz) const {return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));}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));for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * mint(i);return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = mint(0);for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / mint(i + 1);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)[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;for (int i = 0; i < n; i++) {if ((*this)[i] != mint(0)) {if (i * k > deg) return FPS(deg, mint(0));mint rev = mint(1) / (*this)[i];FPS ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, mint(0));return ret;}}return FPS(deg, mint(0));}private:static void *ntt_ptr;static void set_fft();public: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;// FPS sqrt(int deg = -1) const;// pair<FPS, FPS> circular(int deg = -1) const;// FPS shift(mint a, 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/formal-power-series.md*/template <typename mint>void FormalPowerSeries<mint>::set_fft() {if (!ntt_ptr) ntt_ptr = new NTT<mint>;}template <typename mint>FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint>& r) {if (this->empty() || r.empty()) {this->clear();return *this;}set_fft();auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());}template <typename mint>void FormalPowerSeries<mint>::ntt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);}template <typename mint>void FormalPowerSeries<mint>::intt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);}template <typename mint>void FormalPowerSeries<mint>::ntt_doubling() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);}template <typename mint>int FormalPowerSeries<mint>::ntt_pr() {set_fft();return static_cast<NTT<mint>*>(ntt_ptr)->pr;}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {assert((*this)[0] != mint(0));if (deg == -1) deg = (*this).size();FormalPowerSeries<mint> ret({mint(1) / (*this)[0]});for (int i = 1; i < deg; i <<= 1)ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1);return ret.pre(deg);}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {assert((*this)[0] == mint(0));if (deg == -1) deg = (int)this->size();FormalPowerSeries<mint> ret({mint(1)});for (int i = 1; i < deg; i <<= 1) {ret = (ret * (pre(i << 1) + mint(1) - ret.log(i << 1))).pre(i << 1);}return ret.pre(deg);}using namespace std;template <typename T>struct Binomial {vector<T> fac_, finv_, inv_;Binomial(int MAX) : fac_(MAX + 10), finv_(MAX + 10), inv_(MAX + 10) {MAX += 9;fac_[0] = finv_[0] = inv_[0] = 1;for (int i = 1; i <= MAX; i++) fac_[i] = fac_[i - 1] * i;finv_[MAX] = fac_[MAX].inverse();for (int i = MAX - 1; i > 0; i--) finv_[i] = finv_[i + 1] * (i + 1);for (int i = 1; i <= MAX; i++) inv_[i] = finv_[i] * fac_[i - 1];}inline T fac(int i) { return fac_[i]; }inline T finv(int i) { return finv_[i]; }inline T inv(int i) { return inv_[i]; }T C(int n, int r) {if (n < r || r < 0) return T(0);return fac_[n] * finv_[n - r] * finv_[r];}T C_naive(int n, int r) {if (n < r || r < 0) return T(0);T ret = 1;for (T i = 1; i <= r; i += T(1)) {ret *= n--;ret *= i.inverse();}return ret;}T P(int n, int r) {if (n < r || r < 0) return T(0);return fac_[n] * finv_[n - r];}T H(int n, int r) const {if (n < 0 || r < 0) return (0);return r == 0 ? 1 : C(n + r - 1, r);}};using namespace std;template <typename mint>mint LinearRecursionFormula(long long N, FormalPowerSeries<mint> Q,FormalPowerSeries<mint> P) {Q.shrink();mint ret = 0;if (P.size() >= Q.size()) {auto R = P / Q;P -= R * Q;if (N < (int)R.size()) ret += R[N];}if ((int)P.size() == 0) return ret;long long k = 1LL << (32 - __builtin_clz(Q.size() - 1));P.resize(k);Q.resize(k);while (N) {auto Q2 = Q;for (int i = 1; i < (int)Q2.size(); i += 2) Q2[i] = -Q2[i];auto S = P * Q2;auto T = Q * Q2;if (N & 1) {for (int i = 1; i < (int)S.size(); i += 2) P[i >> 1] = S[i];for (int i = 0; i < (int)T.size(); i += 2) Q[i >> 1] = T[i];} else {for (int i = 0; i < (int)S.size(); i += 2) P[i >> 1] = S[i];for (int i = 0; i < (int)T.size(); i += 2) Q[i >> 1] = T[i];}N >>= 1;}return P[0];}template <typename mint>mint kitamasa(long long N, FormalPowerSeries<mint> Q,FormalPowerSeries<mint> a) {int k = Q.size() - 1;assert((int)a.size() == k);auto P = a * Q;P.resize(Q.size() - 1);return LinearRecursionFormula<mint>(N, Q, P);}using mint = LazyMontgomeryModInt<998244353>;using fps = FormalPowerSeries<mint>;void solve() {long long x, y;cin >> x >> y;assert (1 <= x && x <= 100000);assert (1 <= y && y <= 1000000000);ll M = min(x,y);ll N = max(x,y);fps PL(M+5);PL[0] = 1; PL[1] = 2;PL = PL.pow(N+1);//cout << PL.size2() << endl;fps PR(M+5);PR[0] = 0;PR[1] = 1;PR[2] = -1; // = {0 , 1 , -1};PR = PR.pow(N+1);fps P = PL - PR;fps QL(M+5);QL[0] = 1; QL[1] = -1; //QL[] = {1,-1};QL = QL.pow(N+1);fps QR(M+5);QR[0] = 1; QR[1] = 1; QR[2] = 1; // = {1,1,1};fps Q = QL * QR;cout << LinearRecursionFormula(M, Q, P) << endl;}