結果
問題 | No.2904 Distinct Multisets in a Way |
ユーザー |
![]() |
提出日時 | 2024-09-27 20:03:55 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 32 ms / 2,000 ms |
コード長 | 43,122 bytes |
コンパイル時間 | 8,140 ms |
コンパイル使用メモリ | 343,440 KB |
実行使用メモリ | 9,504 KB |
最終ジャッジ日時 | 2024-09-27 20:04:06 |
合計ジャッジ時間 | 9,789 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 42 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"#if defined(LOCAL)#include <my_template_compiled.hpp>#else// https://codeforces.com/blog/entry/96344#pragma GCC optimize("Ofast,unroll-loops")// いまの CF だとこれ入れると動かない?// #pragma GCC target("avx2,popcnt")#include <bits/stdc++.h>using namespace std;using ll = long long;using u32 = unsigned int;using u64 = unsigned long long;using i128 = __int128;using u128 = unsigned __int128;using f128 = __float128;template <class T>constexpr T infty = 0;template <>constexpr int infty<int> = 1'010'000'000;template <>constexpr ll infty<ll> = 2'020'000'000'000'000'000;template <>constexpr u32 infty<u32> = infty<int>;template <>constexpr u64 infty<u64> = infty<ll>;template <>constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;template <>constexpr double infty<double> = infty<ll>;template <>constexpr long double infty<long double> = infty<ll>;using pi = pair<ll, ll>;using vi = vector<ll>;template <class T>using vc = vector<T>;template <class T>using vvc = vector<vc<T>>;template <class T>using vvvc = vector<vvc<T>>;template <class T>using vvvvc = vector<vvvc<T>>;template <class T>using vvvvvc = vector<vvvvc<T>>;template <class T>using pq = priority_queue<T>;template <class T>using pqg = priority_queue<T, vector<T>, greater<T>>;#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))#define vvvv(type, name, a, b, c, ...) \vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))// https://trap.jp/post/1224/#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)#define overload4(a, b, c, d, e, ...) e#define overload3(a, b, c, d, ...) d#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))#define all(x) x.begin(), x.end()#define len(x) ll(x.size())#define elif else if#define eb emplace_back#define mp make_pair#define mt make_tuple#define fi first#define se second#define stoi stollint popcnt(int x) { return __builtin_popcount(x); }int popcnt(u32 x) { return __builtin_popcount(x); }int popcnt(ll x) { return __builtin_popcountll(x); }int popcnt(u64 x) { return __builtin_popcountll(x); }int popcnt_mod_2(int x) { return __builtin_parity(x); }int popcnt_mod_2(u32 x) { return __builtin_parity(x); }int popcnt_mod_2(ll x) { return __builtin_parityll(x); }int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }template <typename T>T floor(T a, T b) {return a / b - (a % b && (a ^ b) < 0);}template <typename T>T ceil(T x, T y) {return floor(x + y - 1, y);}template <typename T>T bmod(T x, T y) {return x - y * floor(x, y);}template <typename T>pair<T, T> divmod(T x, T y) {T q = floor(x, y);return {q, x - q * y};}template <typename T, typename U>T SUM(const vector<U> &A) {T sm = 0;for (auto &&a: A) sm += a;return sm;}#define MIN(v) *min_element(all(v))#define MAX(v) *max_element(all(v))#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()template <typename T>T POP(deque<T> &que) {T a = que.front();que.pop_front();return a;}template <typename T>T POP(pq<T> &que) {T a = que.top();que.pop();return a;}template <typename T>T POP(pqg<T> &que) {T a = que.top();que.pop();return a;}template <typename T>T POP(vc<T> &que) {T a = que.back();que.pop_back();return a;}template <typename F>ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {if (check_ok) assert(check(ok));while (abs(ok - ng) > 1) {auto x = (ng + ok) / 2;(check(x) ? ok : ng) = x;}return ok;}template <typename F>double binary_search_real(F check, double ok, double ng, int iter = 100) {FOR(iter) {double x = (ok + ng) / 2;(check(x) ? ok : ng) = x;}return (ok + ng) / 2;}template <class T, class S>inline bool chmax(T &a, const S &b) {return (a < b ? a = b, 1 : 0);}template <class T, class S>inline bool chmin(T &a, const S &b) {return (a > b ? a = b, 1 : 0);}// ? は -1vc<int> s_to_vi(const string &S, char first_char) {vc<int> A(S.size());FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }return A;}template <typename T, typename U>vector<T> cumsum(vector<U> &A, int off = 1) {int N = A.size();vector<T> B(N + 1);FOR(i, N) { B[i + 1] = B[i] + A[i]; }if (off == 0) B.erase(B.begin());return B;}// stable sorttemplate <typename T>vector<int> argsort(const vector<T> &A) {vector<int> ids(len(A));iota(all(ids), 0);sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });return ids;}// A[I[0]], A[I[1]], ...template <typename T>vc<T> rearrange(const vc<T> &A, const vc<int> &I) {vc<T> B(len(I));FOR(i, len(I)) B[i] = A[I[i]];return B;}template <typename T, typename... Vectors>void concat(vc<T> &first, const Vectors &... others) {vc<T> &res = first;(res.insert(res.end(), others.begin(), others.end()), ...);}#endif#line 1 "/home/maspy/compro/library/other/io.hpp"#define FASTIO#include <unistd.h>// https://judge.yosupo.jp/submission/21623namespace fastio {static constexpr uint32_t SZ = 1 << 17;char ibuf[SZ];char obuf[SZ];char out[100];// pointer of ibuf, obufuint32_t pil = 0, pir = 0, por = 0;struct Pre {char num[10000][4];constexpr Pre() : num() {for (int i = 0; i < 10000; i++) {int n = i;for (int j = 3; j >= 0; j--) {num[i][j] = n % 10 | '0';n /= 10;}}}} constexpr pre;inline void load() {memcpy(ibuf, ibuf + pil, pir - pil);pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);pil = 0;if (pir < SZ) ibuf[pir++] = '\n';}inline void flush() {fwrite(obuf, 1, por, stdout);por = 0;}void rd(char &c) {do {if (pil + 1 > pir) load();c = ibuf[pil++];} while (isspace(c));}void rd(string &x) {x.clear();char c;do {if (pil + 1 > pir) load();c = ibuf[pil++];} while (isspace(c));do {x += c;if (pil == pir) load();c = ibuf[pil++];} while (!isspace(c));}template <typename T>void rd_real(T &x) {string s;rd(s);x = stod(s);}template <typename T>void rd_integer(T &x) {if (pil + 100 > pir) load();char c;doc = ibuf[pil++];while (c < '-');bool minus = 0;if constexpr (is_signed<T>::value || is_same_v<T, i128>) {if (c == '-') { minus = 1, c = ibuf[pil++]; }}x = 0;while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }if constexpr (is_signed<T>::value || is_same_v<T, i128>) {if (minus) x = -x;}}void rd(int &x) { rd_integer(x); }void rd(ll &x) { rd_integer(x); }void rd(i128 &x) { rd_integer(x); }void rd(u32 &x) { rd_integer(x); }void rd(u64 &x) { rd_integer(x); }void rd(u128 &x) { rd_integer(x); }void rd(double &x) { rd_real(x); }void rd(long double &x) { rd_real(x); }void rd(f128 &x) { rd_real(x); }template <class T, class U>void rd(pair<T, U> &p) {return rd(p.first), rd(p.second);}template <size_t N = 0, typename T>void rd_tuple(T &t) {if constexpr (N < std::tuple_size<T>::value) {auto &x = std::get<N>(t);rd(x);rd_tuple<N + 1>(t);}}template <class... T>void rd(tuple<T...> &tpl) {rd_tuple(tpl);}template <size_t N = 0, typename T>void rd(array<T, N> &x) {for (auto &d: x) rd(d);}template <class T>void rd(vc<T> &x) {for (auto &d: x) rd(d);}void read() {}template <class H, class... T>void read(H &h, T &... t) {rd(h), read(t...);}void wt(const char c) {if (por == SZ) flush();obuf[por++] = c;}void wt(const string s) {for (char c: s) wt(c);}void wt(const char *s) {size_t len = strlen(s);for (size_t i = 0; i < len; i++) wt(s[i]);}template <typename T>void wt_integer(T x) {if (por > SZ - 100) flush();if (x < 0) { obuf[por++] = '-', x = -x; }int outi;for (outi = 96; x >= 10000; outi -= 4) {memcpy(out + outi, pre.num[x % 10000], 4);x /= 10000;}if (x >= 1000) {memcpy(obuf + por, pre.num[x], 4);por += 4;} else if (x >= 100) {memcpy(obuf + por, pre.num[x] + 1, 3);por += 3;} else if (x >= 10) {int q = (x * 103) >> 10;obuf[por] = q | '0';obuf[por + 1] = (x - q * 10) | '0';por += 2;} elseobuf[por++] = x | '0';memcpy(obuf + por, out + outi + 4, 96 - outi);por += 96 - outi;}template <typename T>void wt_real(T x) {ostringstream oss;oss << fixed << setprecision(15) << double(x);string s = oss.str();wt(s);}void wt(int x) { wt_integer(x); }void wt(ll x) { wt_integer(x); }void wt(i128 x) { wt_integer(x); }void wt(u32 x) { wt_integer(x); }void wt(u64 x) { wt_integer(x); }void wt(u128 x) { wt_integer(x); }void wt(double x) { wt_real(x); }void wt(long double x) { wt_real(x); }void wt(f128 x) { wt_real(x); }template <class T, class U>void wt(const pair<T, U> val) {wt(val.first);wt(' ');wt(val.second);}template <size_t N = 0, typename T>void wt_tuple(const T t) {if constexpr (N < std::tuple_size<T>::value) {if constexpr (N > 0) { wt(' '); }const auto x = std::get<N>(t);wt(x);wt_tuple<N + 1>(t);}}template <class... T>void wt(tuple<T...> tpl) {wt_tuple(tpl);}template <class T, size_t S>void wt(const array<T, S> val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) wt(' ');wt(val[i]);}}template <class T>void wt(const vector<T> val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) wt(' ');wt(val[i]);}}void print() { wt('\n'); }template <class Head, class... Tail>void print(Head &&head, Tail &&... tail) {wt(head);if (sizeof...(Tail)) wt(' ');print(forward<Tail>(tail)...);}// gcc expansion. called automaticall after main.void __attribute__((destructor)) _d() { flush(); }} // namespace fastiousing fastio::read;using fastio::print;using fastio::flush;#if defined(LOCAL)#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME#define SHOW1(x) print(#x, "=", (x)), flush()#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()#else#define SHOW(...)#endif#define INT(...) \int __VA_ARGS__; \read(__VA_ARGS__)#define LL(...) \ll __VA_ARGS__; \read(__VA_ARGS__)#define U32(...) \u32 __VA_ARGS__; \read(__VA_ARGS__)#define U64(...) \u64 __VA_ARGS__; \read(__VA_ARGS__)#define STR(...) \string __VA_ARGS__; \read(__VA_ARGS__)#define CHAR(...) \char __VA_ARGS__; \read(__VA_ARGS__)#define DBL(...) \double __VA_ARGS__; \read(__VA_ARGS__)#define VEC(type, name, size) \vector<type> name(size); \read(name)#define VV(type, name, h, w) \vector<vector<type>> name(h, vector<type>(w)); \read(name)void YES(bool t = 1) { print(t ? "YES" : "NO"); }void NO(bool t = 1) { YES(!t); }void Yes(bool t = 1) { print(t ? "Yes" : "No"); }void No(bool t = 1) { Yes(!t); }void yes(bool t = 1) { print(t ? "yes" : "no"); }void no(bool t = 1) { yes(!t); }#line 3 "main.cpp"#line 2 "/home/maspy/compro/library/mod/modint_common.hpp"struct has_mod_impl {template <class T>static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});template <class T>static auto check(...) -> std::false_type;};template <class T>class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};template <typename mint>mint inv(int n) {static const int mod = mint::get_mod();static vector<mint> dat = {0, 1};assert(0 <= n);if (n >= mod) n %= mod;while (len(dat) <= n) {int k = len(dat);int q = (mod + k - 1) / k;dat.eb(dat[k * q - mod] * mint::raw(q));}return dat[n];}template <typename mint>mint fact(int n) {static const int mod = mint::get_mod();assert(0 <= n && n < mod);static vector<mint> dat = {1, 1};while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));return dat[n];}template <typename mint>mint fact_inv(int n) {static vector<mint> dat = {1, 1};if (n < 0) return mint(0);while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));return dat[n];}template <class mint, class... Ts>mint fact_invs(Ts... xs) {return (mint(1) * ... * fact_inv<mint>(xs));}template <typename mint, class Head, class... Tail>mint multinomial(Head &&head, Tail &&... tail) {return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);}template <typename mint>mint C_dense(int n, int k) {static vvc<mint> C;static int H = 0, W = 0;auto calc = [&](int i, int j) -> mint {if (i == 0) return (j == 0 ? mint(1) : mint(0));return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);};if (W <= k) {FOR(i, H) {C[i].resize(k + 1);FOR(j, W, k + 1) { C[i][j] = calc(i, j); }}W = k + 1;}if (H <= n) {C.resize(n + 1);FOR(i, H, n + 1) {C[i].resize(W);FOR(j, W) { C[i][j] = calc(i, j); }}H = n + 1;}return C[n][k];}template <typename mint, bool large = false, bool dense = false>mint C(ll n, ll k) {assert(n >= 0);if (k < 0 || n < k) return 0;if constexpr (dense) return C_dense<mint>(n, k);if constexpr (!large) return multinomial<mint>(n, k, n - k);k = min(k, n - k);mint x(1);FOR(i, k) x *= mint(n - i);return x * fact_inv<mint>(k);}template <typename mint, bool large = false>mint C_inv(ll n, ll k) {assert(n >= 0);assert(0 <= k && k <= n);if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);return mint(1) / C<mint, 1>(n, k);}// [x^d](1-x)^{-n}template <typename mint, bool large = false, bool dense = false>mint C_negative(ll n, ll d) {assert(n >= 0);if (d < 0) return mint(0);if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }return C<mint, large, dense>(n + d - 1, d);}#line 3 "/home/maspy/compro/library/mod/modint.hpp"template <int mod>struct modint {static constexpr u32 umod = u32(mod);static_assert(umod < u32(1) << 31);u32 val;static modint raw(u32 v) {modint x;x.val = v;return x;}constexpr modint() : val(0) {}constexpr modint(u32 x) : val(x % umod) {}constexpr modint(u64 x) : val(x % umod) {}constexpr modint(u128 x) : val(x % umod) {}constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};bool operator<(const modint &other) const { return val < other.val; }modint &operator+=(const modint &p) {if ((val += p.val) >= umod) val -= umod;return *this;}modint &operator-=(const modint &p) {if ((val += umod - p.val) >= umod) val -= umod;return *this;}modint &operator*=(const modint &p) {val = u64(val) * p.val % umod;return *this;}modint &operator/=(const modint &p) {*this *= p.inverse();return *this;}modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }modint operator+(const modint &p) const { return modint(*this) += p; }modint operator-(const modint &p) const { return modint(*this) -= p; }modint operator*(const modint &p) const { return modint(*this) *= p; }modint operator/(const modint &p) const { return modint(*this) /= p; }bool operator==(const modint &p) const { return val == p.val; }bool operator!=(const modint &p) const { return val != p.val; }modint inverse() const {int a = val, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}return modint(u);}modint pow(ll n) const {assert(n >= 0);modint ret(1), mul(val);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}static constexpr int get_mod() { return mod; }// (n, r), r は 1 の 2^n 乗根static constexpr pair<int, int> ntt_info() {if (mod == 120586241) return {20, 74066978};if (mod == 167772161) return {25, 17};if (mod == 469762049) return {26, 30};if (mod == 754974721) return {24, 362};if (mod == 880803841) return {23, 211};if (mod == 943718401) return {22, 663003469};if (mod == 998244353) return {23, 31};if (mod == 1004535809) return {21, 836905998};if (mod == 1045430273) return {20, 363};if (mod == 1051721729) return {20, 330};if (mod == 1053818881) return {20, 2789};return {-1, -1};}static constexpr bool can_ntt() { return ntt_info().fi != -1; }};#ifdef FASTIOtemplate <int mod>void rd(modint<mod> &x) {fastio::rd(x.val);x.val %= mod;// assert(0 <= x.val && x.val < mod);}template <int mod>void wt(modint<mod> x) {fastio::wt(x.val);}#endifusing modint107 = modint<1000000007>;using modint998 = modint<998244353>;#line 2 "/home/maspy/compro/library/poly/count_terms.hpp"template<typename mint>int count_terms(const vc<mint>& f){int t = 0;FOR(i, len(f)) if(f[i] != mint(0)) ++t;return t;}#line 2 "/home/maspy/compro/library/mod/mod_inv.hpp"// long でも大丈夫// (val * x - 1) が mod の倍数になるようにする// 特に mod=0 なら x=0 が満たすll mod_inv(ll val, ll mod) {if (mod == 0) return 0;mod = abs(mod);val %= mod;if (val < 0) val += mod;ll a = val, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}if (u < 0) u += mod;return u;}#line 2 "/home/maspy/compro/library/mod/crt3.hpp"constexpr u32 mod_pow_constexpr(u64 a, u64 n, u32 mod) {a %= mod;u64 res = 1;FOR(32) {if (n & 1) res = res * a % mod;a = a * a % mod, n /= 2;}return res;}template <typename T, u32 p0, u32 p1>T CRT2(u64 a0, u64 a1) {static_assert(p0 < p1);static constexpr u64 x0_1 = mod_pow_constexpr(p0, p1 - 2, p1);u64 c = (a1 - a0 + p1) * x0_1 % p1;return a0 + c * p0;}template <typename T, u32 p0, u32 p1, u32 p2>T CRT3(u64 a0, u64 a1, u64 a2) {static_assert(p0 < p1 && p1 < p2);static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);static constexpr u64 p01 = u64(p0) * p1;u64 c = (a1 - a0 + p1) * x1 % p1;u64 ans_1 = a0 + c * p0;c = (a2 - ans_1 % p2 + p2) * x2 % p2;return T(ans_1) + T(c) * T(p01);}template <typename T, u32 p0, u32 p1, u32 p2, u32 p3, u32 p4>T CRT5(u64 a0, u64 a1, u64 a2, u64 a3, u64 a4) {static_assert(p0 < p1 && p1 < p2 && p2 < p3 && p3 < p4);static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);static constexpr u64 x3= mod_pow_constexpr(u64(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);static constexpr u64 x4= mod_pow_constexpr(u64(p0) * p1 % p4 * p2 % p4 * p3 % p4, p4 - 2, p4);static constexpr u64 p01 = u64(p0) * p1;static constexpr u64 p23 = u64(p2) * p3;u64 c = (a1 - a0 + p1) * x1 % p1;u64 ans_1 = a0 + c * p0;c = (a2 - ans_1 % p2 + p2) * x2 % p2;u128 ans_2 = ans_1 + c * static_cast<u128>(p01);c = static_cast<u64>(a3 - ans_2 % p3 + p3) * x3 % p3;u128 ans_3 = ans_2 + static_cast<u128>(c * p2) * p01;c = static_cast<u64>(a4 - ans_3 % p4 + p4) * x4 % p4;return T(ans_3) + T(c) * T(p01) * T(p23);}#line 2 "/home/maspy/compro/library/poly/convolution_naive.hpp"template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>vc<T> convolution_naive(const vc<T>& a, const vc<T>& b) {int n = int(a.size()), m = int(b.size());if (n > m) return convolution_naive<T>(b, a);if (n == 0) return {};vector<T> ans(n + m - 1);FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j];return ans;}template <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>vc<T> convolution_naive(const vc<T>& a, const vc<T>& b) {int n = int(a.size()), m = int(b.size());if (n > m) return convolution_naive<T>(b, a);if (n == 0) return {};vc<T> ans(n + m - 1);if (n <= 16 && (T::get_mod() < (1 << 30))) {for (int k = 0; k < n + m - 1; ++k) {int s = max(0, k - m + 1);int t = min(n, k + 1);u64 sm = 0;for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }ans[k] = sm;}} else {for (int k = 0; k < n + m - 1; ++k) {int s = max(0, k - m + 1);int t = min(n, k + 1);u128 sm = 0;for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }ans[k] = T::raw(sm % T::get_mod());}}return ans;}#line 2 "/home/maspy/compro/library/poly/convolution_karatsuba.hpp"// 任意の環でできるtemplate <typename T>vc<T> convolution_karatsuba(const vc<T>& f, const vc<T>& g) {const int thresh = 30;if (min(len(f), len(g)) <= thresh) return convolution_naive(f, g);int n = max(len(f), len(g));int m = ceil(n, 2);vc<T> f1, f2, g1, g2;if (len(f) < m) f1 = f;if (len(f) >= m) f1 = {f.begin(), f.begin() + m};if (len(f) >= m) f2 = {f.begin() + m, f.end()};if (len(g) < m) g1 = g;if (len(g) >= m) g1 = {g.begin(), g.begin() + m};if (len(g) >= m) g2 = {g.begin() + m, g.end()};vc<T> a = convolution_karatsuba(f1, g1);vc<T> b = convolution_karatsuba(f2, g2);FOR(i, len(f2)) f1[i] += f2[i];FOR(i, len(g2)) g1[i] += g2[i];vc<T> c = convolution_karatsuba(f1, g1);vc<T> F(len(f) + len(g) - 1);assert(2 * m + len(b) <= len(F));FOR(i, len(a)) F[i] += a[i], c[i] -= a[i];FOR(i, len(b)) F[2 * m + i] += b[i], c[i] -= b[i];if (c.back() == T(0)) c.pop_back();FOR(i, len(c)) if (c[i] != T(0)) F[m + i] += c[i];return F;}#line 2 "/home/maspy/compro/library/poly/ntt.hpp"template <class mint>void ntt(vector<mint>& a, bool inverse) {assert(mint::can_ntt());const int rank2 = mint::ntt_info().fi;const int mod = mint::get_mod();static array<mint, 30> root, iroot;static array<mint, 30> rate2, irate2;static array<mint, 30> rate3, irate3;assert(rank2 != -1 && len(a) <= (1 << max(0, rank2)));static bool prepared = 0;if (!prepared) {prepared = 1;root[rank2] = mint::ntt_info().se;iroot[rank2] = mint(1) / root[rank2];FOR_R(i, rank2) {root[i] = root[i + 1] * root[i + 1];iroot[i] = iroot[i + 1] * iroot[i + 1];}mint prod = 1, iprod = 1;for (int i = 0; i <= rank2 - 2; i++) {rate2[i] = root[i + 2] * prod;irate2[i] = iroot[i + 2] * iprod;prod *= iroot[i + 2];iprod *= root[i + 2];}prod = 1, iprod = 1;for (int i = 0; i <= rank2 - 3; i++) {rate3[i] = root[i + 3] * prod;irate3[i] = iroot[i + 3] * iprod;prod *= iroot[i + 3];iprod *= root[i + 3];}}int n = int(a.size());int h = topbit(n);assert(n == 1 << h);if (!inverse) {int len = 0;while (len < h) {if (h - len == 1) {int p = 1 << (h - len - 1);mint rot = 1;FOR(s, 1 << len) {int offset = s << (h - len);FOR(i, p) {auto l = a[i + offset];auto r = a[i + offset + p] * rot;a[i + offset] = l + r;a[i + offset + p] = l - r;}rot *= rate2[topbit(~s & -~s)];}len++;} else {int p = 1 << (h - len - 2);mint rot = 1, imag = root[2];for (int s = 0; s < (1 << len); s++) {mint rot2 = rot * rot;mint rot3 = rot2 * rot;int offset = s << (h - len);for (int i = 0; i < p; i++) {u64 mod2 = u64(mod) * mod;u64 a0 = a[i + offset].val;u64 a1 = u64(a[i + offset + p].val) * rot.val;u64 a2 = u64(a[i + offset + 2 * p].val) * rot2.val;u64 a3 = u64(a[i + offset + 3 * p].val) * rot3.val;u64 a1na3imag = (a1 + mod2 - a3) % mod * imag.val;u64 na2 = mod2 - a2;a[i + offset] = a0 + a2 + a1 + a3;a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));a[i + offset + 2 * p] = a0 + na2 + a1na3imag;a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);}rot *= rate3[topbit(~s & -~s)];}len += 2;}}} else {mint coef = mint(1) / mint(len(a));FOR(i, len(a)) a[i] *= coef;int len = h;while (len) {if (len == 1) {int p = 1 << (h - len);mint irot = 1;FOR(s, 1 << (len - 1)) {int offset = s << (h - len + 1);FOR(i, p) {u64 l = a[i + offset].val;u64 r = a[i + offset + p].val;a[i + offset] = l + r;a[i + offset + p] = (mod + l - r) * irot.val;}irot *= irate2[topbit(~s & -~s)];}len--;} else {int p = 1 << (h - len);mint irot = 1, iimag = iroot[2];FOR(s, (1 << (len - 2))) {mint irot2 = irot * irot;mint irot3 = irot2 * irot;int offset = s << (h - len + 2);for (int i = 0; i < p; i++) {u64 a0 = a[i + offset + 0 * p].val;u64 a1 = a[i + offset + 1 * p].val;u64 a2 = a[i + offset + 2 * p].val;u64 a3 = a[i + offset + 3 * p].val;u64 x = (mod + a2 - a3) * iimag.val % mod;a[i + offset] = a0 + a1 + a2 + a3;a[i + offset + 1 * p] = (a0 + mod - a1 + x) * irot.val;a[i + offset + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * irot2.val;a[i + offset + 3 * p] = (a0 + 2 * mod - a1 - x) * irot3.val;}irot *= irate3[topbit(~s & -~s)];}len -= 2;}}}}#line 1 "/home/maspy/compro/library/poly/fft.hpp"namespace CFFT {using real = double;struct C {real x, y;C() : x(0), y(0) {}C(real x, real y) : x(x), y(y) {}inline C operator+(const C& c) const { return C(x + c.x, y + c.y); }inline C operator-(const C& c) const { return C(x - c.x, y - c.y); }inline C operator*(const C& c) const {return C(x * c.x - y * c.y, x * c.y + y * c.x);}inline C conj() const { return C(x, -y); }};const real PI = acosl(-1);int base = 1;vector<C> rts = {{0, 0}, {1, 0}};vector<int> rev = {0, 1};void ensure_base(int nbase) {if (nbase <= base) return;rev.resize(1 << nbase);rts.resize(1 << nbase);for (int i = 0; i < (1 << nbase); i++) {rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));}while (base < nbase) {real angle = PI * 2.0 / (1 << (base + 1));for (int i = 1 << (base - 1); i < (1 << base); i++) {rts[i << 1] = rts[i];real angle_i = angle * (2 * i + 1 - (1 << base));rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));}++base;}}void fft(vector<C>& a, int n) {assert((n & (n - 1)) == 0);int zeros = __builtin_ctz(n);ensure_base(zeros);int shift = base - zeros;for (int i = 0; i < n; i++) {if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); }}for (int k = 1; k < n; k <<= 1) {for (int i = 0; i < n; i += 2 * k) {for (int j = 0; j < k; j++) {C z = a[i + j + k] * rts[j + k];a[i + j + k] = a[i + j] - z;a[i + j] = a[i + j] + z;}}}}} // namespace CFFT#line 9 "/home/maspy/compro/library/poly/convolution.hpp"template <class mint>vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {if (a.empty() || b.empty()) return {};int n = int(a.size()), m = int(b.size());int sz = 1;while (sz < n + m - 1) sz *= 2;// sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。if ((n + m - 3) <= sz / 2) {auto a_last = a.back(), b_last = b.back();a.pop_back(), b.pop_back();auto c = convolution(a, b);c.resize(n + m - 1);c[n + m - 2] = a_last * b_last;FOR(i, len(a)) c[i + len(b)] += a[i] * b_last;FOR(i, len(b)) c[i + len(a)] += b[i] * a_last;return c;}a.resize(sz), b.resize(sz);bool same = a == b;ntt(a, 0);if (same) {b = a;} else {ntt(b, 0);}FOR(i, sz) a[i] *= b[i];ntt(a, 1);a.resize(n + m - 1);return a;}template <typename mint>vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) {int n = len(a), m = len(b);if (!n || !m) return {};static constexpr int p0 = 167772161;static constexpr int p1 = 469762049;static constexpr int p2 = 754974721;using mint0 = modint<p0>;using mint1 = modint<p1>;using mint2 = modint<p2>;vc<mint0> a0(n), b0(m);vc<mint1> a1(n), b1(m);vc<mint2> a2(n), b2(m);FOR(i, n) a0[i] = a[i].val, a1[i] = a[i].val, a2[i] = a[i].val;FOR(i, m) b0[i] = b[i].val, b1[i] = b[i].val, b2[i] = b[i].val;auto c0 = convolution_ntt<mint0>(a0, b0);auto c1 = convolution_ntt<mint1>(a1, b1);auto c2 = convolution_ntt<mint2>(a2, b2);vc<mint> c(len(c0));FOR(i, n + m - 1) { c[i] = CRT3<mint, p0, p1, p2>(c0[i].val, c1[i].val, c2[i].val); }return c;}template <typename R>vc<double> convolution_fft(const vc<R>& a, const vc<R>& b) {using C = CFFT::C;int need = (int)a.size() + (int)b.size() - 1;int nbase = 1;while ((1 << nbase) < need) nbase++;CFFT::ensure_base(nbase);int sz = 1 << nbase;vector<C> fa(sz);for (int i = 0; i < sz; i++) {double x = (i < (int)a.size() ? a[i] : 0);double y = (i < (int)b.size() ? b[i] : 0);fa[i] = C(x, y);}CFFT::fft(fa, sz);C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);for (int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;fa[i] = z;}for (int i = 0; i < (sz >> 1); i++) {C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * CFFT::rts[(sz >> 1) + i];fa[i] = A0 + A1 * s;}CFFT::fft(fa, sz >> 1);vector<double> ret(need);for (int i = 0; i < need; i++) { ret[i] = (i & 1 ? fa[i >> 1].y : fa[i >> 1].x); }return ret;}vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) {int n = len(a), m = len(b);if (!n || !m) return {};if (min(n, m) <= 2500) return convolution_naive(a, b);ll abs_sum_a = 0, abs_sum_b = 0;ll LIM = 1e15;FOR(i, n) abs_sum_a = min(LIM, abs_sum_a + abs(a[i]));FOR(i, m) abs_sum_b = min(LIM, abs_sum_b + abs(b[i]));if (i128(abs_sum_a) * abs_sum_b < 1e15) {vc<double> c = convolution_fft<ll>(a, b);vc<ll> res(len(c));FOR(i, len(c)) res[i] = ll(floor(c[i] + .5));return res;}static constexpr u32 MOD1 = 167772161; // 2^25static constexpr u32 MOD2 = 469762049; // 2^26static constexpr u32 MOD3 = 754974721; // 2^24using mint1 = modint<MOD1>;using mint2 = modint<MOD2>;using mint3 = modint<MOD3>;vc<mint1> a1(n), b1(m);vc<mint2> a2(n), b2(m);vc<mint3> a3(n), b3(m);FOR(i, n) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];FOR(i, m) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];auto c1 = convolution_ntt<mint1>(a1, b1);auto c2 = convolution_ntt<mint2>(a2, b2);auto c3 = convolution_ntt<mint3>(a3, b3);u128 prod = u128(MOD1) * MOD2 * MOD3;vc<ll> res(n + m - 1);FOR(i, n + m - 1) {u128 x = CRT3<u128, MOD1, MOD2, MOD3>(c1[i].val, c2[i].val, c3[i].val);res[i] = (x < prod / 2 ? ll(x) : -ll(prod - x));}return res;}template <typename mint>vc<mint> convolution(const vc<mint>& a, const vc<mint>& b) {int n = len(a), m = len(b);if (!n || !m) return {};if (mint::can_ntt()) {if (min(n, m) <= 50) return convolution_karatsuba<mint>(a, b);return convolution_ntt(a, b);}if (min(n, m) <= 200) return convolution_karatsuba<mint>(a, b);return convolution_garner(a, b);}#line 2 "/home/maspy/compro/library/poly/integrate.hpp"// 不定積分:integrate(f)// 定積分:integrate(f, L, R)template <typename mint>vc<mint> integrate(const vc<mint>& f) {vc<mint> g(len(f) + 1);FOR3(i, 1, len(g)) g[i] = f[i - 1] * inv<mint>(i);return g;}// 不定積分:integrate(f)// 定積分:integrate(f, L, R)template <typename mint>mint integrate(const vc<mint>& f, mint L, mint R) {mint I = 0;mint pow_L = 1, pow_R = 1;FOR(i, len(f)) {pow_L *= L, pow_R *= R;I += inv<mint>(i + 1) * f[i] * (pow_R - pow_L);}return I;}#line 2 "/home/maspy/compro/library/poly/differentiate.hpp"template <typename mint>vc<mint> differentiate(const vc<mint>& f) {if (len(f) <= 1) return {};vc<mint> g(len(f) - 1);FOR(i, len(g)) g[i] = f[i + 1] * mint(i + 1);return g;}#line 6 "/home/maspy/compro/library/poly/fps_exp.hpp"template <typename mint>vc<mint> fps_exp_sparse(vc<mint>& f) {if (len(f) == 0) return {mint(1)};assert(f[0] == 0);int N = len(f);// df を持たせるvc<pair<int, mint>> dat;FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i - 1, mint(i) * f[i]);vc<mint> F(N);F[0] = 1;FOR(n, 1, N) {mint rhs = 0;for (auto&& [k, fk]: dat) {if (k > n - 1) break;rhs += fk * F[n - 1 - k];}F[n] = rhs * inv<mint>(n);}return F;}template <typename mint>vc<mint> fps_exp_dense(vc<mint>& h) {const int n = len(h);assert(n > 0 && h[0] == mint(0));if (mint::can_ntt()) {vc<mint>& f = h;vc<mint> b = {1, (1 < n ? f[1] : 0)};vc<mint> c = {1}, z1, z2 = {1, 1};while (len(b) < n) {int m = len(b);auto y = b;y.resize(2 * m);ntt(y, 0);z1 = z2;vc<mint> z(m);FOR(i, m) z[i] = y[i] * z1[i];ntt(z, 1);FOR(i, m / 2) z[i] = 0;ntt(z, 0);FOR(i, m) z[i] *= -z1[i];ntt(z, 1);c.insert(c.end(), z.begin() + m / 2, z.end());z2 = c;z2.resize(2 * m);ntt(z2, 0);vc<mint> x(f.begin(), f.begin() + m);FOR(i, len(x) - 1) x[i] = x[i + 1] * mint(i + 1);x.back() = 0;ntt(x, 0);FOR(i, m) x[i] *= y[i];ntt(x, 1);FOR(i, m - 1) x[i] -= b[i + 1] * mint(i + 1);x.resize(m + m);FOR(i, m - 1) x[m + i] = x[i], x[i] = 0;ntt(x, 0);FOR(i, m + m) x[i] *= z2[i];ntt(x, 1);FOR_R(i, len(x) - 1) x[i + 1] = x[i] * inv<mint>(i + 1);x[0] = 0;FOR3(i, m, min(n, m + m)) x[i] += f[i];FOR(i, m) x[i] = 0;ntt(x, 0);FOR(i, m + m) x[i] *= y[i];ntt(x, 1);b.insert(b.end(), x.begin() + m, x.end());}b.resize(n);return b;}const int L = len(h);assert(L > 0 && h[0] == mint(0));int LOG = 0;while (1 << LOG < L) ++LOG;h.resize(1 << LOG);auto dh = differentiate(h);vc<mint> f = {1}, g = {1};int m = 1;vc<mint> p;FOR(LOG) {p = convolution(f, g);p.resize(m);p = convolution(p, g);p.resize(m);g.resize(m);FOR(i, m) g[i] += g[i] - p[i];p = {dh.begin(), dh.begin() + m - 1};p = convolution(f, p);p.resize(m + m - 1);FOR(i, m + m - 1) p[i] = -p[i];FOR(i, m - 1) p[i] += mint(i + 1) * f[i + 1];p = convolution(p, g);p.resize(m + m - 1);FOR(i, m - 1) p[i] += dh[i];p = integrate(p);FOR(i, m + m) p[i] = h[i] - p[i];p[0] += mint(1);f = convolution(f, p);f.resize(m + m);m += m;}f.resize(L);return f;}template <typename mint>vc<mint> fps_exp(vc<mint>& f) {int n = count_terms(f);int t = (mint::can_ntt() ? 320 : 3000);return (n <= t ? fps_exp_sparse<mint>(f) : fps_exp_dense<mint>(f));}#line 2 "/home/maspy/compro/library/poly/fps_log.hpp"#line 4 "/home/maspy/compro/library/poly/fps_inv.hpp"template <typename mint>vc<mint> fps_inv_sparse(const vc<mint>& f) {int N = len(f);vc<pair<int, mint>> dat;FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);vc<mint> g(N);mint g0 = mint(1) / f[0];g[0] = g0;FOR(n, 1, N) {mint rhs = 0;for (auto&& [k, fk]: dat) {if (k > n) break;rhs -= fk * g[n - k];}g[n] = rhs * g0;}return g;}template <typename mint>vc<mint> fps_inv_dense_ntt(const vc<mint>& F) {vc<mint> G = {mint(1) / F[0]};ll N = len(F), n = 1;G.reserve(N);while (n < N) {vc<mint> f(2 * n), g(2 * n);FOR(i, min(N, 2 * n)) f[i] = F[i];FOR(i, n) g[i] = G[i];ntt(f, false), ntt(g, false);FOR(i, 2 * n) f[i] *= g[i];ntt(f, true);FOR(i, n) f[i] = 0;ntt(f, false);FOR(i, 2 * n) f[i] *= g[i];ntt(f, true);FOR(i, n, min(N, 2 * n)) G.eb(-f[i]);n *= 2;}return G;}template <typename mint>vc<mint> fps_inv_dense(const vc<mint>& F) {if (mint::can_ntt()) return fps_inv_dense_ntt(F);const int N = len(F);vc<mint> R = {mint(1) / F[0]};vc<mint> p;int m = 1;while (m < N) {p = convolution(R, R);p.resize(m + m);vc<mint> f = {F.begin(), F.begin() + min(m + m, N)};p = convolution(p, f);R.resize(m + m);FOR(i, m + m) R[i] = R[i] + R[i] - p[i];m += m;}R.resize(N);return R;}template <typename mint>vc<mint> fps_inv(const vc<mint>& f) {assert(f[0] != mint(0));int n = count_terms(f);int t = (mint::can_ntt() ? 160 : 820);return (n <= t ? fps_inv_sparse<mint>(f) : fps_inv_dense<mint>(f));}#line 5 "/home/maspy/compro/library/poly/fps_log.hpp"template <typename mint>vc<mint> fps_log_dense(const vc<mint>& f) {assert(f[0] == mint(1));ll N = len(f);vc<mint> df = f;FOR(i, N) df[i] *= mint(i);df.erase(df.begin());auto f_inv = fps_inv(f);auto g = convolution(df, f_inv);g.resize(N - 1);g.insert(g.begin(), 0);FOR(i, N) g[i] *= inv<mint>(i);return g;}template <typename mint>vc<mint> fps_log_sparse(const vc<mint>& f) {int N = f.size();vc<pair<int, mint>> dat;FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);vc<mint> F(N);vc<mint> g(N - 1);for (int n = 0; n < N - 1; ++n) {mint rhs = mint(n + 1) * f[n + 1];for (auto&& [i, fi]: dat) {if (i > n) break;rhs -= fi * g[n - i];}g[n] = rhs;F[n + 1] = rhs * inv<mint>(n + 1);}return F;}template <typename mint>vc<mint> fps_log(const vc<mint>& f) {assert(f[0] == mint(1));int n = count_terms(f);int t = (mint::can_ntt() ? 200 : 1200);return (n <= t ? fps_log_sparse<mint>(f) : fps_log_dense<mint>(f));}#line 5 "/home/maspy/compro/library/poly/fps_pow.hpp"// fps の k 乗を求める。k >= 0 の前提である。// 定数項が 1 で、k が mint の場合には、fps_pow_1 を使うこと。// ・dense な場合: log, exp を使う O(NlogN)// ・sparse な場合: O(NK)template <typename mint>vc<mint> fps_pow(const vc<mint>& f, ll k) {assert(0 <= k);int n = len(f);if (k == 0) {vc<mint> g(n);g[0] = mint(1);return g;}int d = n;FOR_R(i, n) if (f[i] != 0) d = i;// d * k >= nif (d >= ceil<ll>(n, k)) {vc<mint> g(n);return g;}ll off = d * k;mint c = f[d];mint c_inv = mint(1) / mint(c);vc<mint> g(n - off);FOR(i, n - off) g[i] = f[d + i] * c_inv;g = fps_pow_1(g, mint(k));vc<mint> h(n);c = c.pow(k);FOR(i, len(g)) h[off + i] = g[i] * c;return h;}template <typename mint>vc<mint> fps_pow_1_sparse(const vc<mint>& f, mint K) {int N = len(f);assert(N == 0 || f[0] == mint(1));vc<pair<int, mint>> dat;FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);vc<mint> g(N);g[0] = 1;FOR(n, N - 1) {mint& x = g[n + 1];for (auto&& [d, cf]: dat) {if (d > n + 1) break;mint t = cf * g[n - d + 1];x += t * (K * mint(d) - mint(n - d + 1));}x *= inv<mint>(n + 1);}return g;}template <typename mint>vc<mint> fps_pow_1_dense(const vc<mint>& f, mint K) {assert(f[0] == mint(1));auto log_f = fps_log(f);FOR(i, len(f)) log_f[i] *= K;return fps_exp_dense(log_f);}template <typename mint>vc<mint> fps_pow_1(const vc<mint>& f, mint K) {int n = count_terms(f);int t = (mint::can_ntt() ? 100 : 1300);return (n <= t ? fps_pow_1_sparse(f, K) : fps_pow_1_dense(f, K));}// f^e, sparse, O(NMK)template <typename mint>vvc<mint> fps_pow_1_sparse_2d(vvc<mint> f, mint n) {assert(f[0][0] == mint(1));int N = len(f), M = len(f[0]);vv(mint, dp, N, M);dp[0] = fps_pow_1_sparse<mint>(f[0], n);vc<tuple<int, int, mint>> dat;FOR(i, N) FOR(j, M) {if ((i > 0 || j > 0) && f[i][j] != mint(0)) dat.eb(i, j, f[i][j]);}FOR(i, 1, N) {FOR(j, M) {// F = f^n, f dF = n df F// [x^{i-1}y^j]mint lhs = 0, rhs = 0;for (auto&& [a, b, c]: dat) {if (a < i && b <= j) lhs += dp[i - a][j - b] * mint(i - a);if (a <= i && b <= j) rhs += dp[i - a][j - b] * c * mint(a);}dp[i][j] = (n * rhs - lhs) * inv<mint>(i);}}return dp;}#line 6 "main.cpp"/*(1+x)(1+xx)(1+xxxx)... の 2 乗を 2 つに分けるということちょうど N 個ずつとる[x^N](1+x+xx)^N*/using mint = modint998;void solve() {LL(N);vc<mint> f = {1, 1, 1};f.resize(N + 1);f = fps_pow_1_sparse<mint>(f, N);mint ANS = f[N];ANS -= mint(1);ANS *= inv<mint>(2);print(ANS);}signed main() {int T = 1;// INT(T);FOR(T) solve();return 0;}