結果
問題 | No.2166 Paint and Fill |
ユーザー |
![]() |
提出日時 | 2022-12-18 15:40:08 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
CE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 58,547 bytes |
コンパイル時間 | 30,289 ms |
コンパイル使用メモリ | 6,816 KB |
最終ジャッジ日時 | 2025-02-09 16:22:58 |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。(リジャッジ後のコンパイルエラーは公開されます)
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
コンパイルが30秒の制限時間を超えました
ソースコード
#line 1 "library/my_template.hpp"#if defined(LOCAL)#include <my_template_compiled.hpp>#else#pragma GCC optimize("Ofast")#pragma GCC optimize("unroll-loops")#include <bits/stdc++.h>using namespace std;using ll = long long;using pi = pair<ll, ll>;using vi = vector<ll>;using u32 = unsigned int;using u64 = unsigned long long;using i128 = __int128;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 vec(type, name, ...) vector<type> name(__VA_ARGS__)#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 FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))#define overload4(a, b, c, d, e, ...) e#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)#define FOR_R(...) \overload4(__VA_ARGS__, FOR4_R, 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 stolltemplate <typename T, typename U>T SUM(const vector<U> &A) {T sum = 0;for (auto &&a: A) sum += a;return sum;}#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()int 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); }// (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 pick(deque<T> &que) {T a = que.front();que.pop_front();return a;}template <typename T>T pick(pq<T> &que) {T a = que.top();que.pop();return a;}template <typename T>T pick(pqg<T> &que) {assert(que.size());T a = que.top();que.pop();return a;}template <typename T>T pick(vc<T> &que) {assert(que.size());T a = que.back();que.pop_back();return a;}template <typename T, typename U>T ceil(T x, U y) {return (x > 0 ? (x + y - 1) / y : x / y);}template <typename T, typename U>T floor(T x, U y) {return (x > 0 ? x / y : (x - y + 1) / y);}template <typename T, typename U>pair<T, T> divmod(T x, U y) {T q = floor(x, y);return {q, x - q * y};}template <typename F>ll binary_search(F check, ll ok, ll ng) {assert(check(ok));while (abs(ok - ng) > 1) {auto x = (ng + ok) / 2;tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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;tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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);}vc<int> s_to_vi(const string &S, char first_char) {vc<int> A(S.size());FOR(i, S.size()) { A[i] = S[i] - first_char; }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;}template <typename CNT, typename T>vc<CNT> bincount(const vc<T> &A, int size) {vc<CNT> C(size);for (auto &&x: A) { ++C[x]; }return C;}// stabletemplate <typename T>vector<int> argsort(const vector<T> &A) {vector<int> ids(A.size());iota(all(ids), 0);sort(all(ids),[&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });return ids;}// A[I[0]], A[I[1]], ...template <typename T>vc<T> rearrange(const vc<T> &A, const vc<int> &I) {int n = len(I);vc<T> B(n);FOR(i, n) B[i] = A[I[i]];return B;}#endif#line 1 "library/other/io.hpp"// based on yosupo's fastio#include <unistd.h>namespace fastio {// クラスが read(), print() を持っているかを判定するメタ関数struct has_write_impl {template <class T>static auto check(T &&x) -> decltype(x.write(), std::true_type{});template <class T>static auto check(...) -> std::false_type;};template <class T>class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {};struct has_read_impl {template <class T>static auto check(T &&x) -> decltype(x.read(), std::true_type{});template <class T>static auto check(...) -> std::false_type;};template <class T>class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};struct Scanner {FILE *fp;char line[(1 << 15) + 1];size_t st = 0, ed = 0;void reread() {memmove(line, line + st, ed - st);ed -= st;st = 0;ed += fread(line + ed, 1, (1 << 15) - ed, fp);line[ed] = '\0';}bool succ() {while (true) {if (st == ed) {reread();if (st == ed) return false;}while (st != ed && isspace(line[st])) st++;if (st != ed) break;}if (ed - st <= 50) {bool sep = false;for (size_t i = st; i < ed; i++) {if (isspace(line[i])) {sep = true;break;}}if (!sep) reread();}return true;}template <class T, enable_if_t<is_same<T, string>::value, int> = 0>bool read_single(T &ref) {if (!succ()) return false;while (true) {size_t sz = 0;while (st + sz < ed && !isspace(line[st + sz])) sz++;ref.append(line + st, sz);st += sz;if (!sz || st != ed) break;reread();}return true;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>bool read_single(T &ref) {if (!succ()) return false;bool neg = false;if (line[st] == '-') {neg = true;st++;}ref = T(0);while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }if (neg) ref = -ref;return true;}template <typename T,typename enable_if<has_read<T>::value>::type * = nullptr>inline bool read_single(T &x) {x.read();return true;}bool read_single(double &ref) {string s;if (!read_single(s)) return false;ref = std::stod(s);return true;}bool read_single(char &ref) {string s;if (!read_single(s) || s.size() != 1) return false;ref = s[0];return true;}template <class T>bool read_single(vector<T> &ref) {for (auto &d: ref) {if (!read_single(d)) return false;}return true;}template <class T, class U>bool read_single(pair<T, U> &p) {return (read_single(p.first) && read_single(p.second));}template <size_t N = 0, typename T>void read_single_tuple(T &t) {if constexpr (N < std::tuple_size<T>::value) {auto &x = std::get<N>(t);read_single(x);read_single_tuple<N + 1>(t);}}template <class... T>bool read_single(tuple<T...> &tpl) {read_single_tuple(tpl);return true;}void read() {}template <class H, class... T>void read(H &h, T &... t) {bool f = read_single(h);assert(f);read(t...);}Scanner(FILE *fp) : fp(fp) {}};struct Printer {Printer(FILE *_fp) : fp(_fp) {}~Printer() { flush(); }static constexpr size_t SIZE = 1 << 15;FILE *fp;char line[SIZE], small[50];size_t pos = 0;void flush() {fwrite(line, 1, pos, fp);pos = 0;}void write(const char val) {if (pos == SIZE) flush();line[pos++] = val;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>void write(T val) {if (pos > (1 << 15) - 50) flush();if (val == 0) {write('0');return;}if (val < 0) {write('-');val = -val; // todo min}size_t len = 0;while (val) {small[len++] = char(0x30 | (val % 10));val /= 10;}for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }pos += len;}void write(const string s) {for (char c: s) write(c);}void write(const char *s) {size_t len = strlen(s);for (size_t i = 0; i < len; i++) write(s[i]);}void write(const double x) {ostringstream oss;oss << fixed << setprecision(15) << x;string s = oss.str();write(s);}void write(const long double x) {ostringstream oss;oss << fixed << setprecision(15) << x;string s = oss.str();write(s);}template <typename T,typename enable_if<has_write<T>::value>::type * = nullptr>inline void write(T x) {x.write();}template <class T>void write(const vector<T> val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write(' ');write(val[i]);}}template <class T, class U>void write(const pair<T, U> val) {write(val.first);write(' ');write(val.second);}template <size_t N = 0, typename T>void write_tuple(const T t) {if constexpr (N < std::tuple_size<T>::value) {if constexpr (N > 0) { write(' '); }const auto x = std::get<N>(t);write(x);write_tuple<N + 1>(t);}}template <class... T>bool write(tuple<T...> tpl) {write_tuple(tpl);return true;}template <class T, size_t S>void write(const array<T, S> val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write(' ');write(val[i]);}}void write(i128 val) {string s;bool negative = 0;if (val < 0) {negative = 1;val = -val;}while (val) {s += '0' + int(val % 10);val /= 10;}if (negative) s += "-";reverse(all(s));if (len(s) == 0) s = "0";write(s);}};Scanner scanner = Scanner(stdin);Printer printer = Printer(stdout);void flush() { printer.flush(); }void print() { printer.write('\n'); }template <class Head, class... Tail>void print(Head &&head, Tail &&... tail) {printer.write(head);if (sizeof...(Tail)) printer.write(' ');print(forward<Tail>(tail)...);}void read() {}template <class Head, class... Tail>void read(Head &head, Tail &... tail) {scanner.read(head);read(tail...);}} // namespace fastiousing fastio::print;using fastio::flush;using fastio::read;#define INT(...) \int __VA_ARGS__; \read(__VA_ARGS__)#define LL(...) \ll __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 2 "library/mod/modint.hpp"template <int mod>struct modint {int val;constexpr modint(ll x = 0) noexcept {if (0 <= x && x < mod)val = x;else {x %= mod;val = (x < 0 ? x + mod : x);}}bool operator<(const modint &other) const {return val < other.val;} // To use std::mapmodint &operator+=(const modint &p) {if ((val += p.val) >= mod) val -= mod;return *this;}modint &operator-=(const modint &p) {if ((val += mod - p.val) >= mod) val -= mod;return *this;}modint &operator*=(const modint &p) {val = (int)(1LL * val * p.val % mod);return *this;}modint &operator/=(const modint &p) {*this *= p.inverse();return *this;}modint operator-() const { return modint(-val); }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(int64_t n) const {modint ret(1), mul(val);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}void write() { fastio::printer.write(val); }void read() { fastio::scanner.read(val); }static constexpr int get_mod() { return mod; }};struct ArbitraryModInt {static constexpr bool is_modint = true;int val;ArbitraryModInt() : val(0) {}ArbitraryModInt(int64_t y): val(y >= 0 ? y % get_mod(): (get_mod() - (-y) % get_mod()) % get_mod()) {}bool operator<(const ArbitraryModInt &other) const {return val < other.val;} // To use std::map<ArbitraryModInt, T>static int &get_mod() {static int mod = 0;return mod;}static void set_mod(int md) { get_mod() = md; }ArbitraryModInt &operator+=(const ArbitraryModInt &p) {if ((val += p.val) >= get_mod()) val -= get_mod();return *this;}ArbitraryModInt &operator-=(const ArbitraryModInt &p) {if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod();return *this;}ArbitraryModInt &operator*=(const ArbitraryModInt &p) {long long a = (long long)val * p.val;int xh = (int)(a >> 32), xl = (int)a, d, m;asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod()));val = m;return *this;}ArbitraryModInt &operator/=(const ArbitraryModInt &p) {*this *= p.inverse();return *this;}ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); }ArbitraryModInt operator+(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) += p;}ArbitraryModInt operator-(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) -= p;}ArbitraryModInt operator*(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) *= p;}ArbitraryModInt operator/(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) /= p;}bool operator==(const ArbitraryModInt &p) const { return val == p.val; }bool operator!=(const ArbitraryModInt &p) const { return val != p.val; }ArbitraryModInt inverse() const {int a = val, b = get_mod(), u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}return ArbitraryModInt(u);}ArbitraryModInt pow(int64_t n) const {ArbitraryModInt ret(1), mul(val);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}void write() { fastio::printer.write(val); }void read() { fastio::scanner.read(val); }};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 (int(dat.size()) <= n) {int k = dat.size();auto q = (mod + k - 1) / k;int r = k * q - mod;dat.emplace_back(dat[r] * mint(q));}return dat[n];}template <typename mint>mint fact(int n) {static const int mod = mint::get_mod();static vector<mint> dat = {1, 1};assert(0 <= n);if (n >= mod) return 0;while (int(dat.size()) <= n) {int k = dat.size();dat.emplace_back(dat[k - 1] * mint(k));}return dat[n];}template <typename mint>mint fact_inv(int n) {static const int mod = mint::get_mod();static vector<mint> dat = {1, 1};assert(-1 <= n && n < mod);if (n == -1) return mint(0);while (int(dat.size()) <= n) {int k = dat.size();dat.emplace_back(dat[k - 1] * inv<mint>(k));}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 (dense) return C_dense<mint>(n, k);if (!large) return fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k);k = min(k, n - k);mint x(1);FOR(i, k) { x *= mint(n - i); }x *= fact_inv<mint>(k);return x;}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} の計算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);}using modint107 = modint<1000000007>;using modint998 = modint<998244353>;using amint = ArbitraryModInt;#line 2 "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 "library/mod/mod_inv.hpp"// long でも大丈夫ll mod_inv(ll val, ll 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 1 "library/poly/convolution_naive.hpp"template <class T>vector<T> convolution_naive(const vector<T>& a, const vector<T>& b) {int n = int(a.size()), m = int(b.size());vector<T> ans(n + m - 1);if (n < m) {FOR(j, m) FOR(i, n) ans[i + j] += a[i] * b[j];} else {FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j];}return ans;}#line 2 "library/poly/ntt.hpp"template <class mint>struct ntt_info {static constexpr int bsf_constexpr(unsigned int n) {int x = 0;while (!(n & (1 << x))) x++;return x;}static constexpr int rank2 = bsf_constexpr(mint::get_mod() - 1);array<mint, rank2 + 1> root;array<mint, rank2 + 1> iroot;array<mint, max(0, rank2 - 1)> rate2;array<mint, max(0, rank2 - 1)> irate2;array<mint, max(0, rank2 - 2)> rate3;array<mint, max(0, rank2 - 2)> irate3;ntt_info() {int g = primitive_root(mint::get_mod());root[rank2] = mint(g).pow((mint::get_mod() - 1) >> rank2);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];}}{mint 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];}}}constexpr int primitive_root(int m) {if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 880803841) return 26;if (m == 998244353) return 3;if (m == 924844053) return 5;return -1;}};template <class mint>void ntt(vector<mint>& a, bool inverse) {int n = int(a.size());int h = topbit(n);assert(n == 1 << h);static const ntt_info<mint> info;if (!inverse) {int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformedwhile (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 *= info.rate2[topbit(~s & -~s)];}len++;} else {int p = 1 << (h - len - 2);mint rot = 1, imag = info.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++) {auto mod2 = 1ULL * mint::get_mod() * mint::get_mod();auto a0 = 1ULL * a[i + offset].val;auto a1 = 1ULL * a[i + offset + p].val * rot.val;auto a2 = 1ULL * a[i + offset + 2 * p].val * rot2.val;auto a3 = 1ULL * a[i + offset + 3 * p].val * rot3.val;auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val * imag.val;auto 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 *= info.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) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p]= (unsigned long long)(mint::get_mod() + l.val - r.val)* irot.val;;}irot *= info.irate2[topbit(~s & -~s)];}len--;} else {int p = 1 << (h - len);mint irot = 1, iimag = info.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++) {auto a0 = 1ULL * a[i + offset + 0 * p].val;auto a1 = 1ULL * a[i + offset + 1 * p].val;auto a2 = 1ULL * a[i + offset + 2 * p].val;auto a3 = 1ULL * a[i + offset + 3 * p].val;auto a2na3iimag= 1ULL * mint((mint::get_mod() + a2 - a3) * iimag.val).val;a[i + offset] = a0 + a1 + a2 + a3;a[i + offset + 1 * p]= (a0 + (mint::get_mod() - a1) + a2na3iimag) * irot.val;a[i + offset + 2 * p]= (a0 + a1 + (mint::get_mod() - a2) + (mint::get_mod() - a3))* irot2.val;a[i + offset + 3 * p]= (a0 + (mint::get_mod() - a1) + (mint::get_mod() - a2na3iimag))* irot3.val;}irot *= info.irate3[topbit(~s & -~s)];}len -= 2;}}}}#line 1 "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 7 "library/poly/convolution.hpp"template <class mint>vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {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 const long long nttprimes[] = {754974721, 167772161, 469762049};using mint0 = modint<754974721>;using mint1 = modint<167772161>;using mint2 = modint<469762049>;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);static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];static const long long m0_inv_m1 = mint1(nttprimes[0]).inverse().val;static const long long m01_inv_m2 = mint2(m01).inverse().val;static const int mod = mint::get_mod();auto garner = [&](mint0 x0, mint1 x1, mint2 x2) -> mint {int r0 = x0.val, r1 = x1.val, r2 = x2.val;int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * mint2(m01_inv_m2);return mint(r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val);};vc<mint> c(len(c0));FOR(i, len(c)) c[i] = garner(c0[i], c1[i], c2[i]);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++) {int x = (i < (int)a.size() ? a[i] : 0);int 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) <= 60) 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, n) 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 unsigned long long MOD1 = 754974721; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static constexpr unsigned long long M2M3 = MOD2 * MOD3;static constexpr unsigned long long M1M3 = MOD1 * MOD3;static constexpr unsigned long long M1M2 = MOD1 * MOD2;static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;static const unsigned long long i1 = mod_inv(MOD2 * MOD3, MOD1);static const unsigned long long i2 = mod_inv(MOD1 * MOD3, MOD2);static const unsigned long long i3 = mod_inv(MOD1 * MOD2, MOD3);using 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);vc<ll> c(n + m - 1);FOR(i, n + m - 1) {u64 x = 0;x += (c1[i].val * i1) % MOD1 * M2M3;x += (c2[i].val * i2) % MOD2 * M1M3;x += (c3[i].val * i3) % MOD3 * M1M2;ll diff = c1[i].val - ((long long)(x) % (long long)(MOD1));if (diff < 0) diff += MOD1;static constexpr unsigned long long offset[5]= {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};x -= offset[diff % 5];c[i] = x;}return c;}template <typename mint>enable_if_t<is_same<mint, modint998>::value, vc<mint>> convolution(const vc<mint>& a, const vc<mint>& b) {int n = len(a), m = len(b);if (!n || !m) return {};if (min(n, m) <= 60) return convolution_naive(a, b);return convolution_ntt(a, b);}template <typename mint>enable_if_t<!is_same<mint, modint998>::value, vc<mint>> convolution(const vc<mint>& a, const vc<mint>& b) {int n = len(a), m = len(b);if (!n || !m) return {};if (min(n, m) <= 60) return convolution_naive(a, b);return convolution_garner(a, b);}#line 2 "library/poly/integrate.hpp"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;}#line 2 "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 "library/poly/fps_exp.hpp"template <typename mint>enable_if_t<is_same<mint, modint998>::value, vc<mint>> fps_exp(vc<mint>& f) {if (count_terms(f) <= 300) return fps_exp_sparse(f);return fps_exp_dense(f);}template <typename mint>enable_if_t<!is_same<mint, modint998>::value, vc<mint>> fps_exp(vc<mint>& f) {if (count_terms(f) <= 1000) return fps_exp_sparse(f);return fps_exp_dense(f);}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>enable_if_t<!is_same<mint, modint998>::value, vc<mint>> fps_exp_dense(vc<mint> h) {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;}// ntt 素数専用実装。長さ n の FFT を利用して 2n の FFT// を行うなどの高速化をしている。template <typename mint>enable_if_t<is_same<mint, modint998>::value, vc<mint>> fps_exp_dense(vc<mint>& f) {const int n = len(f);assert(n > 0 && f[0] == mint(0));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;}#line 2 "library/poly/fps_log.hpp"#line 4 "library/poly/fps_inv.hpp"template <typename mint>vc<mint> fps_inv_sparse(const vc<mint>& f) {assert(f[0] != mint(0));int N = len(f);vc<pair<int, mint>> dat;FOR3(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;FOR3(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>enable_if_t<is_same<mint, modint998>::value, vc<mint>> fps_inv_dense(const vc<mint>& F) {assert(F[0] != mint(0));vc<mint> G = {mint(1) / F[0]};G.reserve(len(F));ll N = len(F), n = 1;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);FOR3(i, n, 2 * n) G.eb(f[i] * mint(-1));n *= 2;}G.resize(N);return G;}template <typename mint>enable_if_t<!is_same<mint, modint998>::value, vc<mint>> fps_inv_dense(const vc<mint>& F) {int N = len(F);assert(F[0] != mint(0));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>enable_if_t<is_same<mint, modint998>::value, vc<mint>> fps_inv(const vc<mint>& f) {if (count_terms(f) <= 200) return fps_inv_sparse<mint>(f);return fps_inv_dense<mint>(f);}template <typename mint>enable_if_t<!is_same<mint, modint998>::value, vc<mint>> fps_inv(const vc<mint>& f) {if (count_terms(f) <= 700) return fps_inv_sparse<mint>(f);return fps_inv_dense<mint>(f);}#line 5 "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));if(count_terms(f) <= 200) return fps_log_sparse(f);return fps_log_dense(f);}#line 5 "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(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);vc<pair<int, mint>> dat;FOR3(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(log_f);}template <typename mint>vc<mint> fps_pow_1(const vc<mint>& f, mint K) {if (count_terms(f) <= 100) return fps_pow_1_sparse(f, K);return fps_pow_1_dense(f, K);}#line 2 "library/poly/from_log_differentiation.hpp"#line 2 "library/linalg/mat_mul.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 <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>vc<vc<T>> mat_mul(const vc<vc<T>>& A, const vc<vc<T>>& B) {const int mod = T::get_mod();auto N = len(A), M = len(B), K = len(B[0]);vv(int, b, K, M);FOR(i, M) FOR(j, K) b[j][i] = B[i][j].val;vv(T, C, N, K);FOR(i, N) {FOR(j, K) {i128 sm = 0;FOR(m, M) { sm += ll(A[i][m].val) * b[j][m]; }C[i][j] = sm % mod;}}return C;}template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>vc<vc<T>> mat_mul(const vc<vc<T>>& A, const vc<vc<T>>& B) {auto N = len(A), M = len(B), K = len(B[0]);vv(T, C, N, K);FOR(n, N) FOR(m, M) FOR(k, K) C[n][k] += A[n][m] * B[m][k];return C;}#line 2 "library/alg/monoid/mul.hpp"template <class T>struct Monoid_Mul {using value_type = T;using X = T;static constexpr X op(const X &x, const X &y) noexcept { return x * y; }static constexpr X inverse(const X &x) noexcept { return X(1) / x; }static constexpr X unit() { return X(1); }static constexpr bool commute = true;};#line 1 "library/ds/sliding_window_aggregation.hpp"template <class Monoid>struct Sliding_Window_Aggregation {using X = typename Monoid::value_type;using value_type = X;int sz = 0;vc<X> dat;vc<X> cum_l;X cum_r;Sliding_Window_Aggregation(): cum_l({Monoid::unit()}), cum_r(Monoid::unit()) {}int size() { return sz; }void push(X x) {++sz;cum_r = Monoid::op(cum_r, x);dat.eb(x);}void pop() {--sz;cum_l.pop_back();if (len(cum_l) == 0) {cum_l = {Monoid::unit()};cum_r = Monoid::unit();while (len(dat) > 1) {cum_l.eb(Monoid::op(dat.back(), cum_l.back()));dat.pop_back();}dat.pop_back();}}X lprod() { return cum_l.back(); }X rprod() { return cum_r; }X prod() { return Monoid::op(cum_l.back(), cum_r); }void debug() {print("swag");print("dat", dat);print("cum_l", cum_l);print("cum_r", cum_r);}};// 定数倍は目に見えて遅くなるので、queue でよいときは使わないtemplate <class Monoid>struct SWAG_deque {using X = typename Monoid::value_type;using value_type = X;int sz;vc<X> dat_l, dat_r;vc<X> cum_l, cum_r;SWAG_deque() : sz(0), cum_l({Monoid::unit()}), cum_r({Monoid::unit()}) {}int size() { return sz; }void push_back(X x) {++sz;dat_r.eb(x);cum_r.eb(Monoid::op(cum_r.back(), x));}void push_front(X x) {++sz;dat_l.eb(x);cum_l.eb(Monoid::op(x, cum_l.back()));}void push(X x) { push_back(x); }void clear() {sz = 0;dat_l.clear(), dat_r.clear();cum_l = {Monoid::unit()}, cum_r = {Monoid::unit()};}void pop_front() {if (sz == 1) return clear();if (dat_l.empty()) rebuild();--sz;dat_l.pop_back();cum_l.pop_back();}void pop_back() {if (sz == 1) return clear();if (dat_r.empty()) rebuild();--sz;dat_r.pop_back();cum_r.pop_back();}void pop() { pop_front(); }X lprod() { return cum_l.back(); }X rprod() { return cum_r.back(); }X prod() { return Monoid::op(cum_l.back(), cum_r.back()); }X prod_all() { return prod(); }void debug() {print("swag");print("dat_l", dat_l);print("dat_r", dat_r);print("cum_l", cum_l);print("cum_r", cum_r);}private:void rebuild() {vc<X> X;FOR_R(i, len(dat_l)) X.eb(dat_l[i]);X.insert(X.end(), all(dat_r));clear();int m = len(X) / 2;FOR_R(i, m) push_front(X[i]);FOR(i, m, len(X)) push_back(X[i]);assert(sz == len(X));}};#line 5 "library/poly/lagrange_interpolate_iota.hpp"// Input: f(0), ..., f(n-1) and c, m// Return: f(c), f(c+1), ..., f(c+m-1)// Complexity: M(n, n + m)template <typename mint>vc<mint> lagrange_interpolate_iota(vc<mint> &f, mint c, int m) {if (m <= 60) {vc<mint> ANS(m);FOR(i, m) ANS[i] = lagrange_interpolate_iota(f, c + mint(i));return ANS;}ll n = len(f);auto a = f;FOR(i, n) {a[i] = a[i] * fact_inv<mint>(i) * fact_inv<mint>(n - 1 - i);if ((n - 1 - i) & 1) a[i] = -a[i];}// x = c, c+1, ... に対して a0/x + a1/(x-1) + ... を求めておくvc<mint> b(n + m - 1);FOR(i, n + m - 1) b[i] = mint(1) / (c + mint(i - n + 1));a = convolution(a, b);Sliding_Window_Aggregation<Monoid_Mul<mint>> swag;vc<mint> ANS(m);ll L = 0, R = 0;FOR(i, m) {while (L < i) { swag.pop(), ++L; }while (R - L < n) { swag.push(c + mint((R++) - n + 1)); }auto coef = swag.prod();if (coef == 0) {ANS[i] = f[(c + i).val];} else {ANS[i] = a[i + n - 1] * coef;}}return ANS;}// Input: f(0), ..., f(n-1) and c// Return: f(c)// Complexity: O(n)template <typename mint>mint lagrange_interpolate_iota(vc<mint> &f, mint c) {int n = len(f);if (int(c.val) < n) return f[c.val];auto a = f;FOR(i, n) {a[i] = a[i] * fact_inv<mint>(i) * fact_inv<mint>(n - 1 - i);if ((n - 1 - i) & 1) a[i] = -a[i];}vc<mint> lp(n + 1), rp(n + 1);lp[0] = rp[n] = 1;FOR(i, n) lp[i + 1] = lp[i] * (c - i);FOR_R(i, n) rp[i] = rp[i + 1] * (c - i);mint ANS = 0;FOR(i, n) ANS += a[i] * lp[i] * rp[i + 1];return ANS;}#line 4 "library/poly/prefix_product_of_poly.hpp"// A[k-1]...A[0] を計算する// アルゴリズム参考:https://github.com/noshi91/n91lib_rs/blob/master/src/algorithm/polynomial_matrix_prod.rs// 実装参考:https://nyaannyaan.github.io/library/matrix/polynomial-matrix-prefix-prod.hpptemplate <typename T>vc<vc<T>> prefix_product_of_poly_matrix(vc<vc<vc<T>>>& A, ll k) {int n = len(A);using MAT = vc<vc<T>>;auto shift = [&](vc<MAT>& G, T x) -> vc<MAT> {int d = len(G);vvv(T, H, d, n, n);FOR(i, n) FOR(j, n) {vc<T> g(d);FOR(l, d) g[l] = G[l][i][j];auto h = lagrange_interpolate_iota(g, x, d);FOR(l, d) H[l][i][j] = h[l];}return H;};auto evaluate = [&](vc<T>& f, T x) -> T {T res = 0;T p = 1;FOR(i, len(f)) {res += f[i] * p;p *= x;}return res;};ll deg = 1;FOR(i, n) FOR(j, n) chmax(deg, len(A[i][j]) - 1);vc<MAT> G(deg + 1);ll v = 1;while (deg * v * v < k) v *= 2;T iv = T(1) / T(v);FOR(i, len(G)) {T x = T(v) * T(i);vv(T, mat, n, n);FOR(j, n) FOR(k, n) mat[j][k] = evaluate(A[j][k], x);G[i] = mat;}for (ll w = 1; w != v; w *= 2) {T W = w;auto G1 = shift(G, W * iv);auto G2 = shift(G, (W * T(deg) * T(v) + T(v)) * iv);auto G3 = shift(G, (W * T(deg) * T(v) + T(v) + W) * iv);FOR(i, w * deg + 1) {G[i] = mat_mul(G1[i], G[i]);G2[i] = mat_mul(G3[i], G2[i]);}copy(G2.begin(), G2.end() - 1, back_inserter(G));}vv(T, res, n, n);FOR(i, n) res[i][i] = 1;ll i = 0;while (i + v <= k) res = mat_mul(G[i / v], res), i += v;while (i < k) {vv(T, mat, n, n);FOR(j, n) FOR(k, n) mat[j][k] = evaluate(A[j][k], i);res = mat_mul(mat, res);++i;}return res;}// f[k-1]...f[0] を計算するtemplate <typename T>T prefix_product_of_poly(vc<T>& f, ll k) {vc<vc<vc<T>>> A(1);A[0].resize(1);A[0][0] = f;auto res = prefix_product_of_poly_matrix(A, k);return res[0][0];}#line 2 "library/seq/kth_term_of_p_recursive.hpp"// a0, ..., a_{r-1} および f_0, ..., f_r を与える// a_r f_0(0) + a_{r-1}f_1(0) + ... = 0// a_{r+1} f_0(1) + a_{r}f_1(1) + ... = 0template <typename T>T kth_term_of_p_recursive(vc<T> a, vc<vc<T>>& fs, ll k) {int r = len(a);assert(len(fs) == r + 1);if (k < r) return a[k];vc<vc<vc<T>>> A;A.resize(r);FOR(i, r) A[i].resize(r);FOR(i, r) {// A[0][i] = -fs[i + 1];for (auto&& x: fs[i + 1]) A[0][i].eb(-x);}FOR3(i, 1, r) A[i][i - 1] = fs[0];vc<T> den = fs[0];auto res = prefix_product_of_poly_matrix(A, k - r + 1);reverse(all(a));T ANS = 0;FOR(j, r) ANS += res[0][j] * a[j];ANS /= prefix_product_of_poly(den, k - r + 1);return ANS;}#line 4 "library/poly/from_log_differentiation.hpp"// 対数微分 F'/F = a(x)/b(x) から F を復元する。// a, b が sparse であれば、O(N(K1+K2)) 時間でできるtemplate <typename mint>vc<mint> from_log_differentiation(int N, const vc<mint>& a, const vc<mint>& b) {assert(b[0] == mint(1));using P = pair<int, mint>;vc<P> dat_a, dat_b;FOR(i, len(a)) if (a[i] != mint(0)) dat_a.eb(i, a[i]);FOR(i, 1, len(b)) if (b[i] != mint(0)) dat_b.eb(i, b[i]);vc<mint> f(N + 1);vc<mint> df(N);f[0] = mint(1);FOR(n, N) {mint v = 0;for (auto&& [i, bi]: dat_b) {if (i > n) break;v -= bi * df[n - i];}for (auto&& [i, ai]: dat_a) {if (i > n) break;v += ai * f[n - i];}df[n] = v;f[n + 1] = df[n] * inv<mint>(n + 1);}return f;}// F'/F = a/b の解の、[x^K]F を求める。右辺は低次の有理式。template <typename mint>mint from_log_differentiation_kth(int K, vc<mint>& a, vc<mint>& b) {assert(b[0] == mint(1));int r = max(len(a), len(b) - 1);vvc<mint> c(r + 1);FOR(i, r + 1) {mint c0 = 0, c1 = 0;if (i < len(b)) c0 += mint(r - i) * b[i];if (i < len(b)) c1 += b[i];if (0 <= i - 1 && i - 1 < len(b)) c0 -= a[i - 1];c[i] = {c0, c1};}auto f = from_log_differentiation(r - 1, a, b);mint ANS = kth_term_of_p_recursive(f, c, K);return ANS;}#line 6 "main.cpp"// #include "mod/factorial998.hpp"#line 2 "library/poly/multipoint.hpp"template <typename mint>struct SubproductTree {int m;int sz;vc<vc<mint>> T;SubproductTree(const vc<mint>& x) {m = len(x);sz = 1;while (sz < m) sz *= 2;T.resize(2 * sz);FOR(i, sz) T[sz + i] = {1, (i < m ? -x[i] : 0)};FOR3_R(i, 1, sz) T[i] = convolution(T[2 * i], T[2 * i + 1]);}vc<mint> mid_prod(vc<mint>& a, vc<mint>& b) {assert(len(a) >= len(b) && !b.empty());if (min(len(b), len(a) - len(b) + 1) <= 60) {vc<mint> res(len(a) - len(b) + 1);FOR(i, len(res)) FOR(j, len(b)) res[i] += b[j] * a[i + j];return res;}int n = 1 << std::__lg(2 * len(a) - 1);vc<mint> fa(n), fb(n);std::copy(a.begin(), a.end(), fa.begin());std::copy(b.rbegin(), b.rend(), fb.begin());ntt(fa, 0), ntt(fb, 0);FOR(i, n) fa[i] *= fb[i];ntt(fa, 1);fa.resize(len(a));fa.erase(fa.begin(), fa.begin() + len(b) - 1);return fa;}vc<mint> evaluation(vc<mint> f) {int n = len(f);if (n == 0) return vc<mint>(m, mint(0));f.resize(2 * n - 1);vc<vc<mint>> g(2 * sz);g[1] = T[1];g[1].resize(n);g[1] = fps_inv(g[1]);g[1] = mid_prod(f, g[1]);g[1].resize(sz);FOR3(i, 1, sz) {g[2 * i] = mid_prod(g[i], T[2 * i + 1]);g[2 * i + 1] = mid_prod(g[i], T[2 * i]);}vc<mint> vals(m);FOR(i, m) vals[i] = g[sz + i][0];return vals;}vc<mint> interpolation(vc<mint>& y) {assert(len(y) == m);vc<mint> a(m);FOR(i, m) a[i] = T[1][m - i - 1] * (i + 1);a = evaluation(a);vc<vc<mint>> t(2 * sz);FOR(i, sz) t[sz + i] = {(i < m ? y[i] / a[i] : 0)};FOR3_R(i, 1, sz) {t[i] = convolution(t[2 * i], T[2 * i + 1]);auto tt = convolution(t[2 * i + 1], T[2 * i]);FOR(k, len(t[i])) t[i][k] += tt[k];}t[1].resize(m);reverse(all(t[1]));return t[1];}};template <typename mint>vc<mint> multipoint_eval(vc<mint>& f, vc<mint>& x) {if (x.empty()) return {};SubproductTree<mint> F(x);return F.evaluation(f);}template <typename mint>vc<mint> multipoint_interpolate(vc<mint>& x, vc<mint>& y) {if (x.empty()) return {};SubproductTree<mint> F(x);return F.interpolation(y);}// calculate f(ar^k) for 0 <= k < m// https://noshi91.github.io/algorithm-encyclopedia/chirp-z-transform#noredirecttemplate <typename mint>vc<mint> multipoint_eval_on_geom_seq(vc<mint> f, mint a, mint r, int m) {const int n = len(f);assert(r != mint(0));// a == 1 に帰着mint pow_a = 1;FOR(i, n) f[i] *= pow_a, pow_a *= a;auto calc = [&](mint r, int m) -> vc<mint> {// r^{t_i} の計算vc<mint> res(m);mint pow = 1;res[0] = 1;FOR(i, m - 1) {res[i + 1] = res[i] * pow;pow *= r;}return res;};vc<mint> A = calc(r, n + m - 1), B = calc(r.inverse(), max(n, m));FOR(i, n) f[i] *= B[i];reverse(all(f));f = convolution(f, A);f = {f.begin() + n - 1, f.end()};f.resize(m);FOR(i, m) f[i] *= B[i];return f;}#line 8 "main.cpp"using mint = modint998;using poly = vc<mint>;const int mod = 998244353;using MAT = tuple<int, int, int, int>;struct Mono {using value_type = MAT;using X = value_type;static X op(X x, X y) {auto& [x0, x1, x2, x3] = x;auto& [y0, y1, y2, y3] = y;return {(ll(x0) * y0 + ll(x1) * y2) % mod,(ll(x0) * y1 + ll(x1) * y3) % mod,(ll(x2) * y0 + ll(x3) * y2) % mod,(ll(x2) * y1 + ll(x3) * y3) % mod,};}static constexpr X unit() { return {1, 0, 0, 1}; }static constexpr bool commute = 0;};using PMAT = array<array<poly, 2>, 2>;struct PM {using value_type = PMAT;using X = value_type;static X op(X x, X y) {// これは Nlog^2N なので、雑で大丈夫 → そうでもない説int nx = 0, ny = 0;FOR(i, 2) FOR(j, 2) chmax(nx, len(x[i][j]));FOR(i, 2) FOR(j, 2) chmax(ny, len(y[i][j]));int n = nx + ny - 1;int fft_len = 1;while (fft_len < n) fft_len *= 2;FOR(i, 2) FOR(j, 2) {x[i][j].resize(fft_len);ntt(x[i][j], false);}FOR(i, 2) FOR(j, 2) {y[i][j].resize(fft_len);ntt(y[i][j], false);}X z;FOR(i, 2) FOR(j, 2) z[i][j].resize(fft_len);FOR(i, 2) FOR(j, 2) FOR(k, 2) {FOR(p, fft_len) z[i][k][p] += x[i][j][p] * y[j][k][p];}FOR(i, 2) FOR(j, 2) {ntt(z[i][j], true);z[i][j].resize(n);}/*FOR(i, 2) FOR(j, 2) FOR(k, 2) {if (x[i][j].empty() || y[j][k].empty()) continue;poly f = convolution(x[i][j], y[j][k]);if (len(z[i][k]) < len(f)) z[i][k].resize(len(f));FOR(p, len(f)) z[i][k][p] += f[p];}*/return z;}static X unit() {PMAT x;x[0][0] = x[1][1] = {mint(1)};x[0][1] = x[1][0] = {};return x;}static constexpr bool commute = 0;};void solve_1(int Q) {VEC(pi, query, Q);int MAX = 0;for (auto&& [n, k]: query) chmax(MAX, k);++MAX;/*auto naive = [&](ll N, ll K) -> int {MAT x = Mono::unit();FOR(k, K) x = Mono::op(make_mat_int(N, k), x);return get<2>(x);};*/auto make_mat = [&](ll K) -> PMAT {PMAT x;x[0][0] = {mint(-K - K), mint(2)}; // 2N-2Kx[0][1] = {mint(-K * (K - 1) / 2), mint(K)}; // KN - K(K-1)/2x[1][0] = {mint(1)};x[1][1] = {};return x;};const int b_sz = sqrt(12 * MAX);const int b_num = ceil(MAX, b_sz) + 1;vvc<int> QID(b_num);FOR(q, Q) {auto [n, k] = query[q];QID[k / b_sz].eb(q);}auto prod_range = [&](int L, int R) -> PMAT {assert(L < R);vc<PMAT> dat(R - L);FOR(i, R - L) dat[i] = make_mat(L + i);reverse(all(dat));while (len(dat) > 1) {int n = len(dat);FOR(i, n) if (i % 2 == 1) { dat[i - 1] = PM::op(dat[i - 1], dat[i]); }FOR(i, n) if (i % 2 == 0) dat[i / 2] = dat[i];dat.resize(ceil(n, 2));}return dat[0];};vc<mint> ANS(Q);PMAT suffix_prod = PM::unit();FOR(b, b_num) {// suffix_prod に必要なものたちを ME するvc<mint> X;for (auto&& q: QID[b]) { X.eb(query[q].fi); }if (len(X)) {SubproductTree<mint> ST(X);vc<pi> tmp(len(X));{auto Y = ST.evaluation(suffix_prod[0][0]);FOR(k, len(X)) tmp[k].fi = Y[k].val;}{auto Y = ST.evaluation(suffix_prod[1][0]);FOR(k, len(X)) tmp[k].se = Y[k].val;}FOR(t, len(X)) {int qid = QID[b][t];auto [N, K] = query[qid];N %= mod;pi F = tmp[t];FOR(k, b * b_sz, K) {F = {2 * (N - k) * F.fi + (k * (N + N - k + 1) / 2 % mod) * F.se,F.fi};F.fi %= mod;}ANS[qid] = F.fi;}}suffix_prod = PM::op(prod_range(b * b_sz, b * b_sz + b_sz), suffix_prod);}FOR(q, Q) print(ANS[q]);}mint solve_2(ll N, ll K) {if (K >= mod) return 0;assert(K <= mod);poly f = {mint(2 * N), mint(N)};poly g = {mint(1), mint(2), inv<mint>(2)};mint fa = [&]() -> mint {vc<mint> f = {1, 1};return prefix_product_of_poly(f, K).val;}();mint ANS = fa * from_log_differentiation_kth(K, f, g);return ANS;}void solve() {INT(T);if (T <= 10) {FOR(T) {LL(N, K);print(solve_2(N, K));}return;}return solve_1(T);}signed main() {solve();return 0;}