結果
問題 |
No.3045 反復重み付き累積和
|
ユーザー |
|
提出日時 | 2025-02-28 21:37:48 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 4,932 ms / 5,000 ms |
コード長 | 65,077 bytes |
コンパイル時間 | 5,292 ms |
コンパイル使用メモリ | 262,408 KB |
実行使用メモリ | 8,232 KB |
最終ジャッジ日時 | 2025-02-28 21:38:43 |
合計ジャッジ時間 | 50,538 ms |
ジャッジサーバーID (参考情報) |
judge6 / judge2 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 41 |
ソースコード
#line 2 "library/template/template.hpp" #include <bits/stdc++.h> #line 3 "library/template/alias.hpp" using ll = long long; using ull = unsigned long long; using ld = long double; using i128 = __int128_t; using u128 = __uint128_t; using pi = std::pair<int, int>; using pl = std::pair<ll, ll>; using vi = std::vector<int>; using vl = std::vector<ll>; using vs = std::vector<std::string>; using vc = std::vector<char>; using vvl = std::vector<vl>; using vd = std::vector<double>; using vp = std::vector<pl>; using vb = std::vector<bool>; template <typename T> struct infinity { static constexpr T max = std::numeric_limits<T>::max(); static constexpr T min = std::numeric_limits<T>::min(); static constexpr T value = std::numeric_limits<T>::max() / 2; static constexpr T mvalue = std::numeric_limits<T>::min() / 2; }; template <typename T> constexpr T INF = infinity<T>::value; constexpr ll inf = INF<ll>; constexpr ld EPS = 1e-8; constexpr ld PI = 3.1415926535897932384626; constexpr int dx[8] = {-1, 0, 1, 0, 1, -1, -1, 1}; constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1}; #line 3 "library/template/macro.hpp" #ifndef __COUNTER__ #define __COUNTER__ __LINE__ #endif #define SELECT4(a, b, c, d, e, ...) e #define SELECT3(a, b, c, d, ...) d #define REP_1(a, c) for (ll REP_##c = 0; REP_##c < (ll)(a); ++REP_##c) #define REP1(a) REP_1(a, __COUNTER__) #define REP2(i, a) for (ll i = 0; i < (ll)(a); ++i) #define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i) #define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c)) #define rep(...) SELECT4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__) #define RREP_1(a, c) for (ll RREP_##c = (ll)(a) - 1; RREP_##c >= 0; --RREP_##c) #define RREP1(a) RREP_1(a, __COUNTER__) #define RREP2(i, a) for (ll i = (ll)(a) - 1; i >= 0; --i) #define RREP3(i, a, b) for (ll i = (ll)(b) - 1; i >= (ll)(a); --i) #define rrep(...) SELECT3(__VA_ARGS__, RREP3, RREP2, RREP1)(__VA_ARGS__) #define all(v) std::begin(v), std::end(v) #define rall(v) std::rbegin(v), std::rend(v) #define INT(...) \ int __VA_ARGS__; \ scan(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ scan(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ scan(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ scan(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ scan(__VA_ARGS__) #define LD(...) \ ld __VA_ARGS__; \ scan(__VA_ARGS__) #define pb push_back #define eb emplace_back #line 3 "library/template/type-traits.hpp" #line 5 "library/template/type-traits.hpp" template <typename T, typename... Args> struct function_traits_impl { using return_type = T; static constexpr std::size_t arg_size = sizeof...(Args); template <std::size_t idx> using argument_type = typename std::tuple_element<idx, std::tuple<Args...>>::type; using argument_types = std::tuple<Args...>; }; template <typename> struct function_traits_helper; template <typename T, typename Tp, typename... Args> struct function_traits_helper<T (Tp::*)(Args...)> : function_traits_impl<T, Args...> {}; template <typename T, typename Tp, typename... Args> struct function_traits_helper<T (Tp::*)(Args...) const> : function_traits_impl<T, Args...> {}; template <typename T, typename Tp, typename... Args> struct function_traits_helper<T (Tp::*)(Args...)&> : function_traits_impl<T, Args...> {}; template <typename T, typename Tp, typename... Args> struct function_traits_helper<T (Tp::*)(Args...) const&> : function_traits_impl<T, Args...> {}; template <typename F> using function_traits = function_traits_helper<decltype(&std::remove_reference<F>::type::operator())>; template <typename F> using function_return_type = typename function_traits<F>::return_type; template <typename F, std::size_t idx> using function_argument_type = typename function_traits<F>::template argument_type<idx>; template <typename F> using function_argument_types = typename function_traits<F>::argument_types; template <class T> using is_signed_int = std::integral_constant<bool, (std::is_integral<T>::value && std::is_signed<T>::value) || std::is_same<T, __int128_t>::value>; template <class T> using is_unsigned_int = std::integral_constant<bool, (std::is_integral<T>::value && std::is_unsigned<T>::value) || std::is_same<T, __uint128_t>::value>; template <class T> using is_int = std::integral_constant<bool, is_signed_int<T>::value || is_unsigned_int<T>::value>; template <typename T, typename = void> struct is_range : std::false_type {}; template <typename T> struct is_range< T, decltype(all(std::declval<typename std::add_lvalue_reference<T>::type>()), (void)0)> : std::true_type {}; template <std::size_t size> struct int_least { static_assert(size <= 128, "size must be less than or equal to 128"); using type = typename std::conditional< size <= 8, std::int_least8_t, typename std::conditional< size <= 16, std::int_least16_t, typename std::conditional< size <= 32, std::int_least32_t, typename std::conditional<size <= 64, std::int_least64_t, __int128_t>::type>::type>::type>::type; }; template <std::size_t size> using int_least_t = typename int_least<size>::type; template <std::size_t size> struct uint_least { static_assert(size <= 128, "size must be less than or equal to 128"); using type = typename std::conditional< size <= 8, std::uint_least8_t, typename std::conditional< size <= 16, std::uint_least16_t, typename std::conditional< size <= 32, std::uint_least32_t, typename std::conditional<size <= 64, std::uint_least64_t, __uint128_t>::type>::type>::type>::type; }; template <std::size_t size> using uint_least_t = typename uint_least<size>::type; template <typename T> using double_size_int = int_least<std::numeric_limits<T>::digits * 2 + 1>; template <typename T> using double_size_int_t = typename double_size_int<T>::type; template <typename T> using double_size_uint = uint_least<std::numeric_limits<T>::digits * 2>; template <typename T> using double_size_uint_t = typename double_size_uint<T>::type; template <typename T> using double_size = typename std::conditional<std::is_signed<T>::value, double_size_int<T>, double_size_uint<T>>::type; template <typename T> using double_size_t = typename double_size<T>::type; #line 2 "library/template/in.hpp" #include <unistd.h> #line 5 "library/template/in.hpp" namespace fastio { template <std::size_t BUFF_SIZE = 1 << 17, int decimal_precision = 16> struct Scanner { private: template <typename, typename = void> struct has_scan : std::false_type {}; template <class T> struct has_scan<T, decltype(std::declval<T>().scan(std::declval<Scanner&>()), (void)0)> : std::true_type {}; int fd; char buffer[BUFF_SIZE + 1]; int idx, sz; bool state; inline void load() { int len = sz - idx; if (idx < len) return; std::memcpy(buffer, buffer + idx, len); sz = len + read(fd, buffer + len, BUFF_SIZE - len); idx = 0; buffer[sz] = 0; } inline char cur() { if (idx == sz) load(); if (idx == sz) { state = false; return '\0'; } return buffer[idx]; } inline void next() { if (idx == sz) load(); if (idx == sz) return; idx++; } public: Scanner() : Scanner(0) {} explicit Scanner(int fd) : fd(fd), idx(0), sz(0), state(true) {} explicit Scanner(FILE* file) : fd(fileno(file)), idx(0), sz(0), state(true) {} inline char scan_char() { if (idx == sz) load(); return (idx == sz ? '\0' : buffer[idx++]); } Scanner ignore(int n = 1) { if (idx + n > sz) load(); idx += n; return (*this); } inline void skip_space() { if (idx == sz) load(); while (('\t' <= cur() && cur() <= '\r') || cur() == ' ') { if (++idx == sz) load(); } } void scan(char& a) { skip_space(); a = scan_char(); } void scan(std::string& a) { skip_space(); a.clear(); while (cur() != '\0' && (buffer[idx] < '\t' || '\r' < buffer[idx]) && buffer[idx] != ' ') { a += scan_char(); } } template <std::size_t len> void scan(std::bitset<len>& a) { skip_space(); if (idx + len > sz) load(); rrep(i, len) a[i] = (buffer[idx++] != '0'); } template <typename T, typename std::enable_if<is_int<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { skip_space(); bool neg = false; if constexpr (std::is_signed<T>::value || std::is_same_v<T, __int128_t>) { if (cur() == '-') { neg = true; next(); } } if (idx + 40 > sz && (idx == sz || ('0' <= buffer[sz - 1] && buffer[sz - 1] <= '9'))) load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 + (buffer[idx++] & 15); } if constexpr (std::is_signed<T>::value || std::is_same<T, __int128_t>::value) { if (neg) a = -a; } } template <typename T, typename std::enable_if<std::is_floating_point<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { skip_space(); bool neg = false; if (cur() == '-') { neg = true; next(); } a = 0; while ('0' <= cur() && cur() <= '9') { a = a * 10 + (scan_char() & 15); } if (cur() == '.') { next(); T n = 0, d = 1; for (int i = 0; '0' <= cur() && cur() <= '9' && i < decimal_precision; ++i) { n = n * 10 + (scan_char() & 15); d *= 10; } while ('0' <= cur() && cur() <= '9') next(); a += n / d; } if (neg) a = -a; } private: template <std::size_t i, typename... Args> void scan(std::tuple<Args...>& a) { if constexpr (i < sizeof...(Args)) { scan(std::get<i>(a)); scan<i + 1, Args...>(a); } } public: template <typename... Args> void scan(std::tuple<Args...>& a) { scan<0, Args...>(a); } template <typename T, typename U> void scan(std::pair<T, U>& a) { scan(a.first); scan(a.second); } template <typename T, typename std::enable_if<is_range<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { for (auto& i : a) scan(i); } template <typename T, typename std::enable_if<has_scan<T>::value>::type* = nullptr> void scan(T& a) { a.scan(*this); } void operator()() {} template <typename Head, typename... Tail> void operator()(Head& head, Tail&... tail) { scan(head); operator()(std::forward<Tail&>(tail)...); } template <typename T> Scanner& operator>>(T& a) { scan(a); return *this; } explicit operator bool() const { return state; } friend Scanner& getline(Scanner& sc, std::string& a) { a.clear(); char c; if ((c = sc.scan_char()) == '\0' || c == '\n') return sc; a += c; while ((c = sc.scan_char()) != '\0' && c != '\n') a += c; return sc; } }; Scanner<> sc; } // namespace fastio using fastio::sc; #line 6 "library/template/out.hpp" namespace fastio { struct Pre { char buffer[10000][4]; constexpr Pre() : buffer() { for (int i = 0; i < 10000; ++i) { int n = i; for (int j = 3; j >= 0; --j) { buffer[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; template <std::size_t BUFF_SIZE = 1 << 17, bool debug = false> struct Printer { private: template <typename, bool = debug, class = void> struct has_print : std::false_type {}; template <typename T> struct has_print<T, false, decltype(std::declval<T>().print(std::declval<Printer&>()), (void)0)> : std::true_type {}; template <typename T> struct has_print<T, true, decltype(std::declval<T>().debug(std::declval<Printer&>()), (void)0)> : std::true_type {}; int fd; char buffer[BUFF_SIZE]; int idx; std::size_t decimal_precision; public: Printer() : Printer((debug ? 2 : 1)) {} explicit Printer(int fd) : fd(fd), idx(0), decimal_precision(16) {} explicit Printer(FILE* file) : fd(fileno(file)), idx(0), decimal_precision(16) {} ~Printer() { flush(); } void set_decimal_precision(std::size_t n) { decimal_precision = n; } inline void print_char(char c) { buffer[idx++] = c; if (idx == BUFF_SIZE) flush(); } inline void flush() { idx = write(fd, buffer, idx); idx = 0; } void print(char a) { if constexpr (debug) print_char('\''); print_char(a); if constexpr (debug) print_char('\''); } void print(bool a) { if constexpr (debug) print_char('\''); print_char('0' + a); if constexpr (debug) print_char('\''); } void print(const char* a) { if constexpr (debug) print_char('\"'); for (; *a != '\0'; ++a) print_char(*a); if constexpr (debug) print_char('\"'); } template <std::size_t N> void print(const char (&a)[N]) { if constexpr (debug) print_char('\"'); for (auto i : a) print_char(i); if constexpr (debug) print_char('\"'); } void print(const std::string& a) { if constexpr (debug) print_char('\"'); for (auto i : a) print_char(i); if constexpr (debug) print_char('\"'); } template <std::size_t len> void print(const std::bitset<len>& a) { for (int i = len - 1; i >= 0; --i) print_char('0' + a[i]); } template <typename T, typename std::enable_if<is_int<T>::value && !has_print<T>::value>::type* = nullptr> void print(T a) { if (!a) { print_char('0'); return; } if constexpr (is_signed_int<T>::value) { if (a < 0) { print_char('-'); a = -a; } } if (static_cast<size_t>(idx + 40) >= BUFF_SIZE) flush(); static char stk[40]; int top = 40; while (a >= 10000) { int i = a % 10000; a /= 10000; top -= 4; std::memcpy(stk + top, pre.buffer[i], 4); } if (a >= 1000) { std::memcpy(buffer + idx, pre.buffer[a], 4); idx += 4; } else if (a >= 100) { std::memcpy(buffer + idx, pre.buffer[a] + 1, 3); idx += 3; } else if (a >= 10) { std::memcpy(buffer + idx, pre.buffer[a] + 2, 2); idx += 2; } else { buffer[idx++] = '0' | a; } std::memcpy(buffer + idx, stk + top, 40 - top); idx += 40 - top; } template <typename T, typename std::enable_if<std::is_floating_point<T>::value && !has_print<T>::value>::type* = nullptr> void print(T a) { if (a == infinity<T>::max || a == infinity<T>::value) { print("inf"); return; } if (a == infinity<T>::min || a == infinity<T>::mvalue) { print("-inf"); return; } if (std::isnan(a)) { print("nan"); return; } if (a < 0) { print_char('-'); a = -a; } T b = a; if (b < 1) { print_char('0'); } else { std::string s; while (b >= 1) { s += (char)('0' | (int)std::fmod(b, 10.0)); b /= 10; } for (auto i = s.rbegin(); i != s.rend(); ++i) { print_char(*i); } } print_char('.'); for (std::size_t _ = 0; _ < decimal_precision; ++_) { a *= 10; print_char('0' | (int)std::fmod(a, 10.0)); } } private: template <std::size_t i, typename... Args> void print(const std::tuple<Args...>& a) { if constexpr (i < sizeof...(Args)) { if constexpr (debug) print_char(','); print_char(' '); print(std::get<i>(a)); print<i + 1>(a); } } public: template <typename... Args> void print(const std::tuple<Args...>& a) { if constexpr (debug) print_char('('); if constexpr (sizeof...(Args) != 0) { print(std::get<0>(a)); } print<1, Args...>(a); if constexpr (debug) print_char(')'); } template <typename T, typename U> void print(const std::pair<T, U>& a) { if constexpr (debug) print_char('('); print(a.first); if constexpr (debug) print_char(','); print_char(' '); print(a.second); if constexpr (debug) print_char(')'); } template <typename T, typename std::enable_if<is_range<T>::value>::type* = nullptr> void print(const T& a) { if constexpr (debug) print_char('{'); auto it = std::begin(a); if (it != std::end(a)) { print(*it); while (++it != std::end(a)) { if constexpr (debug) print_char(','); print_char(' '); print(*it); } } if constexpr (debug) print_char('}'); } template <typename T, typename std::enable_if<has_print<T>::value && !debug>::type* = nullptr> void print(const T& a) { a.print(*this); } template <typename T, typename std::enable_if<has_print<T>::value && debug>::type* = nullptr> void print(const T& a) { a.debug(*this); } void operator()() {} template <typename Head, typename... Tail> void operator()(const Head& head, const Tail&... tail) { print(head); operator()(std::forward<const Tail&>(tail)...); } template <typename T> Printer& operator<<(const T& a) { print(a); return *this; } Printer& operator<<(Printer& (*f)(Printer&)) { return f(*this); } }; template <std::size_t BUFF_SIZE, bool debug> Printer<BUFF_SIZE, debug>& endl(Printer<BUFF_SIZE, debug>& out) { out.print_char('\n'); out.flush(); return out; } template <std::size_t BUFF_SIZE, bool debug> Printer<BUFF_SIZE, debug>& flush(Printer<BUFF_SIZE, debug>& out) { out.flush(); return out; } Printer<> pr; Printer<1 << 17, true> prd; } // namespace fastio using fastio::endl; using fastio::flush; using fastio::pr; using fastio::prd; #line 3 "library/template/func.hpp" #line 8 "library/template/func.hpp" inline constexpr int msb(ull x) { int res = x ? 0 : -1; if (x & 0xffffffff00000000) x &= 0xffffffff00000000, res += 32; if (x & 0xffff0000ffff0000) x &= 0xffff0000ffff0000, res += 16; if (x & 0xff00ff00ff00ff00) x &= 0xff00ff00ff00ff00, res += 8; if (x & 0xf0f0f0f0f0f0f0f0) x &= 0xf0f0f0f0f0f0f0f0, res += 4; if (x & 0xcccccccccccccccc) x &= 0xcccccccccccccccc, res += 2; return res + (x & 0xaaaaaaaaaaaaaaaa ? 1 : 0); } inline constexpr int ceil_log2(ull x) { return x ? msb(x - 1) + 1 : 0; } inline constexpr ull reverse(ull x) { x = ((x & 0x5555555555555555) << 1) | ((x & 0xaaaaaaaaaaaaaaaa) >> 1); x = ((x & 0x3333333333333333) << 2) | ((x & 0xcccccccccccccccc) >> 2); x = ((x & 0x0f0f0f0f0f0f0f0f) << 4) | ((x & 0xf0f0f0f0f0f0f0f0) >> 4); x = ((x & 0x00ff00ff00ff00ff) << 8) | ((x & 0xff00ff00ff00ff00) >> 8); x = ((x & 0x0000ffff0000ffff) << 16) | ((x & 0xffff0000ffff0000) >> 16); return (x << 32) | (x >> 32); } inline constexpr ull reverse(ull x, int len) { return reverse(x) >> (64 - len); } inline constexpr int popcnt(ull x) { #if __cplusplus >= 202002L return std::popcount(x); #endif x = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555); x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333); x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f0f0f0f0f); x = (x & 0x00ff00ff00ff00ff) + ((x >> 8) & 0x00ff00ff00ff00ff); x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff); return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff); } template <typename T, typename U> inline constexpr bool chmin(T& a, U b) { return a > b && (a = b, true); } template <typename T, typename U> inline constexpr bool chmax(T& a, U b) { return a < b && (a = b, true); } inline constexpr ll gcd(ll a, ll b) { if (a < 0) a = -a; if (b < 0) b = -b; while (b) { const ll c = b; b = a % b; a = c; } return a; } inline constexpr ll lcm(ll a, ll b) { return a / gcd(a, b) * b; } inline constexpr bool is_prime(ll n) { if (n <= 1) return false; for (ll i = 2; i * i <= n; i++) { if (n % i == 0) return false; } return true; } inline constexpr ll my_pow(ll a, ll b) { ll res = 1; while (b) { if (b & 1) res *= a; a *= a; b >>= 1; } return res; } inline constexpr ll mod_pow(ll a, ll b, const ll& mod) { if (mod == 1) return 0; a %= mod; ll res = 1; while (b) { if (b & 1) (res *= a) %= mod; (a *= a) %= mod; b >>= 1; } return res; } inline ll mod_inv(ll a, const ll& mod) { ll b = mod, x = 1, u = 0, t; while (b) { t = a / b; std::swap(a -= t * b, b); std::swap(x -= t * u, u); } if (x < 0) x += mod; return x; } template <typename T> T binary_gcd(T x_, T y_) { T x = x_ < 0 ? -x_ : x_, y = y_ < 0 ? -y_ : y_; if (!x || !y) return x + y; int n = __builtin_ctzll(x), m = __builtin_ctzll(y); x >>= n, y >>= m; while (x != y) { if (x > y) { x = (x - y) >> __builtin_ctzll(x - y); } else { y = (y - x) >> __builtin_ctzll(y - x); } } return x << std::min(n, m); } template <typename T, typename U> std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> std::istream& operator>>(std::istream& is, std::pair<T, U>& p) { is >> p.first >> p.second; return is; } template <typename T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) { for (auto it = std::begin(v); it != std::end(v);) { os << *it << ((++it) != std::end(v) ? " " : ""); } return os; } template <typename T> std::istream& operator>>(std::istream& is, std::vector<T>& v) { for (T& in : v) { is >> in; } return is; } inline void scan() {} template <class Head, class... Tail> inline void scan(Head& head, Tail&... tail) { sc >> head; scan(tail...); } template <class T> inline void print(const T& t) { pr << t << '\n'; } template <class Head, class... Tail> inline void print(const Head& head, const Tail&... tail) { pr << head << ' '; print(tail...); } template <class... T> inline void fin(const T&... a) { print(a...); exit(0); } template <typename T> inline void dump(const T& a) { prd << a; } inline void trace() { prd << endl; } template <typename Head, typename... Tail> inline void trace(const Head& head, const Tail&... tail) { dump(head); if (sizeof...(tail)) prd.print_char(','), prd.print_char(' '); trace(tail...); } #ifdef ONLINE_JUDGE #define dbg(...) (void(0)) #else #define dbg(...) \ do { \ prd << #__VA_ARGS__; \ prd.print_char(' '), prd.print_char('='), prd.print_char(' '); \ trace(__VA_ARGS__); \ } while (0) #endif #line 3 "library/template/util.hpp" #line 6 "library/template/util.hpp" template <typename F> struct REC { private: F f; public: explicit constexpr REC(F&& f_) : f(std::forward<F>(f_)) {} template <typename... Args> constexpr auto operator()(Args&&... args) const { return f(*this, std::forward<Args>(args)...); } }; template <typename T, typename Comp = std::less<T>> struct compressor { private: std::vector<T> data; Comp cmp; bool sorted = false; public: compressor() : compressor(Comp()) {} compressor(const Comp& cmp) : cmp(cmp) {} compressor(const std::vector<T>& dat, const Comp& cmp = Comp()) : data(dat), cmp(cmp) {} compressor(std::vector<T>&& dat, const Comp& cmp = Comp()) : data(std::move(dat)), cmp(cmp) {} compressor(std::initializer_list<T> li, const Comp& cmp = Comp()) : data(li.begin(), li.end()), cmp(cmp) {} void push_back(const T& v) { assert(!sorted); data.push_back(v); } void push_back(T&& v) { assert(!sorted); data.push_back(std::move(v)); } template <typename... Args> void emplace_back(Args&&... args) { assert(!sorted); data.emplace_back(std::forward<Args>(args)...); } void push(const std::vector<T>& v) { assert(!sorted); const int n = data.size(); data.resize(v.size() + n); for (int i = 0; i < (int)v.size(); i++) data[i + n] = v[i]; } void build() { assert(!sorted); sorted = 1; std::sort(data.begin(), data.end(), cmp); data.erase(unique(data.begin(), data.end(), [&](const T& l, const T& r) -> bool { return !cmp(l, r) && !cmp(r, l); }), data.end()); } const T& operator[](int k) const& { assert(sorted); return data[k]; } int get_index(const T& v) const { assert(sorted); return int(lower_bound(data.begin(), data.end(), v, cmp) - data.begin()); } void press(std::vector<T>& v) const { assert(sorted); for (auto&& i : v) i = get_index(i); } std::vector<int> pressed(const std::vector<T>& v) const { assert(sorted); std::vector<int> ret(v.size()); for (int i = 0; i < (int)v.size(); i++) ret[i] = get_index(v[i]); return ret; } int size() const { assert(sorted); return data.size(); } }; #line 11 "library/template/template.hpp" using namespace std; #line 3 "library/math/modular/modint.hpp" namespace internal { struct modint_base {}; } // namespace internal template <typename T> using is_modint = is_base_of<internal::modint_base, T>; template <typename T, T mod> struct StaticModInt : internal::modint_base { static_assert(is_integral<T>::value, "T must be integral"); static_assert(is_unsigned<T>::value, "T must be unsgined"); static_assert(mod > 0, "mod must be positive"); static_assert(mod <= INF<T>, "mod*2 must be less than or equal to T::max()"); private: using large_t = typename double_size_uint<T>::type; using signed_t = typename make_signed<T>::type; T val; public: constexpr StaticModInt() : val(0) {} template <typename U, typename enable_if<is_integral<U>::value && is_unsigned<U>::value>::type* = nullptr> constexpr StaticModInt(U x) : val(x % mod) {} template <typename U, typename enable_if<is_integral<U>::value && is_signed<U>::value>::type* = nullptr> constexpr StaticModInt(U x) : val{} { x %= static_cast<signed_t>(mod); if (x < 0) x += static_cast<signed_t>(mod); val = static_cast<T>(x); } constexpr T get() const { return val; } static constexpr T get_mod() { return mod; } static constexpr StaticModInt raw(T v) { StaticModInt res; res.val = v; return res; } constexpr StaticModInt inv() const { return mod_inv(val, mod); } constexpr StaticModInt& operator++() { ++val; if (val == mod) val = 0; return *this; } constexpr StaticModInt operator++(int) { StaticModInt res = *this; ++*this; return res; } constexpr StaticModInt& operator--() { if (val == 0) val = mod; --val; return *this; } constexpr StaticModInt operator--(int) { StaticModInt res = *this; --*this; return res; } constexpr StaticModInt& operator+=(const StaticModInt& x) { val += x.val; if (val >= mod) val -= mod; return *this; } constexpr StaticModInt& operator-=(const StaticModInt& x) { if (val < x.val) val += mod; val -= x.val; return *this; } constexpr StaticModInt& operator*=(const StaticModInt& x) { val = static_cast<T>((static_cast<large_t>(val) * x.val) % mod); return *this; } constexpr StaticModInt& operator/=(const StaticModInt& x) { return *this *= x.inv(); } friend constexpr StaticModInt operator+(const StaticModInt& l, const StaticModInt& r) { return StaticModInt(l) += r; } friend constexpr StaticModInt operator-(const StaticModInt& l, const StaticModInt& r) { return StaticModInt(l) -= r; } friend constexpr StaticModInt operator*(const StaticModInt& l, const StaticModInt& r) { return StaticModInt(l) *= r; } friend constexpr StaticModInt operator/(const StaticModInt& l, const StaticModInt& r) { return StaticModInt(l) /= r; } constexpr StaticModInt operator+() const { return StaticModInt(*this); } constexpr StaticModInt operator-() const { return StaticModInt() - *this; } friend constexpr bool operator==(const StaticModInt& l, const StaticModInt& r) { return l.val == r.val; } friend constexpr bool operator!=(const StaticModInt& l, const StaticModInt& r) { return l.val != r.val; } constexpr StaticModInt pow(ll a) const { StaticModInt v = *this, res = 1; if (a < 0) { a = -a; v = v.inv(); } while (a) { if (a & 1) res *= v; v *= v; a >>= 1; } return res; } template <typename Sc> void scan(Sc& a) { ll x; a.scan(x); *this = x; } template <typename Pr> void print(Pr& a) const { a.print(val); } template <typename Pr> void debug(Pr& a) const { a.print(val); } }; template <unsigned int p> using ModInt = StaticModInt<unsigned int, p>; template <typename T, int id> struct DynamicModInt { static_assert(is_integral<T>::value, "T must be integral"); static_assert(is_unsigned<T>::value, "T must be unsigned"); private: using large_t = typename double_size_uint<T>::type; using signed_t = typename make_signed<T>::type; T val; static T mod; public: constexpr DynamicModInt() : val(0) {} template <typename U, typename enable_if<is_integral<U>::value && is_unsigned<U>::value>::type* = nullptr> constexpr DynamicModInt(U x) : val(x % mod) {} template <typename U, typename enable_if<is_integral<U>::value && is_signed<U>::value>::type* = nullptr> constexpr DynamicModInt(U x) : val{} { x %= static_cast<signed_t>(mod); if (x < 0) x += static_cast<signed_t>(mod); val = static_cast<T>(x); } T get() const { return val; } static T get_mod() { return mod; } static void set_mod(T x) { mod = x; assert(mod > 0); assert(mod <= INF<T>); } static DynamicModInt raw(T v) { DynamicModInt res; res.val = v; return res; } DynamicModInt inv() const { return mod_inv(val, mod); } DynamicModInt& operator++() { ++val; if (val == mod) val = 0; return *this; } DynamicModInt operator++(int) { DynamicModInt res = *this; ++*this; return res; } DynamicModInt& operator--() { if (val == 0) val = mod; --val; return *this; } DynamicModInt operator--(int) { DynamicModInt res = *this; --*this; return res; } DynamicModInt& operator+=(const DynamicModInt& x) { val += x.val; if (val >= mod) val -= mod; return *this; } DynamicModInt& operator-=(const DynamicModInt& x) { if (val < x.val) val += mod; val -= x.val; return *this; } DynamicModInt& operator*=(const DynamicModInt& x) { val = static_cast<T>((static_cast<large_t>(val) * x.val) % mod); return *this; } DynamicModInt& operator/=(const DynamicModInt& x) { return *this *= x.inv(); } friend DynamicModInt operator+(const DynamicModInt& l, const DynamicModInt& r) { return DynamicModInt(l) += r; } friend DynamicModInt operator-(const DynamicModInt& l, const DynamicModInt& r) { return DynamicModInt(l) -= r; } friend DynamicModInt operator*(const DynamicModInt& l, const DynamicModInt& r) { return DynamicModInt(l) *= r; } friend DynamicModInt operator/(const DynamicModInt& l, const DynamicModInt& r) { return DynamicModInt(l) /= r; } DynamicModInt operator+() const { return DynamicModInt(*this); } DynamicModInt operator-() const { return DynamicModInt() - *this; } friend bool operator==(const DynamicModInt& l, const DynamicModInt& r) { return l.val == r.val; } friend bool operator!=(const DynamicModInt& l, const DynamicModInt& r) { return l.val != r.val; } DynamicModInt pow(ll a) const { DynamicModInt v = *this, res = 1; if (a < 0) { a = -a; v = v.inv(); } while (a) { if (a & 1) res *= v; v *= v; a >>= 1; } return res; } template <typename Sc> void scan(Sc& a) { ll x; a.scan(x); *this = x; } template <typename Pr> void print(Pr& a) const { a.print(val); } template <typename Pr> void debug(Pr& a) const { a.print(val); } }; template <typename T, int id> T DynamicModInt<T, id>::mod = 998244353; template <int id> using dynamic_modint = DynamicModInt<unsigned int, id>; using modint = dynamic_modint<-1>; /** * @brief ModInt */ #line 4 "library/math/modular/montgomery-modint.hpp" template <typename T> struct MontgomeryReduction { static_assert(is_integral<T>::value, "template argument must be integral"); static_assert(is_unsigned<T>::value, "template argument must be unsigned"); private: using large_t = typename double_size_uint<T>::type; static constexpr int lg = numeric_limits<T>::digits; T mod; T r; T r2; T minv; T calc_inv() const { T t = 0, res = 0; rep(i, lg) { if (~t & 1) { t += mod; res += static_cast<T>(1) << i; } t >>= 1; } return res; } public: MontgomeryReduction(T x) { set_mod(x); } static constexpr int get_lg() { return lg; } void set_mod(T x) { assert(x > 0); assert(x & 1); assert(x <= INF<T>); mod = x; r = (-static_cast<T>(mod)) % mod; r2 = (-static_cast<large_t>(mod)) % mod; minv = calc_inv(); } inline T get_r() const { return r; } inline T get_mod() const { return mod; } T reduce(large_t x) const { large_t tmp = (x + static_cast<large_t>(static_cast<T>(x) * minv) * mod) >> lg; return tmp >= mod ? tmp - mod : tmp; } T transform(large_t x) const { return reduce(x * r2); } }; template <typename T, int id> struct MontgomeryModInt : internal::modint_base { static_assert(is_integral<T>::value, "template argument must be integral"); static_assert(is_unsigned<T>::value, "template argument must be unsigned"); private: using large_t = typename double_size_uint<T>::type; T val; static MontgomeryReduction<T> reduction; public: MontgomeryModInt() : val(0) {} template <typename U, typename enable_if<is_integral<U>::value && is_unsigned<U>::value>::type* = nullptr> MontgomeryModInt(U x) : val(reduction.transform(x < (static_cast<large_t>(reduction.get_mod()) << reduction.get_lg()) ? static_cast<large_t>(x) : static_cast<large_t>(x % reduction.get_mod()))) {} template <typename U, typename enable_if<is_integral<U>::value && is_signed<U>::value>::type* = nullptr> MontgomeryModInt(U x) : MontgomeryModInt(static_cast<typename std::make_unsigned<U>::type>(x < 0 ? -x : x)) { if (x < 0 && val) val = reduction.get_mod() - val; } T get() const { return reduction.reduce(val); } static T get_mod() { return reduction.get_mod(); } static void set_mod(T x) { reduction.set_mod(x); } MontgomeryModInt& operator++() { val += reduction.get_r(); if (val >= reduction.get_mod()) val -= reduction.get_mod(); return *this; } MontgomeryModInt operator++(int) { MontgomeryModInt res = *this; ++*this; return res; } MontgomeryModInt& operator--() { if (val < reduction.get_r()) val += reduction.get_mod(); val -= reduction.get_r(); return *this; } MontgomeryModInt operator--(int) { MontgomeryModInt res = *this; --*this; return res; } MontgomeryModInt& operator+=(const MontgomeryModInt& r) { val += r.val; if (val >= reduction.get_mod()) val -= reduction.get_mod(); return *this; } MontgomeryModInt& operator-=(const MontgomeryModInt& r) { if (val < r.val) val += reduction.get_mod(); val -= r.val; return *this; } MontgomeryModInt& operator*=(const MontgomeryModInt& r) { val = reduction.reduce(static_cast<large_t>(val) * r.val); return *this; } MontgomeryModInt pow(ull n) const { MontgomeryModInt res = 1, tmp = *this; while (n) { if (n & 1) res *= tmp; tmp *= tmp; n >>= 1; } return res; } MontgomeryModInt inv() const { return pow(reduction.get_mod() - 2); } MontgomeryModInt& operator/=(const MontgomeryModInt& r) { return *this *= r.inv(); } friend MontgomeryModInt operator+(const MontgomeryModInt& l, const MontgomeryModInt& r) { return MontgomeryModInt(l) += r; } friend MontgomeryModInt operator-(const MontgomeryModInt& l, const MontgomeryModInt& r) { return MontgomeryModInt(l) -= r; } friend MontgomeryModInt operator*(const MontgomeryModInt& l, const MontgomeryModInt& r) { return MontgomeryModInt(l) *= r; } friend MontgomeryModInt operator/(const MontgomeryModInt& l, const MontgomeryModInt& r) { return MontgomeryModInt(l) /= r; } friend bool operator==(const MontgomeryModInt& l, const MontgomeryModInt& r) { return l.val == r.val; } friend bool operator!=(const MontgomeryModInt& l, const MontgomeryModInt& r) { return l.val != r.val; } template <typename Sc> void scan(Sc& a) { ll x; a.scan(x); *this = x; } template <typename Pr> void print(Pr& a) const { a.print(get()); } template <typename Pr> void debug(Pr& a) const { a.print(get()); } }; template <typename T, int id> MontgomeryReduction<T> MontgomeryModInt<T, id>::reduction = MontgomeryReduction<T>(998244353); using ArbitraryModInt = MontgomeryModInt<unsigned int, -1>; /** * @brief MontgomeryModInt(モンゴメリ乗算) */ #line 4 "library/math/number/miller-rabin.hpp" template <typename T> constexpr bool miller_rabin(ull n, const ull base[], int sz) { if (T::get_mod() != n) T::set_mod(n); ull d = n - 1; while (~d & 1) d >>= 1; const T e1 = 1, e2 = n - 1; rep(i, sz) { ull a = base[i]; if (n <= a) return true; ull t = d; T y = T(a).pow(t); while (t != n - 1 && y != e1 && y != e2) { y *= y; t <<= 1; } if (y != e2 && (~t & 1)) return false; } return true; } constexpr bool is_prime_fast(ull n) { constexpr ull base_int[3] = {2, 7, 61}, base_ll[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; if (n == 2) return true; if (n < 2 || n % 2 == 0) return false; if (n < (1u << 31)) return miller_rabin<MontgomeryModInt<unsigned int, -2>>(n, base_int, 3); return miller_rabin<MontgomeryModInt<ull, -2>>(n, base_ll, 7); } template <ull n> constexpr bool is_prime_v = is_prime(n); /** * @brief Miller-Rabin Primality Test(ミラーラビン素数判定) */ #line 3 "library/others/random.hpp" template <typename Engine> struct Random { private: Engine rnd; public: using result_type = typename Engine::result_type; Random() : Random(random_device{}()) {} Random(result_type seed) : rnd(seed) {} result_type operator()() { return rnd(); } template <typename IntType = ll> IntType uniform(IntType l, IntType r) { static_assert(is_integral<IntType>::value, "template argument must be an integral type"); return uniform_int_distribution<IntType>{l, r}(rnd); } template <typename RealType = double> RealType uniform_real(RealType l, RealType r) { static_assert(is_floating_point<RealType>::value, "template argument must be a floating point type"); return uniform_real_distribution<RealType>{l, r}(rnd); } bool uniform_bool() { return uniform<int>(0, 1); } template <typename T = ll> pair<T, T> uniform_pair(T l, T r) { T a, b; do { a = uniform<T>(l, r); b = uniform<T>(l, r); } while (a == b); if (a > b) swap(a, b); return {a, b}; } template <typename Iter> void shuffle(const Iter& first, const Iter& last) { std::shuffle(first, last, rnd); } template <class T> vector<T> permutalion(T n) { static_assert(is_integral<T>::value, "template argument must be an integral type"); vector<T> res(n); iota(res.begin(), res.end(), T()); shuffle(all(res)); return res; } }; using Random32 = Random<mt19937>; using Random64 = Random<mt19937_64>; Random32 rand32; Random64 rand64; /** * @brief Random(乱数) */ #line 3 "library/string/run-length.hpp" template <typename Cont, typename Comp> vector<pair<typename Cont::value_type, int>> run_length(const Cont& c, const Comp& cmp) { vector<pair<typename Cont::value_type, int>> ret; if (c.empty()) return ret; ret.emplace_back(c.front(), 1); for (int i = 1; i < (int)c.size(); i++) { if (cmp(c[i], ret.back().first)) { ret.back().second++; } else { ret.emplace_back(c[i], 1); } } return ret; } template <typename Cont> vector<pair<typename Cont::value_type, int>> run_length(const Cont& c) { return run_length(c, equal_to<typename Cont::value_type>()); } #line 7 "library/math/number/pollard-rho.hpp" template <typename T, typename Rand> ull pollard_rho(ull n, Rand& rand) { if (~n & 1) return 2; if (T::get_mod() != n) T::set_mod(n); T c, e = 1; auto f = [&](T x) -> T { return x * x + c; }; constexpr int m = 128; while (1) { c = rand.uniform(1ull, n - 1); T x = rand.uniform(2ull, n - 1), y = x; ull g = 1; while (g == 1) { T p = e, tx = x, ty = y; rep(i, m) { x = f(x); y = f(f(y)); p *= x - y; } g = gcd(p.get(), n); if (g == 1) continue; rep(i, m) { tx = f(tx); ty = f(f(ty)); g = gcd((tx - ty).get(), n); if (g != 1) { if (g != n) return g; break; } } } } return -1; } template <typename T = MontgomeryModInt<ull, -3>, typename Rand = Random64> vector<ull> factorize(ull n, Rand& rand = rand64) { if (n == 1) return {}; vector<ull> res; vector<ull> st = {n}; while (!st.empty()) { ull t = st.back(); st.pop_back(); if (t == 1) continue; if (is_prime_fast(t)) { res.push_back(t); continue; } ull p = pollard_rho<T>(t, rand); st.push_back(p); st.push_back(t / p); } sort(all(res)); return res; } template <typename T = MontgomeryModInt<ull, -3>, typename Rand = Random64> vector<pair<ull, int>> expfactorize(ull n, Rand& rand = rand64) { auto res = factorize<T>(n, rand); return run_length(res); } /** * @brief Pollard's Rho Factorization(ポラード・ロー法) */ #line 6 "library/math/number/primitive-root.hpp" template <typename T = MontgomeryModInt<ull, -4>, typename Rand = Random64> ull primitive_root(ull n, Rand rand = rand64) { assert(is_prime_fast(n)); if (n == 2) return 1; if (T::get_mod() != n) T::set_mod(n); auto divs = factorize(n - 1); divs.erase(unique(divs.begin(), divs.end()), divs.end()); for (auto& x : divs) x = (n - 1) / x; const T e = 1; while (1) { ull g = rand.uniform(2ull, n - 1); bool ok = 1; for (auto x : divs) { if (T(g).pow(x) == e) { ok = false; break; } } if (ok) return g; } } template <ull p, enable_if_t<is_prime_v<p>>* = nullptr> constexpr ull constexpr_primitive_root() { if constexpr (p == 2) return 1; if constexpr (p == 167772161) return 3; if constexpr (p == 469762049) return 3; if constexpr (p == 754974721) return 11; if constexpr (p == 998244353) return 3; if constexpr (p == 1224736769) return 3; if constexpr (p == 1811939329) return 11; if constexpr (p == 2013265921) return 11; rep(g, 2, p) { if (mod_pow(g, (p - 1) >> 1, p) != 1) return g; } return -1; } /** * @brief Primitive Root(原始根) */ #line 6 "library/math/convolution/convolution.hpp" template <unsigned int p> struct NthRoot { private: static constexpr unsigned int lg = msb((p - 1) & (1 - p)); public: array<ModInt<p>, lg + 1> root, inv_root; array<ModInt<p>, max(0u, lg - 1)> rate2, irate2; array<ModInt<p>, max(0u, lg - 2)> rate3, irate3; constexpr NthRoot() : root{}, inv_root{} { root[lg] = mod_pow(constexpr_primitive_root<p>(), (p - 1) >> lg, p); inv_root[lg] = root[lg].pow(p - 2); ; rrep(i, lg) { root[i] = root[i + 1] * root[i + 1]; inv_root[i] = inv_root[i + 1] * inv_root[i + 1]; } { ModInt<p> prod = 1, iprod = 1; rep(i, lg - 1) { rate2[i] = root[i + 2] * prod; irate2[i] = inv_root[i + 2] * iprod; prod *= inv_root[i + 2]; iprod *= root[i + 2]; } } { ModInt<p> prod = 1, iprod = 1; rep(i, lg - 2) { rate3[i] = root[i + 3] * prod; irate3[i] = inv_root[i + 3] * iprod; prod *= inv_root[i + 3]; iprod *= root[i + 3]; } } } static constexpr unsigned int get_lg() { return lg; } }; template <unsigned int p> constexpr NthRoot<p> nth_root; template <typename T, enable_if_t<is_modint<T>::value>* = nullptr> void ntt(vector<T>& a) { constexpr unsigned int p = T::get_mod(); const int sz = a.size(); assert((unsigned int)sz <= ((1 - p) & (p - 1))); assert((sz & (sz - 1)) == 0); const int lg = msb(sz); static constexpr T im = nth_root<p>.root[2]; for (int i = lg; i >= 1; i -= 2) { if (i == 1) { T z = 1; for (int j = 0; j < sz; j += (1 << i)) { for (int k = j; k < j + (1 << (i - 1)); ++k) { const T x = a[k], y = a[k + (1 << (i - 1))] * z; a[k] = x + y, a[k + (1 << (i - 1))] = x - y; } if (j + (1 << i) != sz) z *= nth_root<p>.rate2[__builtin_ctz(~(unsigned int)(j >> i))]; } } else { const int offset = 1 << (i - 2); T z = 1; for (int j = 0; j < sz; j += (1 << i)) { for (int k = j; k < j + (1 << (i - 2)); ++k) { const T z2 = z * z, z3 = z2 * z; const T c0 = a[k], c1 = a[k + offset] * z, c2 = a[k + offset * 2] * z2, c3 = a[k + offset * 3] * z3; const T c0c2 = c0 + c2, c0mc2 = c0 - c2, c1c3 = c1 + c3, c1mc3im = (c1 - c3) * im; a[k] = c0c2 + c1c3; a[k + offset] = c0c2 - c1c3; a[k + offset * 2] = c0mc2 + c1mc3im; a[k + offset * 3] = c0mc2 - c1mc3im; } if (j + (1 << i) != sz) z *= nth_root<p>.rate3[__builtin_ctz(~(unsigned int)(j >> i))]; } } } } template <typename T, enable_if_t<is_modint<T>::value>* = nullptr> void intt(vector<T>& a, const bool& f = true) { constexpr unsigned int p = T::get_mod(); const int sz = a.size(); assert((unsigned int)sz <= ((1 - p) & (p - 1))); assert((sz & (sz - 1)) == 0); const int lg = msb(sz); static constexpr T im = nth_root<p>.inv_root[2]; for (int i = 2 - (lg & 1); i <= lg; i += 2) { if (i == 1) { T z = 1; for (int j = 0; j < sz; j += (1 << i)) { for (int k = j; k < j + (1 << (i - 1)); ++k) { const T x = a[k], y = a[k + (1u << (i - 1))]; a[k] = x + y, a[k + (1u << (i - 1))] = (x - y) * z; } if (j + (1 << i) != sz) z *= nth_root<p>.irate2[__builtin_ctz(~(unsigned int)(j >> i))]; } } else { const int offset = 1 << (i - 2); T z = 1; for (int j = 0; j < sz; j += (1 << i)) { for (int k = j; k < j + (1 << (i - 2)); ++k) { const T z2 = z * z, z3 = z2 * z; const T c0 = a[k], c1 = a[k + offset], c2 = a[k + offset * 2], c3 = a[k + offset * 3]; const T c0c1 = c0 + c1, c0mc1 = c0 - c1, c2c3 = c2 + c3, c2mc3im = (c2 - c3) * im; a[k] = c0c1 + c2c3; a[k + offset] = (c0mc1 + c2mc3im) * z; a[k + offset * 2] = (c0c1 - c2c3) * z2; a[k + offset * 3] = (c0mc1 - c2mc3im) * z3; } if (j + (1 << i) != sz) z *= nth_root<p>.irate3[__builtin_ctz(~(unsigned int)(j >> i))]; } } } if (f) { const T inv_sz = T(1) / sz; for (auto& x : a) x *= inv_sz; } } template <typename T> vector<T> convolution_naive(const vector<T>& a, const vector<T>& b) { const int sz1 = a.size(), sz2 = b.size(); vector<T> c(sz1 + sz2 - 1); rep(i, sz1) rep(j, sz2) c[i + j] += a[i] * b[j]; return c; } template <unsigned int p> vector<ModInt<p>> convolution_for_any_mod(const vector<ModInt<p>>& a, const vector<ModInt<p>>& b); template <typename T, enable_if_t<is_modint<T>::value>* = nullptr> vector<T> convole(vector<T> a, vector<T> b) { const int n = a.size() + b.size() - 1; const int lg = ceil_log2(n); const int sz = 1 << lg; a.resize(sz), b.resize(sz); ntt(a), ntt(b); rep(i, sz) a[i] *= b[i]; intt(a); a.resize(n); return a; } template <typename T, enable_if_t<is_modint<T>::value>* = nullptr> vector<T> convolution(const vector<T>& a, const vector<T>& b) { constexpr unsigned int p = T::get_mod(); const unsigned int sz1 = a.size(), sz2 = b.size(); if (sz1 == 0 || sz2 == 0) return {}; if (sz1 <= 64 || sz2 <= 64) return convolution_naive(a, b); if constexpr (((p - 1) & (1 - p)) >= 128) { if (sz1 + sz2 - 1 <= ((p - 1) & (1 - p))) return convole(a, b); } return convolution_for_any_mod(a, b); } template <unsigned int p = 998244353> vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) { const int sz1 = a.size(), sz2 = b.size(); vector<ModInt<p>> a1(sz1), b1(sz2); rep(i, sz1) a1[i] = a[i]; rep(i, sz2) b1[i] = b[i]; auto c1 = convolution(a1, b1); vector<ll> c(sz1 + sz2 - 1); rep(i, sz1 + sz2 - 1) c[i] = c1[i].get(); return c; } template <unsigned int p> vector<ModInt<p>> convolution_for_any_mod(const vector<ModInt<p>>& a, const vector<ModInt<p>>& b) { const int sz1 = a.size(), sz2 = b.size(); assert(sz1 + sz2 - 1 <= (1 << 26)); vector<ll> a1(sz1), b1(sz2); rep(i, sz1) a1[i] = a[i].get(); rep(i, sz2) b1[i] = b[i].get(); static constexpr ull MOD1 = 469762049; static constexpr ull MOD2 = 1811939329; static constexpr ull MOD3 = 2013265921; static constexpr ull INV1_2 = mod_pow(MOD1, MOD2 - 2, MOD2); static constexpr ull INV1_3 = mod_pow(MOD1, MOD3 - 2, MOD3); static constexpr ull INV2_3 = mod_pow(MOD2, MOD3 - 2, MOD3); auto c1 = convolution<MOD1>(a1, b1); auto c2 = convolution<MOD2>(a1, b1); auto c3 = convolution<MOD3>(a1, b1); vector<ModInt<p>> c(sz1 + sz2 - 1); rep(i, sz1 + sz2 - 1) { ull x1 = c1[i]; ull x2 = (c2[i] - x1 + MOD2) * INV1_2 % MOD2; ull x3 = ((c3[i] - x1 + MOD3) * INV1_3 % MOD3 - x2 + MOD3) * INV2_3 % MOD3; c[i] = ModInt<p>(x1 + (x2 + x3 * MOD2) % p * MOD1); } return c; } /** * @brief Convolution(畳み込み) */ #line 4 "library/math/others/combinatorics.hpp" template <typename T> struct Combinatorics { private: static vector<T> dat, idat; public: static void extend(int sz) { const int pre_sz = dat.size(); if (sz < pre_sz) return; dat.resize(sz + 1, 1); idat.resize(sz + 1, 1); for (int i = pre_sz; i <= sz; i++) dat[i] = dat[i - 1] * i; idat[sz] = T(1) / dat[sz]; for (int i = sz - 1; i >= pre_sz; i--) idat[i] = idat[i + 1] * (i + 1); } static T fac(ll n) { if (n < 0) return T(); extend(n); return dat[n]; } static T finv(ll n) { if (n < 0) return T(); extend(n); return idat[n]; } static T inv(ll n) { if (n <= 0) return T(); extend(n); return dat[n - 1] * idat[n]; } static T com(ll n, ll k) { if (k < 0 || n < k || n < 0) return T(); extend(n); return dat[n] * idat[k] * idat[n - k]; } static T hom(ll n, ll k) { if (n < 0 || k < 0) return T(); return k == 0 ? 1 : com(n + k - 1, k); } static inline T per(ll n, ll k) { if (k < 0 || n < k) return T(); extend(n); return dat[n] * idat[n - k]; } }; template <typename T> vector<T> Combinatorics<T>::dat = vector<T>(2, 1); template <typename T> vector<T> Combinatorics<T>::idat = vector<T>(2, 1); template <long long p> struct COMB { private: static vector<vector<ModInt<p>>> comb; static void init() { if (!comb.empty()) return; comb.assign(p, vector<ModInt<p>>(p)); comb[0][0] = 1; for (int i = 1; i < p; i++) { comb[i][0] = 1; for (int j = i; j > 0; j--) comb[i][j] = comb[i - 1][j - 1] + comb[i - 1][j]; } } public: COMB() { init(); } ModInt<p> com(int n, int k) { init(); ModInt<p> ret = 1; while (n > 0 || k > 0) { int ni = n % p, ki = k % p; ret *= comb[ni][ki]; n /= p; k /= p; } return ret; } }; template <long long p> vector<vector<ModInt<p>>> COMB<p>::comb = vector<vector<ModInt<p>>>(); /** * @brief Combinatorics(組み合わせ) */ #line 5 "library/math/fps/fps.hpp" template <typename mint = ModInt<998244353>> struct FormalPowerSeries : vector<mint> { using vector<mint>::vector; using FPS = FormalPowerSeries<mint>; using Comb = Combinatorics<mint>; private: static constexpr unsigned int p = mint::get_mod(); public: FormalPowerSeries() : vector<mint>() {} FormalPowerSeries(const vector<mint>& v) : vector<mint>(v) {} FormalPowerSeries(vector<mint>&& v) : vector<mint>(move(v)) {} inline void shrink() { while (!(*this).empty() && (*this).back() == mint()) (*this).pop_back(); } FPS rev() const { FPS res(*this); reverse(res.begin(), res.end()); return res; } FPS pre(int sz) const { FPS res((*this).begin(), (*this).begin() + min(sz, (int)(*this).size())); if ((int)res.size() < sz) res.resize(sz); return res; } FPS& dot(const FPS& r) { rep(i, min((*this).size(), r.size()))(*this)[i] *= r[i]; return *this; } FPS inv(int d = -1) const { const int n = (*this).size(); if (d == -1) d = n; FPS res(d); res[0] = (*this)[0].inv(); for (int sz = 1; sz < d; sz <<= 1) { FPS f((*this).begin(), (*this).begin() + min(n, 2 * sz)); FPS g(res.begin(), res.begin() + sz); f.resize(2 * sz), g.resize(2 * sz); ntt(f), ntt(g); f.dot(g); intt(f); rep(i, sz) f[i] = 0; ntt(f); f.dot(g); intt(f); rep(j, sz, min(2 * sz, d)) res[j] = -f[j]; } return res; } FPS operator+() const { return *this; } FPS operator-() const { FPS res(*this); for (auto& x : res) x = -x; return res; } FPS& operator+=(const mint& r) { if ((*this).empty()) (*this).resize(1); (*this)[0] += r; return *this; } FPS& operator-=(const mint& r) { if ((*this).empty()) (*this).resize(1); (*this)[0] -= r; return *this; } FPS& operator*=(const mint& r) { for (auto& x : *this) x *= r; return *this; } FPS& operator/=(const mint& r) { (*this) *= r.inv(); return *this; } FPS& operator+=(const FPS& r) { if ((*this).size() < r.size()) (*this).resize(r.size()); rep(i, r.size())(*this)[i] += r[i]; return *this; } FPS& operator-=(const FPS& r) { if ((*this).size() < r.size()) (*this).resize(r.size()); rep(i, r.size())(*this)[i] -= r[i]; return *this; } FPS& operator*=(const FPS& r) { auto ret = convolution(*this, r); (*this) = {ret.begin(), ret.end()}; return *this; } FPS& operator/=(FPS r) { const int n = (*this).size(), m = r.size(); if (n < m) { (*this).clear(); return *this; } const int d = n - m + 1; reverse((*this).begin(), (*this).end()); reverse(r.begin(), r.end()); (*this).resize(d); (*this) *= r.inv(d); (*this).resize(d); reverse((*this).begin(), (*this).end()); return *this; } FPS& operator%=(const FPS& r) { const int n = (*this).size(), m = r.size(); if (n < m) return *this; (*this) -= (*this) / r * r; shrink(); return *this; } FPS& operator<<=(ll k) { (*this).insert((*this).begin(), k, mint(0)); return *this; } FPS& operator>>=(ll k) { if (k > (ll)(*this).size()) (*this).clear(); else (*this).erase((*this).begin(), (*this).begin() + k); return *this; } FPS operator<<(ll k) const { return FPS(*this) <<= k; } FPS operator>>(ll k) const { return FPS(*this) >>= k; } friend FPS operator+(const FPS& l, const mint& r) { return FPS(l) += r; } friend FPS operator-(const FPS& l, const mint& r) { return FPS(l) -= r; } friend FPS operator*(const FPS& l, const mint& r) { return FPS(l) *= r; } friend FPS operator/(const FPS& l, const mint& r) { return FPS(l) /= r; } friend FPS operator+(const mint& l, const FPS& r) { return FPS(r) += l; } friend FPS operator-(const mint& l, const FPS& r) { return FPS(-r) += l; } friend FPS operator*(const mint& l, const FPS& r) { return FPS(r) *= l; } friend FPS operator+(const FPS& l, const FPS& r) { return FPS(l) += r; } friend FPS operator-(const FPS& l, const FPS& r) { return FPS(l) -= r; } friend FPS operator*(const FPS& l, const FPS& r) { return FPS(l) *= r; } friend FPS operator/(const FPS& l, const FPS& r) { return FPS(l) /= r; } friend FPS operator%(const FPS& l, const FPS& r) { return FPS(l) %= r; } pair<FPS, FPS> div_mod(const FPS& r) const { FPS q = (*this) / r; FPS m; if ((*this).size() >= r.size()) m = (*this) - q * r; else m = *this; m.shrink(); return {q, m}; } mint operator()(const mint& x) const { mint res = 0, w = 1; for (auto& v : *this) res += v * w, w *= x; return res; } FPS diff() const { const int n = (*this).size(); FPS res(n - 1); rep(i, 1, n) res[i - 1] = (*this)[i] * i; return res; } FPS& inplace_diff() { (*this).erase((*this).begin()); mint coeff = 1; for (int i = 0; i < (int)(*this).size(); i++) { (*this)[i] *= coeff; coeff++; } return *this; } FPS integral() const { const int n = (*this).size(); FPS res(n + 1); Comb::extend(n); rep(i, n) res[i + 1] = (*this)[i] * Comb::inv(i + 1); return res; } FPS& inplace_integral() { const int n = (*this).size(); vector<mint> iv(n + 1, 1); rep(i, 2, n + 1) iv[i] = -iv[p % i] * (p / i); (*this).insert((*this).begin(), mint(0)); rep(i, 1, n + 1)(*this)[i] *= iv[i]; return *this; } FPS log(int d = -1) const { const int n = (*this).size(); if (d == -1) d = n; FPS res = diff() * inv(d); res.resize(d - 1); return res.integral(); } FPS& inplace_log(int d = -1) { const int n = (*this).size(); if (d == -1) d = n; FPS tmp = inv(d); (*this).inplace_diff() *= tmp; (*this).resize(d - 1); return (*this).inplace_integral(); } FPS exp(int d = -1) const { const int n = (*this).size(); if (d == -1) d = n; if (n <= 1) { FPS res(d, mint()); res[0] = 1; return res; } FPS f = {mint(1) + (*this)[0], (*this)[1]}, res{1, (*this)[1]}; for (int sz = 2; sz < d; sz <<= 1) { f.insert(f.end(), (*this).begin() + min(sz, n), (*this).begin() + min(n, sz << 1)); f.resize(sz << 1); res = res * (f - res.log(sz << 1)); res.resize(sz << 1); } res.resize(d); return res; } FPS pow(ll k, int d = -1) const { const int n = (*this).size(); if (d == -1) d = n; if (k == 0) { FPS ans(d, mint()); ans[0] = 1; return ans; } for (int i = 0; i < n; i++) { if ((*this)[i] != mint()) { if (i > d / k) return FPS(d, mint()); mint rev = (*this)[i].inv(); FPS res = (((*this * rev) >> i).log(d) * k).exp(d) * ((*this)[i].pow(k)); res = (res << (i * k)); res.resize(d); return res; } } return FPS(d, mint()); } FPS sqrt( const function<mint(mint)>& get_sqrt = [](mint) { return mint(1); }, int d = -1) const { const int n = (*this).size(); if (d == -1) d = n; if ((*this)[0] == mint(0)) { rep(i, 1, n) { if ((*this)[i] != mint(0)) { if (i & 1) return {}; if (d - i / 2 <= 0) break; auto res = (*this >> i).sqrt(get_sqrt, d - i / 2); if (res.empty()) return {}; res = res << (i / 2); res.resize(d); return res; } } return FPS(d); } auto sqr = get_sqrt((*this)[0]); if (sqr * sqr != (*this)[0]) return {}; FPS res{sqr}; const mint inv2 = mint(2).inv(); FPS f = {(*this)[0]}; for (int i = 1; i < d; i <<= 1) { if (i < n) f.insert(f.end(), (*this).begin() + i, (*this).begin() + min(n, i << 1)); if ((int)f.size() < (i << 1)) f.resize(i << 1); res = (res + f * res.inv(i << 1)) * inv2; } res.resize(d); return res; } }; /** * @brief Formal Power Series(形式的冪級数) */ #line 4 "code.cpp" using mint = ModInt<998244353>; using FPS = FormalPowerSeries<mint>; int main() { LL(n, q); FPS a(n); sc >> a; rep(q) { LL(t); if (t == 1) { LL(k, x); FPS f(n); mint now = 1; rep(i, n) f[i] = now, now *= k; f = f.pow(x); a *= f; a.resize(n); } if(t==2){ LL(x); x--; print(a[x]); } } }