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#include "string/WildcardPatternMatching.hpp"
ワイルドカードを持つ文字列でパターンマッチングを行う。アルファベットなら MOD 2 つで畳み込めば決定的に可能。
IFFT はまとめていいので FFT 6 回 + IFFT 1 回、また middle product でパターンの長さに計算量が依らない。
Schwartz-Zippel Lemma により、文字をランダムに取れば MOD 1 つでもそれぞれ 3/MOD とかの確率で正しくなる。 TL が厳しいときは試してみると良さそう。
vector<bool> wildcard_pattern_matching(vector<int> a, vector<int> b, bool deterministic = true) : 長さ $n$ の文字列 $a$ と長さ $m$ のパターン $b$ に対して、 $c_i := $ 全ての $0 \leq j \leq m-1$ に対し $a_{i+j} = b_j$ もしくはどちらかが $0$ に等しいか、の長さ $n-m+1$ の文字列を返す。 $\Theta(n \log n)$ 。
vector<bool> wildcard_pattern_matching(vector<int> a, vector<int> b, bool deterministic = true)
vector<bool> wildcard_pattern_matching(string a, string b, char wildcard = '*', bool deterministic = true) : 同上。ワイルドカードを指定できる。
vector<bool> wildcard_pattern_matching(string a, string b, char wildcard = '*', bool deterministic = true)
#pragma once #include "../other/template.hpp" #include "../random/Random.hpp" #include "../math/ModInt.hpp" #include "../math/convolution/Convolution.hpp" namespace internal { template<class T> std::vector<bool> wildcard_mod(const std::vector<int>& a, const std::vector<int>& b) { const int n = a.size(), m = b.size(); const int lg = bitop::ceil_log2(n), N = 1 << lg; std::vector<T> A1(N), B1(N), A2(N), B2(N), A3(N), B3(N); std::vector<T> C1(N), C2(n - m + 1); rep (i, n) A1[i] = a[i] == 0 ? 0 : 1; rep (i, m) B1[i] = b[m - 1 - i] == 0 ? 0 : 1; rep (i, n) A2[i] = a[i] * A1[i]; rep (i, m) B2[i] = b[m - 1 - i] * B1[i]; rep (i, n) A3[i] = a[i] * A2[i]; rep (i, m) B3[i] = b[m - 1 - i] * B2[i]; if (find(all(a), 0) == a.end()) { T sm = 0; rep (i, m) sm += B3[i]; rep (i, n - m + 1) C2[i] += sm; } else { number_theoretic_transform(A1); number_theoretic_transform(B3); rep (i, N) C1[i] += A1[i] * B3[i]; } if (find(all(b), 0) == b.end()) { std::vector<T> cum(n + 1); rep (i, n) cum[i + 1] = cum[i] + A3[i]; rep (i, n - m + 1) C2[i] += cum[i + m] - cum[i]; } else { number_theoretic_transform(A3); number_theoretic_transform(B1); rep (i, N) C1[i] += A3[i] * B1[i]; } number_theoretic_transform(A2); number_theoretic_transform(B2); rep (i, N) C1[i] -= 2 * A2[i] * B2[i]; inverse_number_theoretic_transform(C1); std::vector<bool> c(n - m + 1); rep (i, n - m + 1) c[i] = (C1[i + m - 1] + C2[i] == 0); return c; } template<class T> std::vector<bool> wildcard_random(const std::vector<int>& a, const std::vector<int>& b) { const int n = a.size(), m = b.size(); const int lg = bitop::ceil_log2(n), N = 1 << lg; bool a0 = find(all(a), 0) == a.end(); bool b0 = find(all(b), 0) == b.end(); std::vector<T> A1(N), B1(N), A2(N), B2(N); std::vector<T> C1(N), C2(n - m + 1); if (a0) { rep (i, n) A1[i] = a[i] == 0 ? 0 : 1; rep (i, m) { B1[i] = b[m - 1 - i] == 0 ? 0 : rand32.uniform<int>(1, T::get_mod() - 1); } } else { rep (i, n) { A1[i] = a[i] == 0 ? 0 : rand32.uniform<int>(1, T::get_mod() - 1); } rep (i, m) B1[i] = b[m - 1 - i] == 0 ? 0 : 1; } rep (i, n) A2[i] = a[i] * A1[i]; rep (i, m) B2[i] = b[m - 1 - i] * B1[i]; if (a0) { T sm = 0; rep (i, m) sm += B2[i]; rep (i, n - m + 1) C2[i] -= sm; } else { number_theoretic_transform(A1); number_theoretic_transform(B2); rep (i, N) C1[i] -= A1[i] * B2[i]; } if (!a0 && b0) { std::vector<T> cum(n + 1); rep (i, n) cum[i + 1] = cum[i] + A2[i]; rep (i, n - m + 1) C2[i] += cum[i + m] - cum[i]; } else { number_theoretic_transform(A2); number_theoretic_transform(B1); rep (i, N) C1[i] += A2[i] * B1[i]; } inverse_number_theoretic_transform(C1); std::vector<bool> c(n - m + 1); rep (i, n - m + 1) c[i] = (C1[i + m - 1] + C2[i] == 0); return c; } } // namespace internal std::vector<bool> wildcard_pattern_matching(std::vector<int> a, std::vector<int> b, int MAX, bool deterministic = true) { const int n = a.size(), m = b.size(); if (n < m) return {}; i128 MAX_VAL = (i128)MAX * MAX * m; static constexpr int MOD1 = 2113929217, MOD2 = 2013265921, MOD3 = 1811939329; if (!deterministic) { return internal::wildcard_random<static_modint<MOD1>>(a, b); } std::vector<bool> res = internal::wildcard_mod<static_modint<MOD1>>(a, b); if (MAX_VAL >= MOD1) { auto c = internal::wildcard_mod<static_modint<MOD2>>(a, b); rep (i, n - m + 1) res[i] = res[i] && c[i]; } if (MAX_VAL >= (i128)MOD1 * MOD2) { auto c = internal::wildcard_mod<static_modint<MOD3>>(a, b); rep (i, n - m + 1) res[i] = res[i] && c[i]; } return res; } std::vector<bool> wildcard_pattern_matching(const std::vector<int>& a, const std::vector<int>& b, bool deterministic = true) { compressor<int> comp{0}; comp.push(a); comp.push(b); comp.build(); return wildcard_pattern_matching(comp.pressed(a), comp.pressed(b), comp.size() - 1, deterministic); } std::vector<bool> wildcard_pattern_matching(const std::string& a, const std::string& b, char wildcard = '*', bool deterministic = true) { static std::vector<int> idx(128, -1); std::vector<int> A(a.size()), B(b.size()); int cnt = 1; rep (i, a.size()) { A[i] = a[i] == wildcard ? 0 : idx[a[i]] == -1 ? idx[a[i]] = cnt++ : idx[a[i]]; } rep (i, b.size()) { B[i] = b[i] == wildcard ? 0 : idx[b[i]] == -1 ? idx[b[i]] = cnt++ : idx[b[i]]; } rep (i, a.size()) idx[a[i]] = -1; rep (i, b.size()) idx[b[i]] = -1; return wildcard_pattern_matching(A, B, cnt - 1, deterministic); } /** * @brief WildcardPatternMatching * @docs docs/string/WildcardPatternMatching.md */
#line 2 "string/WildcardPatternMatching.hpp" #line 2 "other/template.hpp" #include <bits/stdc++.h> #line 2 "template/macros.hpp" #line 4 "template/macros.hpp" #ifndef __COUNTER__ #define __COUNTER__ __LINE__ #endif #define OVERLOAD5(a, b, c, d, e, ...) e #define REP1_0(b, c) REP1_1(b, c) #define REP1_1(b, c) \ for (ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(b); ++REP_COUNTER_##c) #define REP1(b) REP1_0(b, __COUNTER__) #define REP2(i, b) for (ll i = 0; i < (ll)(b); ++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(...) OVERLOAD5(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__) #define RREP2(i, a) for (ll i = (ll)(a)-1; i >= 0; --i) #define RREP3(i, a, b) for (ll i = (ll)(a)-1; i >= (ll)(b); --i) #define RREP4(i, a, b, c) for (ll i = (ll)(a)-1; i >= (ll)(b); i -= (ll)(c)) #define rrep(...) OVERLOAD5(__VA_ARGS__, RREP4, RREP3, RREP2)(__VA_ARGS__) #define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i) #define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i) #define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c)) #define reps(...) OVERLOAD5(__VA_ARGS__, REPS4, REPS3, REPS2)(__VA_ARGS__) #define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i) #define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i) #define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c)) #define rreps(...) OVERLOAD5(__VA_ARGS__, RREPS4, RREPS3, RREPS2)(__VA_ARGS__) #define each_for(...) for (auto&& __VA_ARGS__) #define each_const(...) for (const auto& __VA_ARGS__) #define all(v) std::begin(v), std::end(v) #define rall(v) std::rbegin(v), std::rend(v) #if __cpp_if_constexpr >= 201606L #define IF_CONSTEXPR constexpr #else #define IF_CONSTEXPR #endif #define IO_BUFFER_SIZE (1 << 17) #line 2 "template/alias.hpp" #line 4 "template/alias.hpp" using ll = long long; using uint = unsigned int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; using ld = long double; using PLL = std::pair<ll, ll>; template<class T> using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>; template<class T> struct infinity { static constexpr T value = std::numeric_limits<T>::max() / 2; static constexpr T mvalue = std::numeric_limits<T>::lowest() / 2; static constexpr T max = std::numeric_limits<T>::max(); static constexpr T min = std::numeric_limits<T>::lowest(); }; #if __cplusplus <= 201402L template<class T> constexpr T infinity<T>::value; template<class T> constexpr T infinity<T>::mvalue; template<class T> constexpr T infinity<T>::max; template<class T> constexpr T infinity<T>::min; #endif #if __cpp_variable_templates >= 201304L template<class T> constexpr T INF = infinity<T>::value; #endif constexpr ll inf = infinity<ll>::value; constexpr ld EPS = 1e-8; constexpr ld PI = 3.1415926535897932384626; #line 2 "template/type_traits.hpp" #line 5 "template/type_traits.hpp" template<class T, class... Args> struct function_traits_impl { using result_type = T; template<std::size_t idx> using argument_type = typename std::tuple_element<idx, std::tuple<Args...>>::type; using argument_tuple = std::tuple<Args...>; static constexpr std::size_t arg_size() { return sizeof...(Args); } }; template<class> struct function_traits_helper; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...)> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...)&> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) const> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) const&> { using type = function_traits_impl<Res, Args...>; }; #if __cpp_noexcept_function_type >= 201510L template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) noexcept> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...)& noexcept> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) const noexcept> { using type = function_traits_impl<Res, Args...>; }; template<class Res, class Tp, class... Args> struct function_traits_helper<Res (Tp::*)(Args...) const& noexcept> { using type = function_traits_impl<Res, Args...>; }; #endif template<class F> using function_traits = typename function_traits_helper< decltype(&std::remove_reference<F>::type::operator())>::type; template<class F> using function_result_type = typename function_traits<F>::result_type; template<class F, std::size_t idx> using function_argument_type = typename function_traits<F>::template argument_type<idx>; template<class F> using function_argument_tuple = typename function_traits<F>::argument_tuple; 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, i128>::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, u128>::value>; template<class T> using is_int = std::integral_constant<bool, is_signed_int<T>::value || is_unsigned_int<T>::value>; template<class T> using make_signed_int = typename std::conditional< std::is_same<T, i128>::value || std::is_same<T, u128>::value, std::common_type<i128>, std::make_signed<T>>::type; template<class T> using make_unsigned_int = typename std::conditional< std::is_same<T, i128>::value || std::is_same<T, u128>::value, std::common_type<u128>, std::make_unsigned<T>>::type; template<class T, class = void> struct is_range : std::false_type {}; template<class T> struct is_range< T, decltype(all(std::declval<typename std::add_lvalue_reference<T>::type>()), (void)0)> : std::true_type {}; template<class T, bool = is_range<T>::value> struct range_rank : std::integral_constant<std::size_t, 0> {}; template<class T> struct range_rank<T, true> : std::integral_constant<std::size_t, range_rank<typename T::value_type>::value + 1> {}; 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, i128>::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, u128>::type>::type>::type>::type; }; template<std::size_t size> using uint_least_t = typename uint_least<size>::type; template<class T> using double_size_int = int_least<std::numeric_limits<T>::digits * 2 + 1>; template<class T> using double_size_int_t = typename double_size_int<T>::type; template<class T> using double_size_uint = uint_least<std::numeric_limits<T>::digits * 2>; template<class T> using double_size_uint_t = typename double_size_uint<T>::type; template<class T> using double_size = typename std::conditional<is_signed_int<T>::value, double_size_int<T>, double_size_uint<T>>::type; template<class T> using double_size_t = typename double_size<T>::type; #line 2 "template/in.hpp" #line 4 "template/in.hpp" #include <unistd.h> #line 8 "template/in.hpp" template<std::size_t buf_size = IO_BUFFER_SIZE, std::size_t decimal_precision = 16> class Scanner { private: template<class, class = 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; int idx, sz; bool state; std::array<char, IO_BUFFER_SIZE + 1> buffer; 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: inline void load() { int len = sz - idx; if (idx < len) return; std::memcpy(buffer.begin(), buffer.begin() + idx, len); sz = len + read(fd, buffer.data() + len, buf_size - len); buffer[sz] = 0; idx = 0; } Scanner(int fd) : fd(fd), idx(0), sz(0), state(true) {} Scanner(FILE* fp) : fd(fileno(fp)), 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 discard_space() { if (idx == sz) load(); while (('\t' <= buffer[idx] && buffer[idx] <= '\r') || buffer[idx] == ' ') { if (++idx == sz) load(); } } void scan(char& a) { discard_space(); a = scan_char(); } void scan(bool& a) { discard_space(); a = scan_char() != '0'; } void scan(std::string& a) { discard_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) { discard_space(); if (idx + len > sz) load(); rrep (i, len) a[i] = buffer[idx++] != '0'; } template<class T, typename std::enable_if<is_signed_int<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); if (buffer[idx] == '-') { ++idx; 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++] - '0'); } } else { if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9') load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 + (buffer[idx++] - '0'); } } } template<class T, typename std::enable_if<is_unsigned_int<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9') load(); a = 0; while ('0' <= buffer[idx] && buffer[idx] <= '9') { a = a * 10 + (buffer[idx++] - '0'); } } template<class T, typename std::enable_if<std::is_floating_point<T>::value && !has_scan<T>::value>::type* = nullptr> void scan(T& a) { discard_space(); bool sgn = false; if (cur() == '-') { sgn = true; next(); } a = 0; while ('0' <= cur() && cur() <= '9') { a = a * 10 + cur() - '0'; next(); } if (cur() == '.') { next(); T n = 0, d = 1; for (int i = 0; '0' <= cur() && cur() <= '9' && i < (int)decimal_precision; ++i) { n = n * 10 + cur() - '0'; d *= 10; next(); } while ('0' <= cur() && cur() <= '9') next(); a += n / d; } if (sgn) a = -a; } private: template<std::size_t i, class... Args> void scan(std::tuple<Args...>& a) { if IF_CONSTEXPR (i < sizeof...(Args)) { scan(std::get<i>(a)); scan<i + 1, Args...>(a); } } public: template<class... Args> void scan(std::tuple<Args...>& a) { scan<0, Args...>(a); } template<class T, class U> void scan(std::pair<T, U>& a) { scan(a.first); scan(a.second); } template<class 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<class T, typename std::enable_if<has_scan<T>::value>::type* = nullptr> void scan(T& a) { a.scan(*this); } void operator()() {} template<class Head, class... Args> void operator()(Head& head, Args&... args) { scan(head); operator()(args...); } template<class T> Scanner& operator>>(T& a) { scan(a); return *this; } explicit operator bool() const { return state; } friend Scanner& getline(Scanner& scan, std::string& a) { a.erase(); char c; if ((c = scan.scan_char()) == '\n' || c == '\0') return scan; a += c; while ((c = scan.scan_char()) != '\n' && c != '\0') a += c; scan.state = true; return scan; } }; Scanner<> scan(0); #line 2 "template/out.hpp" #line 8 "template/out.hpp" struct NumberToString { char buf[10000][4]; constexpr NumberToString() : buf{} { rep (i, 10000) { int n = i; rrep (j, 4) { buf[i][j] = (char)('0' + n % 10); n /= 10; } } } } constexpr precalc_number_to_string; template<std::size_t buf_size = IO_BUFFER_SIZE, bool debug = false> class Printer { private: template<class, bool = debug, class = void> struct has_print : std::false_type {}; template<class T> struct has_print<T, false, decltype(std::declval<T>().print(std::declval<Printer&>()), (void)0)> : std::true_type {}; template<class T> struct has_print<T, true, decltype(std::declval<T>().debug(std::declval<Printer&>()), (void)0)> : std::true_type {}; int fd; std::size_t idx; std::array<char, buf_size> buffer; std::size_t decimal_precision; public: inline void print_char(char c) { #if SHIO_LOCAL buffer[idx++] = c; if (idx == buf_size) flush(); #else if IF_CONSTEXPR (!debug) { buffer[idx++] = c; if (idx == buf_size) flush(); } #endif } inline void flush() { idx = write(fd, buffer.begin(), idx); idx = 0; } Printer(int fd) : fd(fd), idx(0), decimal_precision(16) {} Printer(FILE* fp) : fd(fileno(fp)), idx(0), decimal_precision(16) {} ~Printer() { flush(); } void set_decimal_precision(std::size_t decimal_precision) { this->decimal_precision = decimal_precision; } void print(char c) { if IF_CONSTEXPR (debug) print_char('\''); print_char(c); if IF_CONSTEXPR (debug) print_char('\''); } void print(bool b) { print_char((char)(b + '0')); } void print(const char* a) { if IF_CONSTEXPR (debug) print_char('"'); for (; *a != '\0'; ++a) print_char(*a); if IF_CONSTEXPR (debug) print_char('"'); } template<std::size_t len> void print(const char (&a)[len]) { if IF_CONSTEXPR (debug) print_char('"'); for (auto i : a) print_char(i); if IF_CONSTEXPR (debug) print_char('"'); } void print(const std::string& a) { if IF_CONSTEXPR (debug) print_char('"'); for (auto i : a) print_char(i); if IF_CONSTEXPR (debug) print_char('"'); } template<std::size_t len> void print(const std::bitset<len>& a) { rrep (i, len) print_char((char)(a[i] + '0')); } template<class 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 IF_CONSTEXPR (is_signed_int<T>::value) { if (a < 0) { print_char('-'); using U = typename make_unsigned_int<T>::type; print(static_cast<U>(-static_cast<U>(a))); return; } } if (idx + 40 >= buf_size) flush(); static char s[40]; int t = 40; while (a >= 10000) { int i = a % 10000; a /= 10000; t -= 4; std::memcpy(s + t, precalc_number_to_string.buf[i], 4); } if (a >= 1000) { std::memcpy(buffer.begin() + idx, precalc_number_to_string.buf[a], 4); idx += 4; } else if (a >= 100) { std::memcpy(buffer.begin() + idx, precalc_number_to_string.buf[a] + 1, 3); idx += 3; } else if (a >= 10) { std::memcpy(buffer.begin() + idx, precalc_number_to_string.buf[a] + 2, 2); idx += 2; } else { buffer[idx++] = '0' | a; } std::memcpy(buffer.begin() + idx, s + t, 40 - t); idx += 40 - t; } template<class T, typename std::enable_if<std::is_floating_point<T>::value && !has_print<T>::value>::type* = nullptr> void print(T a) { if (a == std::numeric_limits<T>::infinity()) { print("inf"); return; } if (a == -std::numeric_limits<T>::infinity()) { 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('.'); rep (decimal_precision) { a *= 10; print_char((char)('0' + (int)std::fmod(a, 10.0))); } } private: template<std::size_t i, class... Args> void print(const std::tuple<Args...>& a) { if IF_CONSTEXPR (i < sizeof...(Args)) { if IF_CONSTEXPR (debug) print_char(','); print_char(' '); print(std::get<i>(a)); print<i + 1, Args...>(a); } } public: template<class... Args> void print(const std::tuple<Args...>& a) { if IF_CONSTEXPR (debug) print_char('('); if IF_CONSTEXPR (sizeof...(Args) != 0) print(std::get<0>(a)); print<1, Args...>(a); if IF_CONSTEXPR (debug) print_char(')'); } template<class T, class U> void print(const std::pair<T, U>& a) { if IF_CONSTEXPR (debug) print_char('('); print(a.first); if IF_CONSTEXPR (debug) print_char(','); print_char(' '); print(a.second); if IF_CONSTEXPR (debug) print_char(')'); } template<class T, typename std::enable_if<is_range<T>::value && !has_print<T>::value>::type* = nullptr> void print(const T& a) { if IF_CONSTEXPR (debug) print_char('{'); for (auto i = std::begin(a); i != std::end(a); ++i) { if (i != std::begin(a)) { if IF_CONSTEXPR (debug) print_char(','); print_char(' '); } print(*i); } if IF_CONSTEXPR (debug) print_char('}'); } template<class T, typename std::enable_if<has_print<T>::value && !debug>::type* = nullptr> void print(const T& a) { a.print(*this); } template<class T, typename std::enable_if<has_print<T>::value && debug>::type* = nullptr> void print(const T& a) { a.debug(*this); } void operator()() {} template<class Head, class... Args> void operator()(const Head& head, const Args&... args) { print(head); operator()(args...); } template<class T> Printer& operator<<(const T& a) { print(a); return *this; } Printer& operator<<(Printer& (*pf)(Printer&)) { return pf(*this); } }; template<std::size_t buf_size, bool debug> Printer<buf_size, debug>& endl(Printer<buf_size, debug>& pr) { pr.print_char('\n'); pr.flush(); return pr; } template<std::size_t buf_size, bool debug> Printer<buf_size, debug>& flush(Printer<buf_size, debug>& pr) { pr.flush(); return pr; } struct SetPrec { int n; template<class Pr> void print(Pr& pr) const { pr.set_decimal_precision(n); } template<class Pr> void debug(Pr& pr) const { pr.set_decimal_precision(n); } }; SetPrec setprec(int n) { return SetPrec{n}; }; Printer<> print(1), eprint(2); void prints() { print.print_char('\n'); } template<class T> auto prints(const T& v) -> decltype(print << v, (void)0) { print << v; print.print_char('\n'); } template<class Head, class... Tail> auto prints(const Head& head, const Tail&... tail) -> decltype(print << head, (void)0) { print << head; print.print_char(' '); prints(tail...); } Printer<IO_BUFFER_SIZE, true> debug(1), edebug(2); void debugs() { debug.print_char('\n'); } template<class T> auto debugs(const T& v) -> decltype(debug << v, (void)0) { debug << v; debug.print_char('\n'); } template<class Head, class... Tail> auto debugs(const Head& head, const Tail&... tail) -> decltype(debug << head, (void)0) { debug << head; debug.print_char(' '); debugs(tail...); } #line 2 "template/bitop.hpp" #line 6 "template/bitop.hpp" namespace bitop { #define KTH_BIT(b, k) (((b) >> (k)) & 1) #define POW2(k) (1ull << (k)) inline ull next_combination(int n, ull x) { if (n == 0) return 1; ull a = x & -x; ull b = x + a; return (x & ~b) / a >> 1 | b; } #define rep_comb(i, n, k) \ for (ull i = (1ull << (k)) - 1; i < (1ull << (n)); \ i = bitop::next_combination((n), i)) 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 & 0xAAAAAAAAAAAAAAAA) >> 1) | ((x & 0x5555555555555555) << 1); x = ((x & 0xCCCCCCCCCCCCCCCC) >> 2) | ((x & 0x3333333333333333) << 2); x = ((x & 0xF0F0F0F0F0F0F0F0) >> 4) | ((x & 0x0F0F0F0F0F0F0F0F) << 4); x = ((x & 0xFF00FF00FF00FF00) >> 8) | ((x & 0x00FF00FF00FF00FF) << 8); x = ((x & 0xFFFF0000FFFF0000) >> 16) | ((x & 0x0000FFFF0000FFFF) << 16); return (x >> 32) | (x << 32); } inline constexpr ull reverse(ull x, int n) { return reverse(x) >> (64 - n); } } // namespace bitop inline constexpr int popcnt(ull x) noexcept { #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); } #line 2 "template/func.hpp" #line 6 "template/func.hpp" template<class T, class U, class Comp = std::less<>> inline constexpr bool chmin(T& a, const U& b, Comp cmp = Comp()) noexcept(noexcept(cmp(b, a))) { return cmp(b, a) ? a = b, true : false; } template<class T, class U, class Comp = std::less<>> inline constexpr bool chmax(T& a, const U& b, Comp cmp = Comp()) noexcept(noexcept(cmp(a, b))) { return cmp(a, b) ? a = b, true : false; } inline constexpr ll gcd(ll a, ll b) { if (a < 0) a = -a; if (b < 0) b = -b; while (b) { const ll c = a; a = b; b = c % b; } 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 std::vector<ll> prime_factor(ll N) { std::vector<ll> res; for (ll i = 2; i * i <= N; ++i) { while (N % i == 0) { res.push_back(i); N /= i; } } if (N != 1) res.push_back(N); return res; } inline constexpr ll my_pow(ll a, ll b) { ll res = 1; while (b) { if (b & 1) res *= a; b >>= 1; a *= a; } return res; } inline constexpr ll mod_pow(ll a, ll b, ll mod) { assert(mod > 0); if (mod == 1) return 0; a %= mod; ll res = 1; while (b) { if (b & 1) (res *= a) %= mod; b >>= 1; (a *= a) %= mod; } return res; } inline PLL extGCD(ll a, ll b) { const ll n = a, m = b; ll x = 1, y = 0, u = 0, v = 1; ll t; while (b) { t = a / b; std::swap(a -= t * b, b); std::swap(x -= t * u, u); std::swap(y -= t * v, v); } if (x < 0) { x += m; y -= n; } return {x, y}; } inline ll mod_inv(ll a, ll mod) { ll b = mod; ll x = 1, u = 0; ll t; while (b) { t = a / b; std::swap(a -= t * b, b); std::swap(x -= t * u, u); } if (x < 0) x += mod; assert(a == 1); return x; } #line 2 "template/util.hpp" #line 6 "template/util.hpp" template<class F> class RecLambda { private: F f; public: explicit constexpr RecLambda(F&& f_) : f(std::forward<F>(f_)) {} template<class... Args> constexpr auto operator()(Args&&... args) -> decltype(f(*this, std::forward<Args>(args)...)) { return f(*this, std::forward<Args>(args)...); } }; template<class F> inline constexpr RecLambda<F> rec_lambda(F&& f) { return RecLambda<F>(std::forward<F>(f)); } template<class Head, class... Tail> struct multi_dim_vector { using type = std::vector<typename multi_dim_vector<Tail...>::type>; }; template<class T> struct multi_dim_vector<T> { using type = T; }; template<class T, class Arg> constexpr std::vector<T> make_vec(int n, Arg&& arg) { return std::vector<T>(n, std::forward<Arg>(arg)); } template<class T, class... Args> constexpr typename multi_dim_vector<Args..., T>::type make_vec(int n, Args&&... args) { return typename multi_dim_vector<Args..., T>::type( n, make_vec<T>(std::forward<Args>(args)...)); } template<class T, class Comp = std::less<T>> class compressor { private: std::vector<T> dat; Comp cmp; bool sorted = false; public: compressor() : compressor(Comp()) {} compressor(const Comp& cmp) : cmp(cmp) {} compressor(const std::vector<T>& vec, bool f = false, const Comp& cmp = Comp()) : dat(vec), cmp(cmp) { if (f) build(); } compressor(std::vector<T>&& vec, bool f = false, const Comp& cmp = Comp()) : dat(std::move(vec)), cmp(cmp) { if (f) build(); } compressor(std::initializer_list<T> il, bool f = false, const Comp& cmp = Comp()) : dat(all(il)), cmp(cmp) { if (f) build(); } void reserve(int n) { assert(!sorted); dat.reserve(n); } void push_back(const T& v) { assert(!sorted); dat.push_back(v); } void push_back(T&& v) { assert(!sorted); dat.push_back(std::move(v)); } template<class... Args> void emplace_back(Args&&... args) { assert(!sorted); dat.emplace_back(std::forward<Args>(args)...); } void push(const std::vector<T>& vec) { assert(!sorted); const int n = dat.size(); dat.resize(n + vec.size()); rep (i, vec.size()) dat[n + i] = vec[i]; } int build() { assert(!sorted); sorted = true; std::sort(all(dat), cmp); dat.erase(std::unique(all(dat), [&](const T& a, const T& b) -> bool { return !cmp(a, b) && !cmp(b, a); }), dat.end()); return dat.size(); } const T& operator[](int k) const& { assert(sorted); assert(0 <= k && k < (int)dat.size()); return dat[k]; } int get(const T& val) const { assert(sorted); auto itr = std::lower_bound(all(dat), val, cmp); assert(itr != dat.end() && !cmp(val, *itr)); return itr - dat.begin(); } int lower_bound(const T& val) const { assert(sorted); auto itr = std::lower_bound(all(dat), val, cmp); return itr - dat.begin(); } int upper_bound(const T& val) const { assert(sorted); auto itr = std::upper_bound(all(dat), val, cmp); return itr - dat.begin(); } bool contains(const T& val) const { assert(sorted); return std::binary_search(all(dat), val, cmp); } std::vector<int> pressed(const std::vector<T>& vec) const { assert(sorted); std::vector<int> res(vec.size()); rep (i, vec.size()) res[i] = get(vec[i]); return res; } void press(std::vector<T>& vec) const { assert(sorted); for (auto&& i : vec) i = get(i); } int size() const { assert(sorted); return dat.size(); } }; #line 2 "random/Random.hpp" #line 4 "random/Random.hpp" template<class Engine> class Random { private: Engine rnd; public: using result_type = typename Engine::result_type; Random() : Random(std::random_device{}()) {} Random(result_type seed) : rnd(seed) {} result_type operator()() { return rnd(); } result_type min() const { return rnd.min(); } result_type max() const { return rnd.max(); } template<class IntType = ll> IntType uniform(IntType l, IntType r) { static_assert(std::is_integral<IntType>::value, "template argument must be an integral type"); assert(l <= r); return std::uniform_int_distribution<IntType>{l, r}(rnd); } template<class RealType = double> RealType uniform_real(RealType l, RealType r) { static_assert(std::is_floating_point<RealType>::value, "template argument must be an floating point type"); assert(l <= r); return std::uniform_real_distribution<RealType>{l, r}(rnd); } bool uniform_bool() { return uniform<int>(0, 1) == 1; } template<class T = ll> std::pair<T, T> uniform_pair(T l, T r) { assert(l < 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<class T = ll> std::vector<T> choice(int n, T l, T r) { assert(l <= r); assert(T(n) <= (r - l + 1)); std::set<T> res; while ((int)res.size() < n) res.insert(uniform<T>(l, r)); return {res.begin(), res.end()}; } template<class Iter> void shuffle(const Iter& first, const Iter& last) { std::shuffle(first, last, rnd); } template<class T> std::vector<T> permutation(T n) { std::vector<T> res(n); rep (i, n) res[i] = i; shuffle(all(res)); return res; } template<class T = ll> std::vector<T> choice_shuffle(int n, T l, T r, bool sorted = true) { assert(l <= r); assert(T(n) <= (r - l + 1)); std::vector<T> res(r - l + 1); rep (i, l, r + 1) res[i - l] = i; shuffle(all(res)); res.erase(res.begin() + n, res.end()); if (sorted) sort(all(res)); return res; } }; using Random32 = Random<std::mt19937>; Random32 rand32; using Random64 = Random<std::mt19937_64>; Random64 rand64; /** * @brief Random * @docs docs/random/Random.md */ #line 2 "math/ModInt.hpp" #line 4 "math/ModInt.hpp" template<class T, T mod> class StaticModInt { static_assert(std::is_integral<T>::value, "T must be integral"); static_assert(std::is_unsigned<T>::value, "T must be unsigned"); static_assert(mod > 0, "mod must be positive"); static_assert(mod <= std::numeric_limits<T>::max() / 2, "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 std::make_signed<T>::type; T val; static constexpr unsigned int inv1000000007[] = { 0, 1, 500000004, 333333336, 250000002, 400000003, 166666668, 142857144, 125000001, 111111112, 700000005}; static constexpr unsigned int inv998244353[] = { 0, 1, 499122177, 332748118, 748683265, 598946612, 166374059, 855638017, 873463809, 443664157, 299473306}; static constexpr ll mod_inv(ll a) { ll b = mod; ll x = 1, u = 0; ll t = 0, tmp = 0; while (b) { t = a / b; tmp = (a - t * b); a = b; b = tmp; tmp = (x - t * u); x = u; u = tmp; } if (x < 0) x += mod; return x; } public: constexpr StaticModInt() : val(0) {} template<class U, typename std::enable_if<std::is_integral<U>::value && std::is_signed<U>::value>::type* = nullptr> constexpr StaticModInt(U v) : val{} { v %= static_cast<signed_t>(mod); if (v < 0) v += static_cast<signed_t>(mod); val = static_cast<T>(v); } template<class U, typename std::enable_if< std::is_integral<U>::value && std::is_unsigned<U>::value>::type* = nullptr> constexpr StaticModInt(U v) : val(v % mod) {} 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 { if IF_CONSTEXPR (mod == 1000000007) { if (val <= 10) return inv1000000007[val]; } else if IF_CONSTEXPR (mod == 998244353) { if (val <= 10) return inv998244353[val]; } return mod_inv(val); } 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& other) { val += other.val; if (val >= mod) val -= mod; return *this; } constexpr StaticModInt& operator-=(const StaticModInt& other) { if (val < other.val) val += mod; val -= other.val; return *this; } constexpr StaticModInt& operator*=(const StaticModInt& other) { large_t a = val; a *= other.val; a %= mod; val = a; return *this; } constexpr StaticModInt& operator/=(const StaticModInt& other) { *this *= other.inv(); return *this; } friend constexpr StaticModInt operator+(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) += rhs; } friend constexpr StaticModInt operator-(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) -= rhs; } friend constexpr StaticModInt operator*(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) *= rhs; } friend constexpr StaticModInt operator/(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) /= rhs; } constexpr StaticModInt operator+() const { return StaticModInt(*this); } constexpr StaticModInt operator-() const { return StaticModInt() - *this; } friend constexpr bool operator==(const StaticModInt& lhs, const StaticModInt& rhs) { return lhs.val == rhs.val; } friend constexpr bool operator!=(const StaticModInt& lhs, const StaticModInt& rhs) { return lhs.val != rhs.val; } constexpr StaticModInt pow(ll a) const { StaticModInt v = *this, res = 1; while (a) { if (a & 1) res *= v; a >>= 1; v *= v; } return res; } template<class Pr> void print(Pr& a) const { a.print(val); } template<class Pr> void debug(Pr& a) const { a.print(val); } template<class Sc> void scan(Sc& a) { ll v; a.scan(v); *this = v; } }; #if __cplusplus < 201703L template<class T, T mod> constexpr unsigned int StaticModInt<T, mod>::inv1000000007[]; template<class T, T mod> constexpr unsigned int StaticModInt<T, mod>::inv998244353[]; #endif template<unsigned int p> using static_modint = StaticModInt<unsigned int, p>; using modint1000000007 = static_modint<1000000007>; using modint998244353 = static_modint<998244353>; template<class T, int id> class DynamicModInt { static_assert(std::is_integral<T>::value, "T must be integral"); static_assert(std::is_unsigned<T>::value, "T must be unsigned"); private: using large_t = typename double_size_uint<T>::type; using signed_t = typename std::make_signed<T>::type; T val; static T mod; public: constexpr DynamicModInt() : val(0) {} template<class U, typename std::enable_if<std::is_integral<U>::value && std::is_signed<U>::value>::type* = nullptr> constexpr DynamicModInt(U v) : val{} { v %= static_cast<signed_t>(mod); if (v < 0) v += static_cast<signed_t>(mod); val = static_cast<T>(v); } template<class U, typename std::enable_if< std::is_integral<U>::value && std::is_unsigned<U>::value>::type* = nullptr> constexpr DynamicModInt(U v) : val(v % mod) {} T get() const { return val; } static T get_mod() { return mod; } static void set_mod(T v) { assert(v > 0); assert(v <= std::numeric_limits<T>::max() / 2); mod = v; } 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& other) { val += other.val; if (val >= mod) val -= mod; return *this; } DynamicModInt& operator-=(const DynamicModInt& other) { if (val < other.val) val += mod; val -= other.val; return *this; } DynamicModInt& operator*=(const DynamicModInt& other) { large_t a = val; a *= other.val; a %= mod; val = a; return *this; } DynamicModInt& operator/=(const DynamicModInt& other) { *this *= other.inv(); return *this; } friend DynamicModInt operator+(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) += rhs; } friend DynamicModInt operator-(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) -= rhs; } friend DynamicModInt operator*(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) *= rhs; } friend DynamicModInt operator/(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) /= rhs; } DynamicModInt operator+() const { return DynamicModInt(*this); } DynamicModInt operator-() const { return DynamicModInt() - *this; } friend bool operator==(const DynamicModInt& lhs, const DynamicModInt& rhs) { return lhs.val == rhs.val; } friend bool operator!=(const DynamicModInt& lhs, const DynamicModInt& rhs) { return lhs.val != rhs.val; } DynamicModInt pow(ll a) const { DynamicModInt v = *this, res = 1; while (a) { if (a & 1) res *= v; a >>= 1; v *= v; } return res; } template<class Pr> void print(Pr& a) const { a.print(val); } template<class Pr> void debug(Pr& a) const { a.print(val); } template<class Sc> void scan(Sc& a) { ll v; a.scan(v); *this = v; } }; template<class 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 * @docs docs/math/ModInt.md */ #line 2 "math/convolution/Convolution.hpp" #line 5 "math/convolution/Convolution.hpp" constexpr ull primitive_root_for_convolution(ull p) { if (p == 2) return 1; if (p == 998244353) return 3; if (p == 469762049) return 3; if (p == 1811939329) return 11; if (p == 2013265921) return 11; rep (g, 2, p) { if (mod_pow(g, (p - 1) >> 1, p) != 1) return g; } return -1; } namespace internal { template<class T> class NthRoot { private: static constexpr unsigned int lg = bitop::msb((T::get_mod() - 1) & (1 - T::get_mod())); T root[lg + 1]; T inv_root[lg + 1]; T rate[lg + 1]; T inv_rate[lg + 1]; public: constexpr NthRoot() : root{}, inv_root{}, rate{}, inv_rate{} { root[lg] = T{primitive_root_for_convolution(T::get_mod())}.pow( (T::get_mod() - 1) >> lg); inv_root[lg] = root[lg].inv(); rrep (i, lg) { root[i] = root[i + 1] * root[i + 1]; inv_root[i] = inv_root[i + 1] * inv_root[i + 1]; } T r = 1; rep (i, 2, lg + 1) { rate[i - 2] = r * root[i]; r = r * inv_root[i]; } r = 1; rep (i, 2, lg + 1) { inv_rate[i - 2] = r * inv_root[i]; r = r * root[i]; } } static constexpr unsigned int get_lg() { return lg; } constexpr T get(int n) const { return root[n]; } constexpr T inv(int n) const { return inv_root[n]; } constexpr T get_rate(int n) const { return rate[n]; } constexpr T get_inv_rate(int n) const { return inv_rate[n]; } }; template<class T> void number_theoretic_transform(std::vector<T>& a) { static constexpr NthRoot<T> nth_root; int n = a.size(); for (int i = n >> 1; i > 0; i >>= 1) { T z = T::raw(1); rep (j, 0, n, i << 1) { rep (k, i) { const T x = a[j + k]; const T y = a[j + i + k] * z; a[j + k] = x + y; a[j + i + k] = x - y; } z *= nth_root.get_rate(popcnt(j & ~(j + (i << 1)))); } } } template<class T> void inverse_number_theoretic_transform(std::vector<T>& a) { static constexpr NthRoot<T> nth_root; int n = a.size(); for (int i = 1; i < n; i <<= 1) { T z = T::raw(1); rep (j, 0, n, i << 1) { rep (k, i) { const T x = a[j + k]; const T y = a[j + i + k]; a[j + k] = x + y; a[j + i + k] = (x - y) * z; } z *= nth_root.get_inv_rate(popcnt(j & ~(j + (i << 1)))); } } T inv_n = T(1) / n; for (auto&& x : a) x *= inv_n; } template<class T> std::vector<T> convolution_naive(const std::vector<T>& a, const std::vector<T>& b) { int n = a.size(), m = b.size(); std::vector<T> c(n + m - 1); rep (i, n) rep (j, m) c[i + j] += a[i] * b[j]; return c; } template<class T> std::vector<T> convolution_pow2(std::vector<T> a) { int n = a.size() * 2 - 1; int lg = bitop::msb(n - 1) + 1; if (n - (1 << (lg - 1)) <= 5) { --lg; int m = a.size() - (1 << (lg - 1)); std::vector<T> a1(a.begin(), a.begin() + m), a2(a.begin() + m, a.end()); std::vector<T> c(n); std::vector<T> c1 = convolution_naive(a1, a1); std::vector<T> c2 = convolution_naive(a1, a2); std::vector<T> c3 = convolution_pow2(a2); rep (i, c1.size()) c[i] += c1[i]; rep (i, c2.size()) c[i + m] += c2[i] * 2; rep (i, c3.size()) c[i + m * 2] += c3[i]; return c; } int m = 1 << lg; a.resize(m); number_theoretic_transform(a); rep (i, m) a[i] *= a[i]; inverse_number_theoretic_transform(a); a.resize(n); return a; } template<class T> std::vector<T> convolution(std::vector<T> a, std::vector<T> b) { int n = a.size() + b.size() - 1; int lg = bitop::ceil_log2(n); int m = 1 << lg; if (n - (1 << (lg - 1)) <= 5) { --lg; if (a.size() < b.size()) std::swap(a, b); int m = n - (1 << lg); std::vector<T> a1(a.begin(), a.begin() + m), a2(a.begin() + m, a.end()); std::vector<T> c(n); std::vector<T> c1 = convolution_naive(a1, b); std::vector<T> c2 = convolution(a2, b); rep (i, c1.size()) c[i] += c1[i]; rep (i, c2.size()) c[i + m] += c2[i]; return c; } a.resize(m); b.resize(m); number_theoretic_transform(a); number_theoretic_transform(b); rep (i, m) a[i] *= b[i]; inverse_number_theoretic_transform(a); a.resize(n); return a; } } // namespace internal using internal::inverse_number_theoretic_transform; using internal::number_theoretic_transform; template<unsigned int p> std::vector<static_modint<p>> convolution_for_any_mod(const std::vector<static_modint<p>>& a, const std::vector<static_modint<p>>& b); template<unsigned int p> std::vector<static_modint<p>> convolution(const std::vector<static_modint<p>>& a, const std::vector<static_modint<p>>& b) { unsigned int n = a.size(), m = b.size(); if (n == 0 || m == 0) return {}; if (n <= 60 || m <= 60) return internal::convolution_naive(a, b); if (n + m - 1 <= ((1 - p) & (p - 1))) { if (n == m && a == b) return internal::convolution_pow2(a); return internal::convolution(a, b); } return convolution_for_any_mod(a, b); } template<unsigned int p> std::vector<ll> convolution(const std::vector<ll>& a, const std::vector<ll>& b) { int n = a.size(), m = b.size(); std::vector<static_modint<p>> a2(n), b2(m); rep (i, n) a2[i] = a[i]; rep (i, m) b2[i] = b[i]; auto c2 = convolution(a2, b2); std::vector<ll> c(c2.size()); rep (i, c2.size()) c[i] = c2[i].get(); return c; } template<unsigned int p> std::vector<static_modint<p>> convolution_for_any_mod(const std::vector<static_modint<p>>& a, const std::vector<static_modint<p>>& b) { int n = a.size(), m = b.size(); assert(n + m - 1 <= (1 << 26)); std::vector<ll> a2(n), b2(m); rep (i, n) a2[i] = a[i].get(); rep (i, m) b2[i] = b[i].get(); static constexpr ll MOD1 = 469762049; static constexpr ll MOD2 = 1811939329; static constexpr ll MOD3 = 2013265921; static constexpr ll INV1_2 = mod_pow(MOD1, MOD2 - 2, MOD2); static constexpr ll INV1_3 = mod_pow(MOD1, MOD3 - 2, MOD3); static constexpr ll INV2_3 = mod_pow(MOD2, MOD3 - 2, MOD3); auto c1 = convolution<MOD1>(a2, b2); auto c2 = convolution<MOD2>(a2, b2); auto c3 = convolution<MOD3>(a2, b2); std::vector<static_modint<p>> res(n + m - 1); rep (i, n + m - 1) { ll t1 = c1[i]; ll t2 = (c2[i] - t1 + MOD2) * INV1_2 % MOD2; if (t2 < 0) t2 += MOD2; ll t3 = ((c3[i] - t1 + MOD3) * INV1_3 % MOD3 - t2 + MOD3) * INV2_3 % MOD3; if (t3 < 0) t3 += MOD3; res[i] = static_modint<p>(t1 + (t2 + t3 * MOD2) % p * MOD1); } return res; } template<class T> void ntt_doubling_(std::vector<T>& a, std::vector<T> b) { static constexpr internal::NthRoot<T> nth_root; int n = a.size(); const T z = nth_root.get(bitop::msb(n) + 1); T r = 1; rep (i, n) { b[i] *= r; r *= z; } number_theoretic_transform(b); a.reserve(2 * n); a.insert(a.end(), all(b)); } template<class T> void ntt_doubling_(std::vector<T>& a) { static constexpr internal::NthRoot<T> nth_root; int n = a.size(); auto b = a; inverse_number_theoretic_transform(b); const T z = nth_root.get(bitop::msb(n) + 1); T r = 1; rep (i, n) { b[i] *= r; r *= z; } number_theoretic_transform(b); a.reserve(2 * n); a.insert(a.end(), all(b)); } template<unsigned int p> struct is_ntt_friendly : std::false_type {}; template<> struct is_ntt_friendly<998244353> : std::true_type {}; /** * @brief Convolution(畳み込み) * @docs docs/math/convolution/Convolution.md */ #line 7 "string/WildcardPatternMatching.hpp" namespace internal { template<class T> std::vector<bool> wildcard_mod(const std::vector<int>& a, const std::vector<int>& b) { const int n = a.size(), m = b.size(); const int lg = bitop::ceil_log2(n), N = 1 << lg; std::vector<T> A1(N), B1(N), A2(N), B2(N), A3(N), B3(N); std::vector<T> C1(N), C2(n - m + 1); rep (i, n) A1[i] = a[i] == 0 ? 0 : 1; rep (i, m) B1[i] = b[m - 1 - i] == 0 ? 0 : 1; rep (i, n) A2[i] = a[i] * A1[i]; rep (i, m) B2[i] = b[m - 1 - i] * B1[i]; rep (i, n) A3[i] = a[i] * A2[i]; rep (i, m) B3[i] = b[m - 1 - i] * B2[i]; if (find(all(a), 0) == a.end()) { T sm = 0; rep (i, m) sm += B3[i]; rep (i, n - m + 1) C2[i] += sm; } else { number_theoretic_transform(A1); number_theoretic_transform(B3); rep (i, N) C1[i] += A1[i] * B3[i]; } if (find(all(b), 0) == b.end()) { std::vector<T> cum(n + 1); rep (i, n) cum[i + 1] = cum[i] + A3[i]; rep (i, n - m + 1) C2[i] += cum[i + m] - cum[i]; } else { number_theoretic_transform(A3); number_theoretic_transform(B1); rep (i, N) C1[i] += A3[i] * B1[i]; } number_theoretic_transform(A2); number_theoretic_transform(B2); rep (i, N) C1[i] -= 2 * A2[i] * B2[i]; inverse_number_theoretic_transform(C1); std::vector<bool> c(n - m + 1); rep (i, n - m + 1) c[i] = (C1[i + m - 1] + C2[i] == 0); return c; } template<class T> std::vector<bool> wildcard_random(const std::vector<int>& a, const std::vector<int>& b) { const int n = a.size(), m = b.size(); const int lg = bitop::ceil_log2(n), N = 1 << lg; bool a0 = find(all(a), 0) == a.end(); bool b0 = find(all(b), 0) == b.end(); std::vector<T> A1(N), B1(N), A2(N), B2(N); std::vector<T> C1(N), C2(n - m + 1); if (a0) { rep (i, n) A1[i] = a[i] == 0 ? 0 : 1; rep (i, m) { B1[i] = b[m - 1 - i] == 0 ? 0 : rand32.uniform<int>(1, T::get_mod() - 1); } } else { rep (i, n) { A1[i] = a[i] == 0 ? 0 : rand32.uniform<int>(1, T::get_mod() - 1); } rep (i, m) B1[i] = b[m - 1 - i] == 0 ? 0 : 1; } rep (i, n) A2[i] = a[i] * A1[i]; rep (i, m) B2[i] = b[m - 1 - i] * B1[i]; if (a0) { T sm = 0; rep (i, m) sm += B2[i]; rep (i, n - m + 1) C2[i] -= sm; } else { number_theoretic_transform(A1); number_theoretic_transform(B2); rep (i, N) C1[i] -= A1[i] * B2[i]; } if (!a0 && b0) { std::vector<T> cum(n + 1); rep (i, n) cum[i + 1] = cum[i] + A2[i]; rep (i, n - m + 1) C2[i] += cum[i + m] - cum[i]; } else { number_theoretic_transform(A2); number_theoretic_transform(B1); rep (i, N) C1[i] += A2[i] * B1[i]; } inverse_number_theoretic_transform(C1); std::vector<bool> c(n - m + 1); rep (i, n - m + 1) c[i] = (C1[i + m - 1] + C2[i] == 0); return c; } } // namespace internal std::vector<bool> wildcard_pattern_matching(std::vector<int> a, std::vector<int> b, int MAX, bool deterministic = true) { const int n = a.size(), m = b.size(); if (n < m) return {}; i128 MAX_VAL = (i128)MAX * MAX * m; static constexpr int MOD1 = 2113929217, MOD2 = 2013265921, MOD3 = 1811939329; if (!deterministic) { return internal::wildcard_random<static_modint<MOD1>>(a, b); } std::vector<bool> res = internal::wildcard_mod<static_modint<MOD1>>(a, b); if (MAX_VAL >= MOD1) { auto c = internal::wildcard_mod<static_modint<MOD2>>(a, b); rep (i, n - m + 1) res[i] = res[i] && c[i]; } if (MAX_VAL >= (i128)MOD1 * MOD2) { auto c = internal::wildcard_mod<static_modint<MOD3>>(a, b); rep (i, n - m + 1) res[i] = res[i] && c[i]; } return res; } std::vector<bool> wildcard_pattern_matching(const std::vector<int>& a, const std::vector<int>& b, bool deterministic = true) { compressor<int> comp{0}; comp.push(a); comp.push(b); comp.build(); return wildcard_pattern_matching(comp.pressed(a), comp.pressed(b), comp.size() - 1, deterministic); } std::vector<bool> wildcard_pattern_matching(const std::string& a, const std::string& b, char wildcard = '*', bool deterministic = true) { static std::vector<int> idx(128, -1); std::vector<int> A(a.size()), B(b.size()); int cnt = 1; rep (i, a.size()) { A[i] = a[i] == wildcard ? 0 : idx[a[i]] == -1 ? idx[a[i]] = cnt++ : idx[a[i]]; } rep (i, b.size()) { B[i] = b[i] == wildcard ? 0 : idx[b[i]] == -1 ? idx[b[i]] = cnt++ : idx[b[i]]; } rep (i, a.size()) idx[a[i]] = -1; rep (i, b.size()) idx[b[i]] = -1; return wildcard_pattern_matching(A, B, cnt - 1, deterministic); } /** * @brief WildcardPatternMatching * @docs docs/string/WildcardPatternMatching.md */