#line 2 "library/other/template.hpp" #include #line 2 "library/template/macros.hpp" #line 4 "library/template/macros.hpp" #ifndef __COUNTER__ #define __COUNTER__ __LINE__ #endif #define REP_SELECTER(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(...) REP_SELECTER(__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(...) REP_SELECTER(__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(...) REP_SELECTER(__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(...) \ REP_SELECTER(__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) #if __cplusplus >= 201402L #define rall(v) std::rbegin(v), std::rend(v) #else #define rall(v) v.rbegin(), v.rend() #endif #if __cpp_constexpr >= 201304L #define CONSTEXPR constexpr #else #define CONSTEXPR #endif #if __cpp_if_constexpr >= 201606L #define IF_CONSTEXPR constexpr #else #define IF_CONSTEXPR #endif #define IO_BUFFER_SIZE 2048 #line 2 "library/template/alias.hpp" #line 4 "library/template/alias.hpp" using ll = long long; using ull = unsigned long long; using ld = long double; using PLL = std::pair; template using prique = std::priority_queue, std::greater>; template class infinity { public: static constexpr T value = std::numeric_limits::max() / 2; static constexpr T mvalue = std::numeric_limits::min() / 2; static constexpr T max = std::numeric_limits::max(); static constexpr T min = std::numeric_limits::min(); }; #if __cplusplus <= 201402L template constexpr T infinity::value; template constexpr T infinity::mvalue; template constexpr T infinity::max; template constexpr T infinity::min; #endif #if __cpp_variable_templates >= 201304L template constexpr T INF = infinity::value; #endif constexpr ll inf = infinity::value; constexpr ld EPS = 1e-8; constexpr ld PI = 3.1415926535897932384626; #line 2 "library/template/type_traits.hpp" #line 5 "library/template/type_traits.hpp" template struct function_traits_impl { using result_type = T; template using argument_type = typename std::tuple_element>::type; using argument_tuple = std::tuple; static constexpr std::size_t arg_size() { return sizeof...(Args); } }; template struct function_traits_helper; template struct function_traits_helper { using type = function_traits_impl; }; template struct function_traits_helper { using type = function_traits_impl; }; template struct function_traits_helper { using type = function_traits_impl; }; template struct function_traits_helper { using type = function_traits_impl; }; #if __cpp_noexcept_function_type >= 201510L template struct function_traits_helper { using type = function_traits_impl; }; template struct function_traits_helper { using type = function_traits_impl; }; template struct function_traits_helper { using type = function_traits_impl; }; template struct function_traits_helper { using type = function_traits_impl; }; #endif template using function_traits = typename function_traits_helper::type; template using is_signed_int = std::disjunction, std::is_signed>, std::is_same>; template using is_unsigned_int = std::disjunction, std::is_unsigned>, std::is_same>; template using is_int = std::disjunction, is_unsigned_int>; template using make_signed_int = typename std::conditional< std::is_same::value || std::is_same::value, std::common_type<__int128_t>, std::make_signed>::type; template using make_unsigned_int = typename std::conditional< std::is_same::value || std::is_same::value, std::common_type<__uint128_t>, std::make_unsigned>::type; template struct is_range : std::false_type {}; template struct is_range< T, decltype(all(std::declval::type>()), (void)0)> : std::true_type {}; template::value> struct range_rank : std::integral_constant {}; template struct range_rank : std::integral_constant::value + 1> {}; template 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::type>::type>::type>:: type; }; template using int_least_t = typename int_least::type; template 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::type>::type>::type>:: type; }; template using uint_least_t = typename uint_least::type; template using double_size_int = int_least::digits * 2 + 1>; template using double_size_int_t = typename double_size_int::type; template using double_size_uint = uint_least::digits * 2>; template using double_size_uint_t = typename double_size_uint::type; template using double_size = typename std::conditional::value, double_size_int, double_size_uint>::type; template using double_size_t = typename double_size::type; #line 2 "library/template/in.hpp" #line 4 "library/template/in.hpp" #include #line 8 "library/template/in.hpp" template class Reader { private: int fd, idx, sz; bool state; std::array buffer; inline void read_buf() { sz = read(fd, buffer.begin(), buf_size); idx = 0; if (sz < 0) throw std::runtime_error("input failed"); } public: static constexpr int get_buf_size() { return buf_size; } Reader() noexcept : fd(0), idx(0), sz(0), state(true) {} Reader(int fd) noexcept : fd(fd), idx(0), sz(0), state(true) {} Reader(FILE* fp) noexcept : fd(fileno(fp)), idx(0), sz(0), state(true) {} class iterator { private: Reader* reader; public: using difference_type = void; using value_type = void; using pointer = void; using reference = void; using iterator_category = std::input_iterator_tag; iterator() : reader(nullptr) {} explicit iterator(Reader& reader) : reader(&reader) {} explicit iterator(Reader* reader) : reader(reader) {} iterator& operator++() { if (reader->idx == reader->sz) reader->read_buf(); ++reader->idx; return *this; } iterator operator++(int) { iterator res = *this; ++(*this); return res; } char operator*() const { if (reader->idx == reader->sz) reader->read_buf(); if (reader->idx < reader->sz) return reader->buffer[reader->idx]; reader->state = false; return '\0'; } bool rdstate() const { return reader->state; } void setstate(bool state) { reader->state = state; } }; iterator begin() noexcept { return iterator(this); } }; Reader<> reader(0); template class Scanner { public: using iterator_type = Iterator; private: template struct has_scan : std::false_type {}; template struct has_scan< T, decltype(std::declval().scan(std::declval()), (void)0)> : std::true_type {}; Iterator itr; public: Scanner() = default; Scanner(const Iterator& itr) : itr(itr) {} char scan_char() { char c = *itr; ++itr; return c; } Scanner ignore(int n = 1) { rep (n) ++itr; return *this; } inline void discard_space() { while (('\t' <= *itr && *itr <= '\r') || *itr == ' ') ++itr; } void scan(char& a) { discard_space(); a = *itr; ++itr; } void scan(bool& a) { discard_space(); a = *itr != '0'; ++itr; } void scan(std::string& a) { discard_space(); a.clear(); while ((*itr < '\t' || '\r' < *itr) && *itr != ' ' && *itr != '\0') { a += *itr; ++itr; } } template void scan(std::bitset& a) { discard_space(); rrep (i, len) { a[i] = *itr != '0'; ++itr; } } template::value && !has_scan::value>::type* = nullptr> void scan(T& a) { discard_space(); if (*itr == '-') { ++itr; a = 0; while ('0' <= *itr && *itr <= '9') { a = a * 10 - (*itr - '0'); ++itr; } } else { a = 0; while ('0' <= *itr && *itr <= '9') { a = a * 10 + (*itr - '0'); ++itr; } } } template::value && !has_scan::value>::type* = nullptr> void scan(T& a) { discard_space(); a = 0; while ('0' <= *itr && *itr <= '9') { a = a * 10 + *itr - '0'; ++itr; } } template::value && !has_scan::value>::type* = nullptr> void scan(T& a) { discard_space(); bool sgn = false; if (*itr == '-') { sgn = true; ++itr; } a = 0; while ('0' <= *itr && *itr <= '9') { a = a * 10 + *itr - '0'; ++itr; } if (*itr == '.') { ++itr; T n = 0, d = 1; for (int i = 0; '0' <= *itr && *itr <= '9' && i < (int)decimal_precision; ++i) { n = n * 10 + *itr - '0'; d *= 10; ++itr; } while ('0' <= *itr && *itr <= '9') ++itr; a += n / d; } if (sgn) a = -a; } private: template void scan(std::tuple& a) { if IF_CONSTEXPR (i < sizeof...(Args)) { scan(std::get(a)); scan(a); } } public: template void scan(std::tuple& a) { scan<0, Args...>(a); } template void scan(std::pair& a) { scan(a.first); scan(a.second); } template::value && !has_scan::value>::type* = nullptr> void scan(T& a) { each_for (i : a) scan(i); } template::value>::type* = nullptr> void scan(T& a) { a.scan(*this); } void operator()() {} template void operator()(Head& head, Args&... args) { scan(head); operator()(args...); } template Scanner& operator>>(T& a) { scan(a); return *this; } explicit operator bool() const { return itr.rdstate(); } 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.itr.setstate(true); return scan; } }; Scanner::iterator> scan(reader.begin()); #line 2 "library/template/out.hpp" #line 8 "library/template/out.hpp" template class Writer { private: int fd, idx; std::array buffer; inline void write_buf() { int num = write(fd, buffer.begin(), idx); idx = 0; if (num < 0) throw std::runtime_error("output failed"); } public: Writer() noexcept : fd(1), idx(0) {} Writer(int fd) noexcept : fd(fd), idx(0) {} Writer(FILE* fp) noexcept : fd(fileno(fp)), idx(0) {} ~Writer() { write_buf(); } class iterator { private: Writer* writer; public: using difference_type = void; using value_type = void; using pointer = void; using reference = void; using iterator_category = std::output_iterator_tag; iterator() noexcept : writer(nullptr) {} explicit iterator(Writer& writer) noexcept : writer(&writer) {} explicit iterator(Writer* writer) noexcept : writer(writer) {} iterator& operator++() { ++writer->idx; if (writer->idx == buf_size) writer->write_buf(); return *this; } iterator operator++(int) { iterator res = *this; ++(*this); return res; } char& operator*() const { return writer->buffer[writer->idx]; } void flush() const { writer->write_buf(); } }; iterator begin() noexcept { return iterator(this); } }; Writer<> writer(1), ewriter(2); template class Printer { public: using iterator_type = Iterator; private: template struct has_print : std::false_type {}; template struct has_print().print(std::declval()), (void)0)> : std::true_type {}; template struct has_print().debug(std::declval()), (void)0)> : std::true_type {}; Iterator itr; std::size_t decimal_precision; public: void print_char(char c) { *itr = c; ++itr; } void flush() { itr.flush(); } Printer() noexcept = default; explicit Printer(const Iterator& itr) noexcept : itr(itr), decimal_precision(16) {} 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 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 void print(const std::bitset& a) { rrep (i, len) print_char((char)(a[i] + '0')); } template::value && !has_print::value>::type* = nullptr> void print(T a) { if (!a) { print_char('0'); return; } if IF_CONSTEXPR (is_signed_int::value) { if (a < 0) { print_char('-'); using U = typename make_unsigned_int::type; print(static_cast(-static_cast(a))); return; } } std::string s; while (a) { s += (char)(a % 10 + '0'); a /= 10; } for (auto i = s.rbegin(); i != s.rend(); ++i) print_char(*i); } template::value && !has_print::value>::type* = nullptr> void print(T a) { if (a == std::numeric_limits::infinity()) { print("inf"); return; } if (a == -std::numeric_limits::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 void print(const std::tuple& a) { if IF_CONSTEXPR (i < sizeof...(Args)) { if IF_CONSTEXPR (debug) print_char(','); print_char(' '); print(std::get(a)); print(a); } } public: template void print(const std::tuple& 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 void print(const std::pair& 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::value && !has_print::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::value && !debug>::type* = nullptr> void print(const T& a) { a.print(*this); } template::value && debug>::type* = nullptr> void print(const T& a) { a.debug(*this); } void operator()() {} template void operator()(const Head& head, const Args&... args) { print(head); operator()(args...); } template Printer& operator<<(const T& a) { print(a); return *this; } Printer& operator<<(Printer& (*pf)(Printer&)) { return pf(*this); } }; template Printer& endl(Printer& pr) { pr.print_char('\n'); pr.flush(); return pr; } template Printer& flush(Printer& pr) { pr.flush(); return pr; } struct SetPrec { int n; template void print(Pr& pr) const { pr.set_decimal_precision(n); } template void debug(Pr& pr) const { pr.set_decimal_precision(n); } }; SetPrec setprec(int n) { return SetPrec{n}; }; Printer::iterator> print(writer.begin()), eprint(ewriter.begin()); template auto prints(const T& v) -> decltype(print << v, (void)0) { print << v; print.print_char('\n'); } template auto prints(const Head& head, const Tail&... tail) -> decltype(print << head, (void)0) { print << head; print.print_char(' '); prints(tail...); } #ifdef SHIO_LOCAL Printer::iterator, true> debug(writer.begin()), edebug(ewriter.begin()); #else char debug_iterator_character; class DebugIterator { public: DebugIterator() noexcept = default; DebugIterator& operator++() { return *this; } DebugIterator& operator++(int) { return *this; } char& operator*() const { return debug_iterator_character; } void flush() const {} }; Printer debug, edebug; #endif template auto debugs(const T& v) -> decltype(debug << v, (void)0) { debug << v; debug.print_char('\n'); } template auto debugs(const Head& head, const Tail&... tail) -> decltype(debug << head, (void)0) { debug << head; debug.print_char(' '); debugs(tail...); } #line 2 "library/template/bitop.hpp" #line 6 "library/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 "library/template/func.hpp" #line 6 "library/template/func.hpp" template> 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> 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) noexcept { 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) noexcept { return a / gcd(a, b) * b; } inline CONSTEXPR bool is_prime(ll N) noexcept { if (N <= 1) return false; for (ll i = 2; i * i <= N; ++i) { if (N % i == 0) return false; } return true; } inline std::vector prime_factor(ll N) { std::vector 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) noexcept { 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 "library/template/util.hpp" #line 6 "library/template/util.hpp" template class RecLambda { private: F f; public: explicit constexpr RecLambda(F&& f_) : f(std::forward(f_)) {} template constexpr auto operator()(Args&&... args) -> decltype(f(*this, std::forward(args)...)) { return f(*this, std::forward(args)...); } }; template inline constexpr RecLambda rec_lambda(F&& f) { return RecLambda(std::forward(f)); } template struct multi_dim_vector { using type = std::vector::type>; }; template struct multi_dim_vector { using type = T; }; template constexpr std::vector make_vec(int n, Arg&& arg) { return std::vector(n, std::forward(arg)); } template constexpr typename multi_dim_vector::type make_vec(int n, Args&&... args) { return typename multi_dim_vector::type( n, make_vec(std::forward(args)...)); } template> class presser { private: std::vector dat; Comp cmp; bool sorted = false; public: presser() : presser(Comp()) {} presser(const Comp& cmp) : cmp(cmp) {} presser(const std::vector& vec, const Comp& cmp = Comp()) : dat(vec), cmp(cmp) {} presser(std::vector&& vec, const Comp& cmp = Comp()) : dat(std::move(vec)), cmp(cmp) {} presser(std::initializer_list il, const Comp& cmp = Comp()) : dat(all(il)), cmp(cmp) {} 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 void emplace_back(Args&&... args) { assert(!sorted); dat.emplace_back(std::forward(args)...); } void push(const std::vector& 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]; } T operator[](int k) && { assert(sorted); assert(0 <= k && k < (int)dat.size()); return std::move(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 pressed(const std::vector& vec) const { assert(sorted); std::vector res(vec.size()); rep (i, vec.size()) res[i] = get(vec[i]); return res; } void press(std::vector& vec) const { static_assert(std::is_convertible::value, "template argument must be convertible from int type"); assert(sorted); each_for (i : vec) i = get(i); } int size() const { assert(sorted); return dat.size(); } const std::vector& data() const& { return dat; } std::vector data() && { return std::move(dat); } }; #line 2 "library/math/ModInt.hpp" #line 4 "library/math/ModInt.hpp" template class StaticModInt { static_assert(std::is_integral::value, "T must be integral"); static_assert(std::is_unsigned::value, "T must be unsigned"); static_assert(mod > 0, "mod must be positive"); static_assert(mod <= std::numeric_limits::max() / 2, "mod * 2 must be less than or equal to T::max()"); private: using large_t = typename double_size_uint::type; using signed_t = typename std::make_signed::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}; public: constexpr StaticModInt() : val(0) {} template::value && std::is_signed::value>::type* = nullptr> constexpr StaticModInt(U v) : val{} { v %= static_cast(mod); if (v < 0) v += static_cast(mod); val = static_cast(v); } template::value && std::is_unsigned::value>::type* = nullptr> constexpr StaticModInt(U v) : val(v % mod) {} T get() const { return val; } static constexpr T get_mod() { return mod; } static StaticModInt raw(T v) { StaticModInt res; res.val = v; return res; } 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, mod); } StaticModInt& operator++() { ++val; if (val == mod) val = 0; return *this; } StaticModInt operator++(int) { StaticModInt res = *this; ++*this; return res; } StaticModInt& operator--() { if (val == 0) val = mod; --val; return *this; } StaticModInt operator--(int) { StaticModInt res = *this; --*this; return res; } StaticModInt& operator+=(const StaticModInt& other) { val += other.val; if (val >= mod) val -= mod; return *this; } StaticModInt& operator-=(const StaticModInt& other) { if (val < other.val) val += mod; val -= other.val; return *this; } StaticModInt& operator*=(const StaticModInt& other) { large_t a = val; a *= other.val; a %= mod; val = a; return *this; } StaticModInt& operator/=(const StaticModInt& other) { *this *= other.inv(); return *this; } friend StaticModInt operator+(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) += rhs; } friend StaticModInt operator-(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) -= rhs; } friend StaticModInt operator*(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) *= rhs; } friend StaticModInt operator/(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) /= rhs; } StaticModInt operator+() const { return StaticModInt(*this); } StaticModInt operator-() const { return StaticModInt() - *this; } friend bool operator==(const StaticModInt& lhs, const StaticModInt& rhs) { return lhs.val == rhs.val; } friend bool operator!=(const StaticModInt& lhs, const StaticModInt& rhs) { return lhs.val != rhs.val; } StaticModInt pow(ll a) const { StaticModInt v = *this, res = 1; while (a) { if (a & 1) res *= v; a >>= 1; v *= v; } return res; } template void print(Pr& a) const { a.print(val); } template void debug(Pr& a) const { a.print(val); } template void scan(Sc& a) { ll v; a.scan(v); *this = v; } }; #if __cplusplus < 201703L template constexpr unsigned int StaticModInt::inv1000000007[]; template constexpr unsigned int StaticModInt::inv998244353[]; #endif template using static_modint = StaticModInt; using modint1000000007 = static_modint<1000000007>; using modint998244353 = static_modint<998244353>; template class DynamicModInt { static_assert(std::is_integral::value, "T must be integral"); static_assert(std::is_unsigned::value, "T must be unsigned"); private: using large_t = typename double_size_uint::type; using signed_t = typename std::make_signed::type; T val; static T mod; public: constexpr DynamicModInt() : val(0) {} template::value && std::is_signed::value>::type* = nullptr> constexpr DynamicModInt(U v) : val{} { v %= static_cast(mod); if (v < 0) v += static_cast(mod); val = static_cast(v); } template::value && std::is_unsigned::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::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 void print(Pr& a) const { a.print(val); } template void debug(Pr& a) const { a.print(val); } template void scan(Sc& a) { ll v; a.scan(v); *this = v; } }; template T DynamicModInt::mod = 998244353; template using dynamic_modint = DynamicModInt; using modint = dynamic_modint<-1>; /** * @brief ModInt * @docs docs/math/ModInt.md */ #line 2 "library/math/Combinatorics.hpp" #line 5 "library/math/Combinatorics.hpp" template class IntCombinatorics { private: static std::vector factorial; public: static void init(ll n) { const int b = factorial.size(); if (n < b) return; factorial.resize(n + 1); rep (i, b, n + 1) factorial[i] = factorial[i - 1] * i; } static T fact(ll x) { init(x); return factorial[x]; } static T perm(ll n, ll r) { if (r < 0 || r > n) return T(0); init(n); return factorial[n] / factorial[n - r]; } static T comb(ll n, ll r) { if (n < 0) return T(0); if (r < 0 || r > n) return T(0); init(n); return factorial[n] / factorial[n - r] / factorial[r]; } static T homo(ll n, ll r) { return comb(n + r - 1, r); } static T small_perm(ll n, ll r) { if (r < 0 || r > n) return 0; chmin(r, n - r); T res = 1; reps (i, r) res *= n - r + i; return res; } static T small_comb(ll n, ll r) { if (r < 0 || r > n) return 0; chmin(r, n - r); init(r); T res = 1; reps (i, r) res *= n - r + i; return res / factorial[r]; } static T small_homo(ll n, ll r) { return small_comb(n + r - 1, r); } }; template std::vector IntCombinatorics::factorial = std::vector(1, 1); template class Combinatorics { private: static std::vector factorial; static std::vector factinv; public: static void init(ll n) { const int b = factorial.size(); if (n < b) return; factorial.resize(n + 1); rep (i, b, n + 1) factorial[i] = factorial[i - 1] * i; factinv.resize(n + 1); factinv[n] = T(1) / factorial[n]; rreps (i, n, b) factinv[i - 1] = factinv[i] * i; } static T fact(ll x) { init(x); return factorial[x]; } static T finv(ll x) { init(x); return factinv[x]; } static T perm(ll n, ll r) { if (r < 0 || r > n) return 0; init(n); return factorial[n] * factinv[n - r]; } static T comb(ll n, ll r) { if (n < 0) return 0; if (r < 0 || r > n) return 0; init(n); return factorial[n] * factinv[n - r] * factinv[r]; } static T homo(ll n, ll r) { return comb(n + r - 1, r); } static T small_perm(ll n, ll r) { if (r < 0 || r > n) return 0; T res = 1; reps (i, r) res *= n - r + i; return res; } static T small_comb(ll n, ll r) { if (r < 0 || r > n) return 0; chmin(r, n - r); init(r); T res = factinv[r]; reps (i, r) res *= n - r + i; return res; } static T small_homo(ll n, ll r) { return small_comb(n + r - 1, r); } }; template std::vector Combinatorics::factorial = std::vector(1, 1); template std::vector Combinatorics::factinv = std::vector(1, 1); /** * @brief Combinatorics * @docs docs/math/Combinatorics.md */ #line 4 "main.cpp" using namespace std; using mint = modint998244353; using comb = Combinatorics; void solve(); int main() { int T; scan >> T; rep (T) solve(); } void solve() { int N, M; scan >> N >> M; map mp; rep (N) { int a; scan >> a; ++mp[a]; } // 端から順に配置していく int l = 0, r = 0, cur = N; // 左に置いた人、右に置いた人、まだ置いてない人 mint ans = 1; int pos = 0; for (auto [v, cnt] : vector(rall(mp))) { cur -= cnt; // 値 v の人を cnt 人配置する // 現時点で l=r の場合 if (cur == 0) { // 最後の 1 つは真ん中に置かれるので選択肢はない if (v == r) { ++pos; } else { prints(0); return; } } else if (l == r) { // 片方の端(l)にまとめて置く場合、その人の値は r+cur になる // 両方の端に置く場合、同数配置する必要があり、その人の値は r+cur+cnt/2 になる if (v == r + cur) { ans *= 2; r += cnt; ++pos; } else if (cnt % 2 == 0 && v == r + cur + cnt / 2) { ans *= comb::comb(cnt, cnt / 2); l += cnt / 2; r += cnt / 2; pos += 2; } else { prints(0); return; } } else { // l < r を仮定する // 片方の端(l)にまとめて置く場合、その人の値は max(l, r+cur)=r+cur になる // 片方の端(r)にまとめて置く場合、その人の値は max(l+cur,r) になる // ここで、この値が r に等しいとき、次に置く人の値は cnt+r になり、これは r より大きくなって不適 // よって l+cur // 両方の端に置く場合、 a, b 配置するとして、左の人は max(l, r+cur+b) 右の人は max(l+a+cur, r) になり、これが等しくなる必要がある // l=l+a+cur と r=r+cur+b はあり得ず、 l=r となると l+r>=l+r+a+b+cur+cur となり、成り立たない // よって r+cur+b=l+a+cur になり、 l+a=r+b なる a,b を選べばよい // a+b=cnt を考えると、 (l+r+cnt)%2=0 と a=(r-l+cnt)/2 が分かる if (v == r + cur) { l += cnt; ++pos; } else if (v == l + cur) { r += cnt; ++pos; } else if ((l + r + cnt) % 2 == 0 && l - r + cnt >= 0 && v == (l + r + cnt) / 2) { ans *= comb::comb(cnt, (r - l + cnt) / 2); l += (r - l + cnt) / 2; r += (l - r + cnt) / 2; pos += 2; } else { prints(0); return; } } if (l > r) swap(l, r); } prints(ans * comb::comb(M, pos)); }