結果
| 問題 |
No.2330 Eat Slime
|
| コンテスト | |
| ユーザー |
 shiomusubi496
|
| 提出日時 | 2023-05-28 14:21:58 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 60,964 bytes |
| コンパイル時間 | 4,352 ms |
| コンパイル使用メモリ | 255,088 KB |
| 最終ジャッジ日時 | 2025-02-13 11:17:38 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 22 WA * 8 |
ソースコード
#line 2 "library/other/template.hpp"
#include <bits/stdc++.h>
#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<ll, ll>;
template<class T>
using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template<class T> class infinity {
public:
static constexpr T value = std::numeric_limits<T>::max() / 2;
static constexpr T mvalue = std::numeric_limits<T>::min() / 2;
static constexpr T max = std::numeric_limits<T>::max();
static constexpr T min = std::numeric_limits<T>::min();
};
#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 "library/template/type_traits.hpp"
#line 5 "library/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(&F::operator())>::type;
template<class T>
using is_signed_int =
std::disjunction<std::conjunction<std::is_integral<T>, std::is_signed<T>>,
std::is_same<T, __int128_t>>;
template<class T>
using is_unsigned_int =
std::disjunction<std::conjunction<std::is_integral<T>, std::is_unsigned<T>>,
std::is_same<T, __uint128_t>>;
template<class T>
using is_int = std::disjunction<is_signed_int<T>, is_unsigned_int<T>>;
template<class T>
using make_signed_int = typename std::conditional<
std::is_same<T, __int128_t>::value || std::is_same<T, __uint128_t>::value,
std::common_type<__int128_t>, std::make_signed<T>>::type;
template<class T>
using make_unsigned_int = typename std::conditional<
std::is_same<T, __int128_t>::value || std::is_same<T, __uint128_t>::value,
std::common_type<__uint128_t>, 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,
__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<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 "library/template/in.hpp"
#line 4 "library/template/in.hpp"
#include <unistd.h>
#line 8 "library/template/in.hpp"
template<std::size_t buf_size = IO_BUFFER_SIZE> class Reader {
private:
int fd, idx, sz;
bool state;
std::array<char, buf_size> 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; }
};
iterator begin() noexcept { return iterator(this); }
};
Reader<> reader(0);
template<class Iterator, std::size_t decimal_precision = 16> class Scanner {
public:
using iterator_type = Iterator;
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 {};
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<std::size_t len> void scan(std::bitset<len>& a) {
discard_space();
rrep (i, len) {
a[i] = *itr != '0';
++itr;
}
}
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 (*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<class T,
typename std::enable_if<is_unsigned_int<T>::value &&
!has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
discard_space();
a = 0;
while ('0' <= *itr && *itr <= '9') {
a = a * 10 + *itr - '0';
++itr;
}
}
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 (*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<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) {
each_for (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 itr.rdstate(); }
};
Scanner<Reader<>::iterator> scan(reader.begin());
template<class Iterator, std::size_t decimal_precision>
Scanner<Iterator, decimal_precision>&
getline(Scanner<Iterator, decimal_precision>& scan, std::string& a) {
a.clear();
char c;
while ((c = scan.scan_char()) != '\n') {
a += c;
}
return scan;
}
#line 2 "library/template/out.hpp"
#line 8 "library/template/out.hpp"
template<std::size_t buf_size = IO_BUFFER_SIZE> class Writer {
private:
int fd, idx;
std::array<char, buf_size> 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 Iterator, bool debug = false> class Printer {
public:
using iterator_type = Iterator;
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 {};
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<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;
}
}
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<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<class Iterator, bool debug>
Printer<Iterator, debug>& endl(Printer<Iterator, debug>& pr) {
pr.print_char('\n');
pr.flush();
return pr;
}
template<class Iterator, bool debug>
Printer<Iterator, debug>& flush(Printer<Iterator, 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<Writer<>::iterator> print(writer.begin()), eprint(ewriter.begin());
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...);
}
#ifdef SHIO_LOCAL
Printer<Writer<>::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<DebugIterator> debug, edebug;
#endif
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 "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<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) 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<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) 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 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 presser {
private:
std::vector<T> dat;
Comp cmp;
bool sorted = false;
public:
presser() : presser(Comp()) {}
presser(const Comp& cmp) : cmp(cmp) {}
presser(const std::vector<T>& vec, const Comp& cmp = Comp())
: dat(vec), cmp(cmp) {}
presser(std::vector<T>&& vec, const Comp& cmp = Comp())
: dat(std::move(vec)), cmp(cmp) {}
presser(std::initializer_list<T> 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<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];
}
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<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 {
static_assert(std::is_convertible<T, int>::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<T>& data() const& { return dat; }
std::vector<T> data() && { return std::move(dat); }
};
#line 2 "library/math/convolution/Convolution.hpp"
#line 2 "library/math/ModInt.hpp"
#line 4 "library/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};
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) {}
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<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 "library/math/PrimitiveRoot.hpp"
#line 2 "library/random/Random.hpp"
#line 4 "library/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(); }
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 "library/math/MontgomeryModInt.hpp"
#line 4 "library/math/MontgomeryModInt.hpp"
template<class T> class MontgomeryReduction {
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;
static constexpr int lg = std::numeric_limits<T>::digits;
T mod;
T r;
T r2; // r^2 mod m
T calc_minv() {
T t = 0, res = 0;
rep (i, lg) {
if (~t & 1) {
t += mod;
res += static_cast<T>(1) << i;
}
t >>= 1;
}
return res;
}
T minv;
public:
MontgomeryReduction(T v) { set_mod(v); }
static constexpr int get_lg() { return lg; }
void set_mod(T v) {
assert(v > 0);
assert(v & 1);
assert(v <= std::numeric_limits<T>::max() / 2);
mod = v;
r = (-static_cast<T>(mod)) % mod;
r2 = (-static_cast<large_t>(mod)) % mod;
minv = calc_minv();
}
inline T get_mod() const { return mod; }
inline T get_r() const { return r; }
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<class T, int id> class MontgomeryModInt {
private:
using large_t = typename double_size_uint<T>::type;
using signed_t = typename std::make_signed<T>::type;
T val;
static MontgomeryReduction<T> mont;
public:
MontgomeryModInt() : val(0) {}
template<class U, typename std::enable_if<
std::is_integral<U>::value &&
std::is_unsigned<U>::value>::type* = nullptr>
MontgomeryModInt(U x)
: val(mont.transform(
x < (static_cast<large_t>(mont.get_mod()) << mont.get_lg())
? x
: x % mont.get_mod())) {}
template<class U,
typename std::enable_if<std::is_integral<U>::value &&
std::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 = mont.get_mod() - val;
}
T get() const { return mont.reduce(val); }
static T get_mod() { return mont.get_mod(); }
static void set_mod(T v) { mont.set_mod(v); }
MontgomeryModInt operator+() const { return *this; }
MontgomeryModInt operator-() const {
MontgomeryModInt res;
if (val) res.val = mont.get_mod() - val;
return res;
}
MontgomeryModInt& operator++() {
val += mont.get_r();
if (val >= mont.get_mod()) val -= mont.get_mod();
return *this;
}
MontgomeryModInt& operator--() {
if (val < mont.get_r()) val += mont.get_mod();
val -= mont.get_r();
return *this;
}
MontgomeryModInt operator++(int) {
MontgomeryModInt res = *this;
++*this;
return res;
}
MontgomeryModInt operator--(int) {
MontgomeryModInt res = *this;
--*this;
return res;
}
MontgomeryModInt& operator+=(const MontgomeryModInt& rhs) {
val += rhs.val;
if (val >= mont.get_mod()) val -= mont.get_mod();
return *this;
}
MontgomeryModInt& operator-=(const MontgomeryModInt& rhs) {
if (val < rhs.val) val += mont.get_mod();
val -= rhs.val;
return *this;
}
MontgomeryModInt& operator*=(const MontgomeryModInt& rhs) {
val = mont.reduce(static_cast<large_t>(val) * rhs.val);
return *this;
}
MontgomeryModInt pow(ull n) const {
MontgomeryModInt res = 1, x = *this;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
MontgomeryModInt inv() const { return pow(mont.get_mod() - 2); }
MontgomeryModInt& operator/=(const MontgomeryModInt& rhs) {
return *this *= rhs.inv();
}
friend MontgomeryModInt operator+(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return MontgomeryModInt(lhs) += rhs;
}
friend MontgomeryModInt operator-(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return MontgomeryModInt(lhs) -= rhs;
}
friend MontgomeryModInt operator*(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return MontgomeryModInt(lhs) *= rhs;
}
friend MontgomeryModInt operator/(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return MontgomeryModInt(lhs) /= rhs;
}
friend bool operator==(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return lhs.val != rhs.val;
}
template<class Pr> void print(Pr& a) const { a.print(mont.reduce(val)); }
template<class Pr> void debug(Pr& a) const { a.print(mont.reduce(val)); }
template<class Sc> void scan(Sc& a) {
ll v;
a.scan(v);
*this = v;
}
};
template<class T, int id>
MontgomeryReduction<T>
MontgomeryModInt<T, id>::mont = MontgomeryReduction<T>(998244353);
using mmodint = MontgomeryModInt<unsigned int, -1>;
/**
* @brief MontgomeryModInt(モンゴメリ乗算)
* @docs docs/math/MontgomeryModInt.md
*/
#line 2 "library/math/MillerRabin.hpp"
#line 5 "library/math/MillerRabin.hpp"
constexpr ull base_miller_rabin_int[3] = {2, 7, 61};
constexpr ull base_miller_rabin_ll[7] = {2, 325, 9375, 28178,
450775, 9780504, 1795265022};
template<class T> CONSTEXPR bool miller_rabin(ull n, const ull base[], int s) {
if (T::get_mod() != n) T::set_mod(n);
ull d = n - 1;
while (~d & 1) d >>= 1;
T e{1}, re{n - 1};
rep (i, s) {
ull a = base[i];
if (a >= n) return true;
ull t = d;
T y = T(a).pow(t);
while (t != n - 1 && y != e && y != re) {
y *= y;
t <<= 1;
}
if (y != re && !(t & 1)) return false;
}
return true;
}
CONSTEXPR bool is_prime_mr(ll n) {
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_miller_rabin_int, 3);
return miller_rabin<MontgomeryModInt<ull, -2>>(n, base_miller_rabin_ll, 7);
}
#if __cpp_variable_templates >= 201304L && __cpp_constexpr >= 201304L
template<ull n> constexpr bool is_prime_v = is_prime_mr(n);
#endif
/**
* @brief MillerRabin(ミラーラビン素数判定)
* @docs docs/math/MillerRabin.md
*/
#line 2 "library/math/PollardRho.hpp"
#line 2 "library/string/RunLength.hpp"
#line 4 "library/string/RunLength.hpp"
template<class Cont, class Comp>
std::vector<std::pair<typename Cont::value_type, int>>
RunLength(const Cont& str, const Comp& cmp) {
std::vector<std::pair<typename Cont::value_type, int>> res;
if (str.size() == 0) return res;
res.emplace_back(str[0], 1);
rep (i, 1, str.size()) {
if (cmp(res.back().first, str[i])) ++res.back().second;
else res.emplace_back(str[i], 1);
}
return res;
}
template<class Cont>
std::vector<std::pair<typename Cont::value_type, int>>
RunLength(const Cont& str) {
return RunLength(str, std::equal_to<typename Cont::value_type>());
}
/**
* @brief RunLength(ランレングス圧縮)
* @docs docs/string/RunLength.md
*/
#line 8 "library/math/PollardRho.hpp"
template<class T, class Rnd> ull pollard_rho(ull n, Rnd& rnd) {
if (~n & 1) return 2;
if (T::get_mod() != n) T::set_mod(n);
T c, one = 1;
auto f = [&](T x) -> T { return x * x + c; };
constexpr int M = 128;
while (1) {
c = rnd.uniform(1ull, n - 1);
T x = rnd.uniform(2ull, n - 1), y = x;
ull g = 1;
while (g == 1) {
T p = one, tx = x, ty = y;
rep (M) {
x = f(x);
y = f(f(y));
p *= x - y;
}
g = gcd(p.get(), n);
if (g == 1) continue;
rep (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<class T = MontgomeryModInt<ull, -3>, class Rnd = Random64>
std::vector<ull> factorize(ull n, Rnd& rnd = rand64) {
if (n == 1) return {};
std::vector<ull> res;
std::vector<ull> st = {n};
while (!st.empty()) {
ull t = st.back();
st.pop_back();
if (t == 1) continue;
if (is_prime_mr(t)) {
res.push_back(t);
continue;
}
ull f = pollard_rho<T>(t, rnd);
st.push_back(f);
st.push_back(t / f);
}
std::sort(all(res));
return res;
}
template<class T = MontgomeryModInt<ull, -3>, class Rnd = Random64>
std::vector<std::pair<ull, int>> expfactorize(ull n, Rnd& rnd = rand64) {
auto f = factorize<T, Rnd>(n, rnd);
return RunLength(f);
}
std::vector<ll> divisors_pr(ll n) {
std::vector<ll> res;
auto r = expfactorize(n);
int m = r.size();
rec_lambda([&](auto&& self, int k, ll d) -> void {
if (k == m) {
res.push_back(d);
return;
}
ll t = d;
rep (r[k].second) {
self(k + 1, d);
d *= r[k].first;
}
self(k + 1, d);
d = t;
})(0, 1);
std::sort(all(res));
return res;
}
/**
* @brief PollardRho(素因数分解)
* @docs docs/math/PollardRho.md
*/
#line 9 "library/math/PrimitiveRoot.hpp"
template<class T = MontgomeryModInt<ull, -4>> ull primitive_root(ull p) {
assert(is_prime_mr(p));
if (p == 2) return 1;
if (T::get_mod() != p) T::set_mod(p);
auto pf = factorize(p - 1);
pf.erase(std::unique(all(pf)), pf.end());
each_for (x : pf) x = (p - 1) / x;
T one = 1;
while (1) {
ull g = rand64.uniform(2ull, p - 1);
bool ok = true;
each_const (x : pf) {
if (T(g).pow(x) == one) {
ok = false;
break;
}
}
if (ok) return g;
}
}
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;
}
/**
* @brief PrimitiveRoot(原始根)
* @docs docs/math/PrimitiveRoot.md
*/
#line 6 "library/math/convolution/Convolution.hpp"
namespace internal {
template<unsigned int p> class NthRoot {
private:
static constexpr unsigned int lg = bitop::msb((p - 1) & (1 - p));
unsigned int root[lg + 1];
unsigned int inv_root[lg + 1];
public:
constexpr NthRoot() : root{}, inv_root{} {
root[lg] = mod_pow(primitive_root_for_convolution(p), (p - 1) >> lg, p);
inv_root[lg] = mod_pow(root[lg], p - 2, p);
rrep (i, lg) {
root[i] = (ull)root[i + 1] * root[i + 1] % p;
inv_root[i] = (ull)inv_root[i + 1] * inv_root[i + 1] % p;
}
}
static constexpr unsigned int get_lg() { return lg; }
constexpr unsigned int get(int n) const { return root[n]; }
constexpr unsigned int inv(int n) const { return inv_root[n]; }
};
template<unsigned int p> constexpr NthRoot<p> nth_root;
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::msb(n - 1) + 1;
int m = 1 << lg;
a.resize(m);
b.resize(m);
rep (i, m) {
int j = bitop::reverse(i, lg);
if (i < j) {
std::swap(a[i], a[j]);
std::swap(b[i], b[j]);
}
}
rep (i, lg) {
const T w = nth_root<T::get_mod()>.get(i + 1);
rep (j, 0, m, 1 << (i + 1)) {
T z = 1;
rep (k, 1 << i) {
T x = a[j + k];
T y = a[j + k + (1 << i)] * z;
a[j + k] = x + y;
a[j + k + (1 << i)] = x - y;
x = b[j + k];
y = b[j + k + (1 << i)] * z;
b[j + k] = x + y;
b[j + k + (1 << i)] = x - y;
z *= w;
}
}
}
rep (i, m) a[i] *= b[i];
rep (i, m) {
int j = bitop::reverse(i, lg);
if (i < j) std::swap(a[i], a[j]);
}
rep (i, lg) {
const T w = nth_root<T::get_mod()>.inv(i + 1);
rep (j, 0, m, 1 << (i + 1)) {
T z = 1;
rep (k, 1 << i) {
T x = a[j + k];
T y = a[j + k + (1 << i)] * z;
a[j + k] = x + y;
a[j + k + (1 << i)] = x - y;
z *= w;
}
}
}
a.resize(n);
T inv_m = T(1) / m;
each_for (x : a) x *= inv_m;
return a;
}
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;
}
} // namespace internal
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))) return convolution_for_any_mod(a, b);
return internal::convolution(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(n + m - 1);
rep (i, n + m - 1) 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 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>(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) {
ull t1 = c1[i];
ull t2 = (c2[i] - t1 + MOD2) * INV1_2 % MOD2;
if (t2 < 0) t2 += MOD2;
ull t3 =
((c3[i] - t1 + MOD3) * INV1_3 % MOD3 - t2 + MOD3) * INV2_3 % MOD3;
if (t3 < 0) t3 += MOD3;
assert(0 <= t1 && t1 < MOD1);
assert(0 <= t2 && t2 < MOD2);
assert(0 <= t3 && t3 < MOD3);
res[i] = static_modint<p>(t1 + (t2 + t3 * MOD2) % p * MOD1);
}
return res;
}
/**
* @brief Convolution(畳み込み)
* @docs docs/math/convolution.md
*/
#line 3 "main.cpp"
using namespace std;
int main() {
ll N, M, X; scan >> N >> M >> X;
vector<ll> C(N); scan >> C;
vector<array<ll, 3>> A(M); scan >> A;
rep (i, N) --C[i];
rep (i, M) {
--A[i][0];
--A[i][1];
}
vector<ll> ans(N);
rep (i, 5) {
vector<ll> X(N);
rep (j, N) {
if (C[j] == i) X[j] = 1;
}
vector<ll> Y(N);
rep (j, M) {
if (A[j][1] == i) Y[N - 1 - A[j][0]] += A[j][2];
}
auto Z = convolution<998244353>(X, Y);
rep (i, N) ans[i] += Z[N - 1 + i];
}
ll mx = 0;
rep (i, N) chmax(mx, ans[i] + i * X);
prints(mx);
}