結果
| 問題 | No.1520 Zigzag Sum |
| ユーザー |
 jell
|
| 提出日時 | 2021-05-28 21:44:03 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 65 ms / 2,000 ms |
| コード長 | 54,472 bytes |
| コンパイル時間 | 2,945 ms |
| コンパイル使用メモリ | 274,768 KB |
| 実行使用メモリ | 7,580 KB |
| 最終ジャッジ日時 | 2023-08-07 05:44:59 |
| 合計ジャッジ時間 | 4,295 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge15 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 32 ms
6,680 KB |
| testcase_01 | AC | 2 ms
4,376 KB |
| testcase_02 | AC | 25 ms
4,376 KB |
| testcase_03 | AC | 64 ms
7,312 KB |
| testcase_04 | AC | 65 ms
7,580 KB |
| testcase_05 | AC | 64 ms
7,052 KB |
| testcase_06 | AC | 60 ms
6,872 KB |
| testcase_07 | AC | 60 ms
5,528 KB |
ソースコード
#line 1 "other-workspace\\yuki.cc"
// #undef _GLIBCXX_DEBUG
// #define NDEBUG
#include <bits/extc++.h>
#line 2 "Library\\lib\\alias"
/**
* @file alias
* @brief Alias
*/
#line 10 "Library\\lib\\alias"
#line 2 "Library\\lib\\bit"
#if __cplusplus > 201703L
#include <bit>
#else
#ifndef _GLIBCXX_BIT
#define _GLIBCXX_BIT 1
#include <limits>
#include <type_traits>
namespace std {
template <typename _Tp> constexpr int __countl_zero(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return _Nd;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if
_GLIBCXX17_CONSTEXPR(_Nd <= _Nd_u) {
constexpr int __diff = _Nd_u - _Nd;
return __builtin_clz(__x) - __diff;
}
else if
_GLIBCXX17_CONSTEXPR(_Nd <= _Nd_ul) {
constexpr int __diff = _Nd_ul - _Nd;
return __builtin_clzl(__x) - __diff;
}
else if
_GLIBCXX17_CONSTEXPR(_Nd <= _Nd_ull) {
constexpr int __diff = _Nd_ull - _Nd;
return __builtin_clzll(__x) - __diff;
}
else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
unsigned long long __high = __x >> _Nd_ull;
if (__high != 0) {
constexpr int __diff = (2 * _Nd_ull) - _Nd;
return __builtin_clzll(__high) - __diff;
}
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
return (_Nd - _Nd_ull) + __builtin_clzll(__low);
}
}
template <typename _Tp> constexpr int __countr_zero(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return _Nd;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if
_GLIBCXX17_CONSTEXPR(_Nd <= _Nd_u)
return __builtin_ctz(__x);
else if _GLIBCXX17_CONSTEXPR(_Nd <= _Nd_ul) return __builtin_ctzl(__x);
else if _GLIBCXX17_CONSTEXPR(_Nd <= _Nd_ull) return __builtin_ctzll(__x);
else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
if (__low != 0) return __builtin_ctzll(__low);
unsigned long long __high = __x >> _Nd_ull;
return __builtin_ctzll(__high) + _Nd_ull;
}
}
template <typename _Tp> constexpr int __popcount(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return 0;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if
_GLIBCXX17_CONSTEXPR(_Nd <= _Nd_u)
return __builtin_popcount(__x);
else if _GLIBCXX17_CONSTEXPR(_Nd <= _Nd_ul) return __builtin_popcountl(__x);
else if _GLIBCXX17_CONSTEXPR(_Nd <= _Nd_ull) return __builtin_popcountll(__x);
else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
unsigned long long __high = __x >> _Nd_ull;
return __builtin_popcountll(__low) + __builtin_popcountll(__high);
}
}
template <typename _Tp> constexpr _Tp __bit_ceil(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0 || __x == 1) return 1;
auto __shift_exponent = _Nd - __countl_zero((_Tp)(__x - 1u));
#ifdef _GLIBCXX_HAVE_BUILTIN_IS_CONSTANT_EVALUATED
if (!__builtin_is_constant_evaluated()) {
__glibcxx_assert(__shift_exponent != numeric_limits<_Tp>::digits);
}
#endif
using __promoted_type = decltype(__x << 1);
if
_GLIBCXX17_CONSTEXPR(!is_same<__promoted_type, _Tp>::value) {
const int __extra_exp = sizeof(__promoted_type) / sizeof(_Tp) / 2;
__shift_exponent |= (__shift_exponent & _Nd) << __extra_exp;
}
return (_Tp)1u << __shift_exponent;
}
template <typename _Tp> constexpr _Tp __bit_floor(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return 0;
return (_Tp)1u << (_Nd - __countl_zero((_Tp)(__x >> 1)));
}
template <typename _Tp> constexpr _Tp __bit_width(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
return _Nd - __countl_zero(__x);
}
} // namespace std
#endif
#endif
#line 2 "Library\\lib\\limits"
#line 4 "Library\\lib\\limits"
namespace workspace {
template <class _Tp> struct numeric_limits : std::numeric_limits<_Tp> {};
#ifdef __SIZEOF_INT128__
template <> struct numeric_limits<__uint128_t> {
constexpr static __uint128_t max() { return ~__uint128_t(0); }
constexpr static __uint128_t min() { return 0; }
};
template <> struct numeric_limits<__int128_t> {
constexpr static __int128_t max() {
return numeric_limits<__uint128_t>::max() >> 1;
}
constexpr static __int128_t min() { return -max() - 1; }
};
#endif
} // namespace workspace
#line 13 "Library\\lib\\alias"
namespace workspace {
constexpr static char eol = '\n';
using namespace std;
using i32 = int_least32_t;
using u32 = uint_least32_t;
using i64 = int_least64_t;
using u64 = uint_least64_t;
#ifdef __SIZEOF_INT128__
using i128 = __int128_t;
using u128 = __uint128_t;
#else
#warning 128-bit integer is not available.
#endif
template <class _T1, class _T2,
typename = decltype(std::declval<const _T2 &>() <
std::declval<const _T1 &>())>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
min(const _T1 &__x, const _T2 &__y) noexcept {
return __y < __x ? __y : __x;
}
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _T2 &>(), std::declval<const _T1 &>()))>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
min(const _T1 &__x, const _T2 &__y, _Compare __comp) noexcept {
return __comp(__y, __x) ? __y : __x;
}
template <class _Tp, typename = decltype(std::declval<const _Tp &>() <
std::declval<const _Tp &>())>
constexpr _Tp min(std::initializer_list<_Tp> __x) noexcept {
return *std::min_element(__x.begin(), __x.end());
}
template <class _Tp, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _Tp &>(), std::declval<const _Tp &>()))>
constexpr _Tp min(std::initializer_list<_Tp> __x, _Compare __comp) noexcept {
return *std::min_element(__x.begin(), __x.end(), __comp);
}
template <class _T1, class _T2,
typename = decltype(std::declval<const _T1 &>() <
std::declval<const _T2 &>())>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
max(const _T1 &__x, const _T2 &__y) noexcept {
return __x < __y ? __y : __x;
}
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _T1 &>(), std::declval<const _T2 &>()))>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
max(const _T1 &__x, const _T2 &__y, _Compare __comp) noexcept {
return __comp(__x, __y) ? __y : __x;
}
template <class _Tp, typename = decltype(std::declval<const _Tp &>() <
std::declval<const _Tp &>())>
constexpr _Tp max(std::initializer_list<_Tp> __x) noexcept {
return *std::max_element(__x.begin(), __x.end());
}
template <class _Tp, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _Tp &>(), std::declval<const _Tp &>()))>
constexpr _Tp max(std::initializer_list<_Tp> __x, _Compare __comp) noexcept {
return *std::max_element(__x.begin(), __x.end(), __comp);
}
template <typename _Tp> constexpr _Tp __bsf(_Tp __x) noexcept {
return std::__countr_zero(__x);
}
template <typename _Tp> constexpr _Tp __bsr(_Tp __x) noexcept {
return std::__bit_width(__x) - 1;
}
} // namespace workspace
#line 6 "other-workspace\\yuki.cc"
// #include "lib/cxx20"
#line 1 "Library\\lib\\direct"
#ifdef ONLINE_JUDGE
#pragma GCC optimize("O3")
#pragma GCC target("avx,avx2")
#pragma GCC optimize("unroll-loops")
#endif
#line 8 "other-workspace\\yuki.cc"
// #include "lib/opt"
#line 2 "Library\\src\\sys\\call_once.hpp"
/**
* @file call_once.hpp
* @brief Call Once
*/
#line 9 "Library\\src\\sys\\call_once.hpp"
namespace workspace {
/**
* @brief Call once.
*/
template <class _F> void call_once(_F &&__f) {
static std::unordered_set<void *> __called;
if (__called.count(std::addressof(__f))) return;
__called.emplace(std::addressof(__f));
__f();
}
} // namespace workspace
#line 2 "Library\\src\\sys\\clock.hpp"
/*
* @fn clock.hpp
* @brief Clock
*/
#line 9 "Library\\src\\sys\\clock.hpp"
namespace workspace {
using namespace std::chrono;
namespace internal {
// The start time of the program.
const auto start_time{system_clock::now()};
} // namespace internal
/*
* @fn elapsed
* @return elapsed time of the program
*/
int64_t elapsed() {
const auto end_time{system_clock::now()};
return duration_cast<milliseconds>(end_time - internal::start_time).count();
}
} // namespace workspace
#line 2 "Library\\src\\sys\\ejection.hpp"
/**
* @file ejection.hpp
* @brief Ejection
*/
#line 9 "Library\\src\\sys\\ejection.hpp"
namespace workspace {
namespace internal {
struct ejection {
bool exit = 0;
};
} // namespace internal
/**
* @brief eject from a try block, throw nullptr
* @param arg output
*/
template <class Tp> void eject(Tp const &arg) {
std::cout << arg << "\n";
throw internal::ejection{};
}
void exit() { throw internal::ejection{true}; }
} // namespace workspace
#line 2 "Library\\src\\sys\\iteration.hpp"
/**
* @file iteration.hpp
* @brief Case Iteration
*/
#line 9 "Library\\src\\sys\\iteration.hpp"
#line 11 "Library\\src\\sys\\iteration.hpp"
namespace workspace {
void main();
struct {
// 1-indexed
unsigned current{0};
unsigned total{1};
void read() { (std::cin >> total).ignore(); }
int iterate() {
static bool once = false;
assert(!once);
once = true;
while (current++ < total) {
try {
main();
} catch (internal::ejection const& status) {
if (status.exit) break;
}
}
return 0;
}
} case_info;
} // namespace workspace
#line 2 "Library\\lib\\utils"
// #include "src/utils/cached.hpp"
#line 2 "Library\\src\\utils\\cat.hpp"
/**
* @file cat.hpp
* @brief Cat
*/
#line 9 "Library\\src\\utils\\cat.hpp"
namespace workspace {
/**
* @brief Concatenate two sequences.
*
* @param __c1
* @param __c2
* @return Concatenated sequence.
*/
template <class _C1, class _C2>
constexpr decltype(auto) cat(_C1 &&__c1, _C2 &&__c2) noexcept {
auto __c = std::forward<_C1>(__c1);
if constexpr (std::is_rvalue_reference<decltype(__c2)>::value)
__c.insert(std::end(__c), std::move_iterator(std::begin(__c2)),
std::move_iterator(std::end(__c2)));
else
__c.insert(std::end(__c), std::cbegin(__c2), std::cend(__c2));
return __c;
}
/**
* @return Concatenated sequence.
*/
template <class _C1, class _C2, class... _Args>
constexpr decltype(auto) cat(_C1 &&__c1, _C2 &&__c2,
_Args &&...__args) noexcept {
return cat(cat(std::forward<_C1>(__c1), std::forward<_C2>(__c2)),
std::forward<_Args>(__args)...);
}
} // namespace workspace
#line 2 "Library\\src\\utils\\chval.hpp"
/**
* @file chval.hpp
* @brief Change Less/Greater
*/
#line 9 "Library\\src\\utils\\chval.hpp"
namespace workspace {
/**
* @brief Substitute __y for __x if __y < __x.
* @param __x Reference
* @param __y Comparison target
* @return Whether or not __x is updated.
*/
template <class _T1, class _T2,
typename = decltype(std::declval<_T2>() < std::declval<_T1 &>())>
typename std::enable_if<std::is_assignable<_T1 &, _T2>::value, bool>::type chle(
_T1 &__x, _T2 &&__y) noexcept {
return __y < __x ? __x = std::forward<_T2>(__y), true : false;
}
/**
* @brief Substitute __y for __x if __x < __y.
* @param __x Reference
* @param __y Comparison target
* @return Whether or not __x is updated.
*/
template <class _T1, class _T2,
typename = decltype(std::declval<_T1 &>() < std::declval<_T2>())>
typename std::enable_if<std::is_assignable<_T1 &, _T2>::value, bool>::type chgr(
_T1 &__x, _T2 &&__y) noexcept {
return __x < __y ? __x = std::forward<_T2>(__y), true : false;
}
/**
* @brief Substitute __y for __x if __comp(__y, __x) is true.
* @param __x Reference
* @param __y Comparison target
* @param __comp Compare function object
* @return Whether or not __x is updated.
*/
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(std::declval<_T2>(),
std::declval<_T1 &>()))>
typename std::enable_if<std::is_assignable<_T1 &, _T2>::value, bool>::type chle(
_T1 &__x, _T2 &&__y, _Compare __comp) noexcept {
return __comp(__y, __x) ? __x = std::forward<_T2>(__y), true : false;
}
/**
* @brief Substitute __y for __x if __comp(__x, __y) is true.
* @param __x Reference
* @param __y Comparison target
* @param __comp Compare function object
* @return Whether or not __x is updated.
*/
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(std::declval<_T1 &>(),
std::declval<_T2>()))>
typename std::enable_if<std::is_assignable<_T1 &, _T2>::value, bool>::type chgr(
_T1 &__x, _T2 &&__y, _Compare __comp) noexcept {
return __comp(__x, __y) ? __x = std::forward<_T2>(__y), true : false;
}
} // namespace workspace
#line 1 "Library\\src\\utils\\compare.hpp"
/**
* @file compare.hpp
* @brief Compare
*/
#line 2 "Library\\src\\utils\\sfinae.hpp"
/**
* @file sfinae.hpp
* @brief SFINAE
*/
#line 10 "Library\\src\\utils\\sfinae.hpp"
#include <type_traits>
#ifndef __INT128_DEFINED__
#ifdef __SIZEOF_INT128__
#define __INT128_DEFINED__ 1
#else
#define __INT128_DEFINED__ 0
#endif
#endif
namespace std {
#if __INT128_DEFINED__
template <> struct make_signed<__uint128_t> { using type = __int128_t; };
template <> struct make_signed<__int128_t> { using type = __int128_t; };
template <> struct make_unsigned<__uint128_t> { using type = __uint128_t; };
template <> struct make_unsigned<__int128_t> { using type = __uint128_t; };
template <> struct is_signed<__uint128_t> : std::false_type {};
template <> struct is_signed<__int128_t> : std::true_type {};
template <> struct is_unsigned<__uint128_t> : std::true_type {};
template <> struct is_unsigned<__int128_t> : std::false_type {};
#endif
} // namespace std
namespace workspace {
template <class Tp, class... Args> struct variadic_front { using type = Tp; };
template <class... Args> struct variadic_back;
template <class Tp> struct variadic_back<Tp> { using type = Tp; };
template <class Tp, class... Args> struct variadic_back<Tp, Args...> {
using type = typename variadic_back<Args...>::type;
};
template <class type, template <class> class trait>
using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type;
/**
* @brief Return type of subscripting ( @c [] ) access.
*/
template <class _Tp>
using subscripted_type =
typename std::decay<decltype(std::declval<_Tp&>()[0])>::type;
template <class Container>
using element_type = typename std::decay<decltype(
*std::begin(std::declval<Container&>()))>::type;
template <class _Tp, class = std::nullptr_t>
struct has_begin : std::false_type {};
template <class _Tp>
struct has_begin<_Tp, decltype(std::begin(std::declval<_Tp>()), nullptr)>
: std::true_type {};
template <class _Tp, class = void> struct has_mod : std::false_type {};
template <class _Tp>
struct has_mod<_Tp, std::__void_t<decltype(_Tp::mod)>> : std::true_type {};
template <class _Tp, class = void> struct is_integral_ext : std::false_type {};
template <class _Tp>
struct is_integral_ext<
_Tp, typename std::enable_if<std::is_integral<_Tp>::value>::type>
: std::true_type {};
#if __INT128_DEFINED__
template <> struct is_integral_ext<__int128_t> : std::true_type {};
template <> struct is_integral_ext<__uint128_t> : std::true_type {};
#endif
#if __cplusplus >= 201402
template <class _Tp>
constexpr static bool is_integral_ext_v = is_integral_ext<_Tp>::value;
#endif
template <typename _Tp, typename = void> struct multiplicable_uint {
using type = uint_least32_t;
};
template <typename _Tp>
struct multiplicable_uint<
_Tp,
typename std::enable_if<(2 < sizeof(_Tp)) &&
(!__INT128_DEFINED__ || sizeof(_Tp) <= 4)>::type> {
using type = uint_least64_t;
};
#if __INT128_DEFINED__
template <typename _Tp>
struct multiplicable_uint<_Tp,
typename std::enable_if<(4 < sizeof(_Tp))>::type> {
using type = __uint128_t;
};
#endif
template <typename _Tp> struct multiplicable_int {
using type =
typename std::make_signed<typename multiplicable_uint<_Tp>::type>::type;
};
template <typename _Tp> struct multiplicable {
using type = std::conditional_t<
is_integral_ext<_Tp>::value,
std::conditional_t<std::is_signed<_Tp>::value,
typename multiplicable_int<_Tp>::type,
typename multiplicable_uint<_Tp>::type>,
_Tp>;
};
template <class> struct first_arg { using type = void; };
template <class _R, class _Tp, class... _Args>
struct first_arg<_R(_Tp, _Args...)> {
using type = _Tp;
};
template <class _R, class _Tp, class... _Args>
struct first_arg<_R (*)(_Tp, _Args...)> {
using type = _Tp;
};
template <class _G, class _R, class _Tp, class... _Args>
struct first_arg<_R (_G::*)(_Tp, _Args...)> {
using type = _Tp;
};
template <class _G, class _R, class _Tp, class... _Args>
struct first_arg<_R (_G::*)(_Tp, _Args...) const> {
using type = _Tp;
};
template <class _Tp, class = void> struct parse_compare : first_arg<_Tp> {};
template <class _Tp>
struct parse_compare<_Tp, std::__void_t<decltype(&_Tp::operator())>>
: first_arg<decltype(&_Tp::operator())> {};
} // namespace workspace
#line 7 "Library\\src\\utils\\compare.hpp"
namespace workspace {
/**
* @brief Compare 2 points by their value of `atan2`.
*
* @return
*/
template <class _Tp>
bool compare_arg(const _Tp& __p1, const _Tp& __p2) noexcept {
const auto& [__x1, __y1] = __p1;
const auto& [__x2, __y2] = __p2;
using value_type = std::decay_t<decltype(__x1)>;
using mul_type = typename multiplicable<value_type>::type;
if (__y1 == value_type(0))
return value_type(0) <= __x1 &&
(value_type(0) < __y2 ||
(__y2 == value_type(0) && __x2 < value_type(0)));
return value_type(0) < __y1
? value_type(0) <= __y2 &&
mul_type(__y1) * __x2 < mul_type(__x1) * __y2
: value_type(0) <= __y2 ||
mul_type(__y1) * __x2 < mul_type(__x1) * __y2;
}
} // namespace workspace
#line 2 "Library\\src\\utils\\fixed_point.hpp"
/**
* @file fixed_point.hpp
* @brief Fixed Point Combinator
*/
#line 9 "Library\\src\\utils\\fixed_point.hpp"
namespace workspace {
/**
* @brief Fixed Point Combinator
*/
template <class _F> class fixed_point {
_F __fn;
public:
/**
* @brief Construct a new fixed point object
*
* @param __fn 1st argument callable with the rest of its arguments.
* Return type specified.
*/
fixed_point(_F __fn) noexcept : __fn(std::forward<_F>(__fn)) {}
/**
* @brief Apply *this to 1st argument.
* @param __args Rest of arguments.
*/
template <class... _Args> decltype(auto) operator()(_Args &&...__args) const {
return __fn(*this, std::forward<_Args>(__args)...);
}
};
} // namespace workspace
#line 2 "Library\\src\\utils\\hash.hpp"
#line 8 "Library\\src\\utils\\hash.hpp"
#line 10 "Library\\src\\utils\\hash.hpp"
namespace workspace {
template <class T, class = void> struct hash : std::hash<T> {};
template <class _Tp> struct hash<_Tp *> : std::hash<_Tp *> {};
#if __cplusplus >= 201703L
template <class Unique_bits_type>
struct hash<Unique_bits_type,
enable_if_trait_type<Unique_bits_type,
std::has_unique_object_representations>> {
size_t operator()(uint64_t x) const {
static const uint64_t m = std::random_device{}();
x ^= x >> 23;
x ^= m;
x ^= x >> 47;
return x - (x >> 32);
}
};
#endif
template <class Key> size_t hash_combine(const size_t &seed, const Key &key) {
return seed ^
(hash<Key>()(key) + 0x9e3779b9 /* + (seed << 6) + (seed >> 2) */);
}
template <class T1, class T2> struct hash<std::pair<T1, T2>> {
size_t operator()(const std::pair<T1, T2> &pair) const {
return hash_combine(hash<T1>()(pair.first), pair.second);
}
};
template <class... T> class hash<std::tuple<T...>> {
template <class Tuple, size_t index = std::tuple_size<Tuple>::value - 1>
struct tuple_hash {
static uint64_t apply(const Tuple &t) {
return hash_combine(tuple_hash<Tuple, index - 1>::apply(t),
std::get<index>(t));
}
};
template <class Tuple> struct tuple_hash<Tuple, size_t(-1)> {
static uint64_t apply(const Tuple &t) { return 0; }
};
public:
uint64_t operator()(const std::tuple<T...> &t) const {
return tuple_hash<std::tuple<T...>>::apply(t);
}
};
template <class hash_table> struct hash_table_wrapper : hash_table {
using key_type = typename hash_table::key_type;
size_t count(const key_type &key) const {
return hash_table::find(key) != hash_table::end();
}
template <class... Args> auto emplace(Args &&... args) {
return hash_table::insert(typename hash_table::value_type(args...));
}
};
template <class Key, class Mapped = __gnu_pbds::null_type>
using cc_hash_table =
hash_table_wrapper<__gnu_pbds::cc_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped = __gnu_pbds::null_type>
using gp_hash_table =
hash_table_wrapper<__gnu_pbds::gp_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped>
using unordered_map = std::unordered_map<Key, Mapped, hash<Key>>;
template <class Key> using unordered_set = std::unordered_set<Key, hash<Key>>;
} // namespace workspace
#line 2 "Library\\src\\utils\\io\\istream.hpp"
/**
* @file istream.hpp
* @brief Input Stream
*/
#include <cxxabi.h>
#line 13 "Library\\src\\utils\\io\\istream.hpp"
#line 15 "Library\\src\\utils\\io\\istream.hpp"
namespace workspace {
namespace _istream_impl {
template <class _Tp, typename = std::nullptr_t> struct istream_helper {
istream_helper(std::istream &__is, _Tp &__x) {
if constexpr (has_begin<_Tp>::value)
for (auto &&__e : __x)
istream_helper<std::decay_t<decltype(__e)>>(__is, __e);
else
static_assert(has_begin<_Tp>::value, "istream unsupported type.");
}
};
template <class _Tp>
struct istream_helper<
_Tp,
decltype(std::declval<std::decay_t<decltype(
std::declval<std::istream &>() >> std::declval<_Tp &>())>>(),
nullptr)> {
istream_helper(std::istream &__is, _Tp &__x) { __is >> __x; }
};
#ifdef __SIZEOF_INT128__
template <> struct istream_helper<__uint128_t, std::nullptr_t> {
istream_helper(std::istream &__is, __uint128_t &__x) {
std::string __s;
__is >> __s;
bool __neg = false;
if (__s.front() == '-') __neg = true, __s.erase(__s.begin());
__x = 0;
for (char __d : __s) {
__x *= 10;
__d -= '0';
if (__neg)
__x -= __d;
else
__x += __d;
}
}
};
template <> struct istream_helper<__int128_t, std::nullptr_t> {
istream_helper(std::istream &__is, __int128_t &__x) {
std::string __s;
__is >> __s;
bool __neg = false;
if (__s.front() == '-') __neg = true, __s.erase(__s.begin());
__x = 0;
for (char __d : __s) {
__x *= 10;
__d -= '0';
if (__neg)
__x -= __d;
else
__x += __d;
}
}
};
#endif // INT128
template <class T1, class T2> struct istream_helper<std::pair<T1, T2>> {
istream_helper(std::istream &__is, std::pair<T1, T2> &__x) {
istream_helper<T1>(__is, __x.first), istream_helper<T2>(__is, __x.second);
}
};
template <class... Tps> struct istream_helper<std::tuple<Tps...>> {
istream_helper(std::istream &__is, std::tuple<Tps...> &__x) {
iterate(__is, __x);
}
private:
template <class _Tp, size_t N = 0>
void iterate(std::istream &__is, _Tp &__x) {
if constexpr (N == std::tuple_size<_Tp>::value)
return;
else
istream_helper<typename std::tuple_element<N, _Tp>::type>(
__is, std::get<N>(__x)),
iterate<_Tp, N + 1>(__is, __x);
}
};
} // namespace _istream_impl
/**
* @brief A wrapper class for std::istream.
*/
class istream : public std::istream {
public:
/**
* @brief Wrapped operator.
*/
template <typename _Tp> istream &operator>>(_Tp &__x) {
_istream_impl::istream_helper<_Tp>(*this, __x);
if (std::istream::fail()) {
static auto once = atexit([] {
std::cerr << "\n\033[43m\033[30mwarning: failed to read \'"
<< abi::__cxa_demangle(typeid(_Tp).name(), 0, 0, 0)
<< "\'.\033[0m\n\n";
});
assert(!once);
}
return *this;
}
};
decltype(auto) cin = static_cast<istream &>(std::cin);
} // namespace workspace
#line 9 "Library\\lib\\utils"
// #include "src/utils/io/ostream.hpp"
// #include "src/utils/io/read.hpp"
#line 2 "Library\\src\\utils\\grid\\motion.hpp"
/**
* @file motion.hpp
* @brief Motion
*/
#line 9 "Library\\src\\utils\\grid\\motion.hpp"
namespace workspace {
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Grid,
typename = decltype(std::declval<std::decay_t<_Grid>>()[0].resize(0))>
constexpr decltype(auto) transpose(_Grid &&__grid) noexcept {
auto __h = std::size(__grid), __w = std::size(__grid[0]);
std::decay_t<_Grid> __t(__w);
for (auto &&__r : __t) __r.resize(__h);
for (size_t __i = 0; __i != __h; ++__i)
for (size_t __j = 0; __j != __w; ++__j)
if constexpr (std::is_rvalue_reference<decltype(__grid)>::value)
__t[__j][__i] = std::move(__grid[__i][__j]);
else
__t[__j][__i] = __grid[__i][__j];
return __t;
}
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Tp, size_t _Rows, size_t _Cols>
constexpr decltype(auto) transpose(const _Tp (&__grid)[_Rows][_Cols]) noexcept {
std::array<std::array<_Tp, _Rows>, _Cols> __t;
for (size_t __i = 0; __i != _Rows; ++__i)
for (size_t __j = 0; __j != _Cols; ++__j) __t[__j][__i] = __grid[__i][__j];
return __t;
}
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Tp, size_t _Rows, size_t _Cols>
constexpr decltype(auto) transpose(_Tp(&&__grid)[_Rows][_Cols]) noexcept {
std::array<std::array<_Tp, _Rows>, _Cols> __t;
for (size_t __i = 0; __i != _Rows; ++__i)
for (size_t __j = 0; __j != _Cols; ++__j)
__t[__j][__i] = std::move(__grid[__i][__j]);
return __t;
}
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Tp, size_t _Rows, size_t _Cols>
constexpr decltype(auto) transpose(
const std::array<std::array<_Tp, _Cols>, _Rows> &__grid) noexcept {
std::array<std::array<_Tp, _Rows>, _Cols> __t;
for (size_t __i = 0; __i != _Rows; ++__i)
for (size_t __j = 0; __j != _Cols; ++__j) __t[__j][__i] = __grid[__i][__j];
return __t;
}
/**
* @brief Transpose.
*
* @param __grid
*/
template <class _Tp, size_t _Rows, size_t _Cols>
constexpr decltype(auto) transpose(
std::array<std::array<_Tp, _Cols>, _Rows> &&__grid) noexcept {
std::array<std::array<_Tp, _Rows>, _Cols> __t;
for (size_t __i = 0; __i != _Rows; ++__i)
for (size_t __j = 0; __j != _Cols; ++__j)
__t[__j][__i] = std::move(__grid[__i][__j]);
return __t;
}
/**
* @brief Roll the grid counter-clockwise.
*
* @param __grid
* @return
*/
template <class _Grid> decltype(auto) roll_ccw(_Grid &&__grid) noexcept {
if constexpr (std::is_rvalue_reference<decltype(__grid)>::value) {
auto __t = transpose(std::move(__grid));
std::reverse(std::begin(__t), std::end(__t));
return __t;
}
else {
auto __t = transpose(__grid);
std::reverse(std::begin(__t), std::end(__t));
return __t;
}
}
/**
* @brief Roll the grid clockwise.
*
* @param __grid
* @return
*/
template <class _Grid> decltype(auto) roll_cw(_Grid &&__grid) noexcept {
if constexpr (std::is_rvalue_reference<decltype(__grid)>::value) {
std::reverse(std::begin(__grid), std::end(__grid));
return transpose(std::move(__grid));
}
else {
auto __t = transpose(__grid);
for (auto &&__r : __t) std::reverse(std::begin(__r), std::end(__r));
return __t;
}
}
} // namespace workspace
#line 2 "Library\\src\\utils\\io\\setup.hpp"
/**
* @file setup.hpp
* @brief I/O Setup
*/
#line 10 "Library\\src\\utils\\io\\setup.hpp"
namespace workspace {
/**
* @brief Setup I/O.
* @param __n Standard output precision
*/
void io_setup(int __n) {
std::cin.tie(0)->sync_with_stdio(0);
std::cout << std::fixed << std::setprecision(__n);
#ifdef _buffer_check
atexit([] {
char bufc;
if (std::cin >> bufc)
std::cerr << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n";
});
#endif
}
} // namespace workspace
#line 2 "Library\\src\\utils\\iterator\\category.hpp"
/*
* @file category.hpp
* @brief Iterator Category
*/
#line 10 "Library\\src\\utils\\iterator\\category.hpp"
namespace workspace {
/*
* @tparam Tuple Tuple of iterator types
*/
template <class Tuple, size_t N = std::tuple_size<Tuple>::value - 1>
struct common_iterator_category {
using type = typename std::common_type<
typename common_iterator_category<Tuple, N - 1>::type,
typename std::iterator_traits<typename std::tuple_element<
N, Tuple>::type>::iterator_category>::type;
};
template <class Tuple> struct common_iterator_category<Tuple, 0> {
using type = typename std::iterator_traits<
typename std::tuple_element<0, Tuple>::type>::iterator_category;
};
} // namespace workspace
#line 2 "Library\\src\\utils\\iterator\\reverse.hpp"
/*
* @file reverse_iterator.hpp
* @brief Reverse Iterator
*/
#if __cplusplus >= 201703L
#include <iterator>
#include <optional>
namespace workspace {
/*
* @class reverse_iterator
* @brief Wrapper class for `std::reverse_iterator`.
* @see http://gcc.gnu.org/PR51823
*/
template <class Iterator>
class reverse_iterator : public std::reverse_iterator<Iterator> {
using base_std = std::reverse_iterator<Iterator>;
std::optional<typename base_std::value_type> deref;
public:
using base_std::reverse_iterator;
constexpr typename base_std::reference operator*() noexcept {
if (!deref) {
Iterator tmp = base_std::current;
deref = *--tmp;
}
return deref.value();
}
constexpr reverse_iterator &operator++() noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator &operator--() noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator operator++(int) noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator operator--(int) noexcept {
base_std::operator++();
deref.reset();
return *this;
}
};
} // namespace workspace
#endif
#line 15 "Library\\lib\\utils"
// #include "src/utils/make_vector.hpp"
// #include "src/utils/py-like/enumerate.hpp"
#line 2 "Library\\src\\utils\\py-like\\range.hpp"
/**
* @file range.hpp
* @brief Range
*/
#line 9 "Library\\src\\utils\\py-like\\range.hpp"
#line 2 "Library\\src\\utils\\py-like\\reversed.hpp"
/**
* @file reversed.hpp
* @brief Reversed
*/
#include <initializer_list>
#line 10 "Library\\src\\utils\\py-like\\reversed.hpp"
namespace workspace {
namespace _reversed_impl {
template <class _Container> class reversed {
_Container __cont;
public:
constexpr reversed(_Container &&__cont) noexcept : __cont(__cont) {}
constexpr decltype(auto) begin() noexcept { return std::rbegin(__cont); }
constexpr decltype(auto) begin() const noexcept {
return std::rbegin(__cont);
}
constexpr decltype(auto) end() noexcept { return std::rend(__cont); }
constexpr decltype(auto) end() const noexcept { return std::rend(__cont); }
constexpr decltype(auto) size() const noexcept { return std::size(__cont); }
};
} // namespace _reversed_impl
template <class _Container>
constexpr decltype(auto) reversed(_Container &&__cont) noexcept {
return _reversed_impl::reversed<_Container>{std::forward<_Container>(__cont)};
}
template <class _Tp>
constexpr decltype(auto) reversed(
std::initializer_list<_Tp> &&__cont) noexcept {
return _reversed_impl::reversed<std::initializer_list<_Tp>>{
std::forward<std::initializer_list<_Tp>>(__cont)};
}
} // namespace workspace
#line 12 "Library\\src\\utils\\py-like\\range.hpp"
#if __cplusplus >= 201703L
namespace workspace {
template <class _Index> class range {
_Index __first, __last;
public:
class iterator {
_Index current;
public:
using difference_type = std::ptrdiff_t;
using value_type = _Index;
using reference = typename std::add_const<_Index>::type &;
using pointer = iterator;
using iterator_category = std::random_access_iterator_tag;
constexpr iterator(const _Index &__i = _Index()) noexcept : current(__i) {}
constexpr bool operator==(const iterator &__x) const noexcept {
return current == __x.current;
}
constexpr bool operator!=(const iterator &__x) const noexcept {
return current != __x.current;
}
constexpr bool operator<(const iterator &__x) const noexcept {
return current < __x.current;
}
constexpr bool operator<=(const iterator &__x) const noexcept {
return current <= __x.current;
}
constexpr bool operator>(const iterator &__x) const noexcept {
return current > __x.current;
}
constexpr bool operator>=(const iterator &__x) const noexcept {
return current >= __x.current;
}
constexpr iterator &operator++() noexcept {
++current;
return *this;
}
constexpr iterator &operator++(int) noexcept {
auto __tmp = *this;
++current;
return __tmp;
}
constexpr iterator &operator--() noexcept {
--current;
return *this;
}
constexpr iterator &operator--(int) noexcept {
auto __tmp = *this;
--current;
return __tmp;
}
constexpr difference_type operator-(const iterator &__x) const noexcept {
return current - __x.current;
}
constexpr iterator &operator+=(difference_type __x) noexcept {
current += __x;
return *this;
}
constexpr iterator operator+(difference_type __x) const noexcept {
return iterator(*this) += __x;
}
constexpr iterator &operator-=(difference_type __x) noexcept {
current -= __x;
return *this;
}
constexpr iterator operator-(difference_type __x) const noexcept {
return iterator(*this) -= __x;
}
constexpr reference operator*() const noexcept { return current; }
};
constexpr range(_Index __first, _Index __last) noexcept
: __first(__first), __last(__last) {}
constexpr range(_Index __last) noexcept : __first(), __last(__last) {}
constexpr iterator begin() const noexcept { return iterator{__first}; }
constexpr iterator end() const noexcept { return iterator{__last}; }
constexpr reverse_iterator<iterator> rbegin() const noexcept {
return reverse_iterator<iterator>(end());
}
constexpr reverse_iterator<iterator> rend() const noexcept {
return reverse_iterator<iterator>(begin());
}
constexpr size_t size() const noexcept {
return std::distance(__first, __last);
}
};
template <class... _Args>
constexpr decltype(auto) rrange(_Args &&...__args) noexcept {
return reversed(range(std::forward<_Args>(__args)...));
}
template <class _Container>
constexpr decltype(auto) iterate(_Container &&__cont) noexcept {
return range(std::begin(__cont), std::end(__cont));
}
template <class _Container>
constexpr decltype(auto) riterate(_Container &&__cont) noexcept {
return range(std::rbegin(__cont), std::rend(__cont));
}
} // namespace workspace
#endif
#line 18 "Library\\lib\\utils"
// #include "src/utils/py-like/reversed.hpp"
// #include "src/utils/py-like/zip.hpp"
#line 2 "Library\\src\\utils\\rand\\rng.hpp"
/**
* @file rng.hpp
* @brief Random Number Generator
*/
#line 9 "Library\\src\\utils\\rand\\rng.hpp"
namespace workspace {
template <typename _Arithmetic>
using uniform_distribution = typename std::conditional<
std::is_integral<_Arithmetic>::value,
std::uniform_int_distribution<_Arithmetic>,
std::uniform_real_distribution<_Arithmetic>>::type;
template <typename _Arithmetic, class _Engine = std::mt19937>
class random_number_generator : uniform_distribution<_Arithmetic> {
using base = uniform_distribution<_Arithmetic>;
_Engine __engine;
public:
random_number_generator(_Arithmetic __min, _Arithmetic __max)
: base(__min, __max), __engine(std::random_device{}()) {}
random_number_generator(_Arithmetic __max = 1)
: random_number_generator(0, __max) {}
random_number_generator(typename base::param_type const& __param)
: base(__param), __engine(std::random_device{}()) {}
decltype(auto) operator()() noexcept { return base::operator()(__engine); }
};
} // namespace workspace
#line 2 "Library\\src\\utils\\rand\\shuffle.hpp"
/**
* @file shuffle.hpp
* @brief Shuffle
*/
#line 10 "Library\\src\\utils\\rand\\shuffle.hpp"
namespace workspace {
template <class _RAIter, class _Engine = std::mt19937>
void shuffle(_RAIter __first, _RAIter __last) {
static _Engine __engine(std::random_device{}());
std::shuffle(__first, __last, __engine);
}
} // namespace workspace
#line 2 "Library\\src\\utils\\rand\\tree.hpp"
#line 4 "Library\\src\\utils\\rand\\tree.hpp"
#line 6 "Library\\src\\utils\\rand\\tree.hpp"
namespace workspace {
auto random_tree(std::size_t __n) {
std::vector<std::pair<std::size_t, std::size_t>> __edges;
random_number_generator rng(std::size_t(0), __n);
for (std::size_t __i = 1; __i != __n; ++__i)
__edges.emplace_back(__i + 1, rng() % __i + 1);
return __edges;
}
} // namespace workspace
#line 2 "Library\\src\\utils\\round_div.hpp"
/*
* @file round_div.hpp
* @brief Round Integer Division
*/
#line 9 "Library\\src\\utils\\round_div.hpp"
#line 11 "Library\\src\\utils\\round_div.hpp"
namespace workspace {
/*
* @fn floor_div
* @brief floor of fraction.
* @param x the numerator
* @param y the denominator
* @return maximum integer z s.t. z <= x / y
* @note y must be nonzero.
*/
template <typename T1, typename T2>
constexpr typename std::enable_if<(is_integral_ext<T1>::value &&
is_integral_ext<T2>::value),
typename std::common_type<T1, T2>::type>::type
floor_div(T1 x, T2 y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x < 0 ? (x - y + 1) / y : x / y;
}
/*
* @fn ceil_div
* @brief ceil of fraction.
* @param x the numerator
* @param y the denominator
* @return minimum integer z s.t. z >= x / y
* @note y must be nonzero.
*/
template <typename T1, typename T2>
constexpr typename std::enable_if<(is_integral_ext<T1>::value &&
is_integral_ext<T2>::value),
typename std::common_type<T1, T2>::type>::type
ceil_div(T1 x, T2 y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x < 0 ? x / y : (x + y - 1) / y;
}
} // namespace workspace
#line 24 "Library\\lib\\utils"
// #include "src\utils\reference_list.hpp"
#line 11 "other-workspace\\yuki.cc"
signed main() {
using namespace workspace;
io_setup(15);
//* given
case_info.read(); //*/
/* unspecified
case_info.total = -1; //*/
return case_info.iterate();
}
#line 2 "Library\\src\\combinatorics\\binomial.hpp"
/**
* @file binomial.hpp
* @brief Binomial Coefficient
*/
#line 2 "Library\\src\\modular\\modint.hpp"
/**
* @file modint.hpp
*
* @brief Modular Arithmetic
*/
#line 12 "Library\\src\\modular\\modint.hpp"
#line 2 "Library\\src\\number_theory\\sqrt_mod.hpp"
/**
* @file sqrt_mod.hpp
* @brief Tonelli-Shanks Algorithm
*/
#line 2 "Library\\src\\number_theory\\pow_mod.hpp"
/**
* @file mod_pow.hpp
* @brief Modular Exponentiation
*/
#line 9 "Library\\src\\number_theory\\pow_mod.hpp"
#line 11 "Library\\src\\number_theory\\pow_mod.hpp"
namespace workspace {
/**
* @brief Compile time modular exponentiation.
*
* @param __x
* @param __n Exponent
* @param __mod Modulus
* @return
*/
template <class _Tp>
constexpr std::enable_if_t<(is_integral_ext<_Tp>::value), _Tp> pow_mod(
_Tp __x, _Tp __n, _Tp __mod) noexcept {
assert(__mod > 0);
using mul_type = typename multiplicable_uint<_Tp>::type;
if ((__x %= __mod) < 0) __x += __mod;
mul_type __y{1};
while (__n) {
if (__n & 1) (__y *= __x) %= __mod;
__x = (mul_type)__x * __x % __mod;
__n >>= 1;
}
return __y;
};
} // namespace workspace
#line 10 "Library\\src\\number_theory\\sqrt_mod.hpp"
namespace workspace {
/**
* @brief Compile time modular square root.
*
* @param __x
* @param __mod Modulus
* @return One if it exists. Otherwise -1.
*/
template <class _Tp>
constexpr std::enable_if_t<(is_integral_ext<_Tp>::value), _Tp> sqrt_mod(
_Tp __x, _Tp __mod) noexcept {
assert(__mod > 0);
using mul_type = typename multiplicable_uint<_Tp>::type;
if ((__x %= __mod) < 0) __x += __mod;
if (!__x) return 0;
if (__mod == 2) return __x;
if (pow_mod(__x, __mod >> 1, __mod) != 1) return -1;
_Tp __z = __builtin_ctz(__mod - 1), __q = __mod >> __z;
mul_type __a = pow_mod(__x, (__q + 1) >> 1, __mod), __b = 2;
while (pow_mod<_Tp>(__b, __mod >> 1, __mod) == 1) ++__b;
__b = pow_mod<_Tp>(__b, __q, __mod);
_Tp __shift = 0;
for (auto __r = __a * __a % __mod * pow_mod(__x, __mod - 2, __mod) % __mod;
__r != 1; (__r *= (__b *= __b) %= __mod) %= __mod) {
auto __bsf = __z;
for (auto __e = __r; __e != 1; --__bsf) (__e *= __e) %= __mod;
while (++__shift != __bsf) (__b *= __b) %= __mod;
(__a *= __b) %= __mod;
}
return __a;
};
} // namespace workspace
#line 15 "Library\\src\\modular\\modint.hpp"
namespace workspace {
namespace _modint_impl {
template <auto _Mod, unsigned _Storage> struct modint {
static_assert(is_integral_ext<decltype(_Mod)>::value,
"_Mod must be integral type.");
using mod_type = std::make_signed_t<typename std::conditional<
0 < _Mod, std::add_const_t<decltype(_Mod)>, decltype(_Mod)>::type>;
using value_type = std::decay_t<mod_type>;
using mul_type = typename multiplicable_uint<value_type>::type;
// Modulus
static mod_type mod;
static unsigned storage;
private:
value_type value = 0;
struct direct_ctor_t {};
constexpr static direct_ctor_t direct_ctor_tag{};
// Direct constructor
template <class _Tp>
constexpr modint(_Tp __n, direct_ctor_t) noexcept : value(__n) {}
public:
constexpr modint() noexcept = default;
template <class _Tp, typename = std::enable_if_t<is_integral_ext<_Tp>::value>>
constexpr modint(_Tp __n) noexcept
: value((__n %= mod) < 0 ? __n += mod : __n) {}
constexpr modint(bool __n) noexcept : value(__n) {}
constexpr operator value_type() const noexcept { return value; }
// unary operators {{
constexpr modint operator++(int) noexcept {
modint __t{*this};
operator++();
return __t;
}
constexpr modint operator--(int) noexcept {
modint __t{*this};
operator--();
return __t;
}
constexpr modint &operator++() noexcept {
if (++value == mod) value = 0;
return *this;
}
constexpr modint &operator--() noexcept {
if (!value)
value = mod - 1;
else
--value;
return *this;
}
constexpr modint operator+() const noexcept { return *this; }
constexpr modint operator-() const noexcept {
return {value ? mod - value : 0, direct_ctor_tag};
}
// }} unary operators
// operator+= {{
constexpr modint &operator+=(const modint &__x) noexcept {
if ((value += __x.value) >= mod) value -= mod;
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator+=(
_Tp const &__x) noexcept {
if (((value += __x) %= mod) < 0) value += mod;
return *this;
}
// }} operator+=
// operator+ {{
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator+(
_Tp const &__x) const noexcept {
return modint{*this} += __x;
}
constexpr modint operator+(modint __x) const noexcept { return __x += *this; }
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator+(_Tp const &__x, modint __y) noexcept {
return __y += __x;
}
// }} operator+
// operator-= {{
constexpr modint &operator-=(const modint &__x) noexcept {
if ((value -= __x.value) < 0) value += mod;
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator-=(
_Tp __x) noexcept {
if (((value -= __x) %= mod) < 0) value += mod;
return *this;
}
// }} operator-=
// operator- {{
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator-(
_Tp const &__x) const noexcept {
return modint{*this} -= __x;
}
constexpr modint operator-(const modint &__x) const noexcept {
return modint{*this} -= __x;
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator-(_Tp __x, const modint &__y) noexcept {
if (((__x -= __y.value) %= mod) < 0) __x += mod;
return {__x, direct_ctor_tag};
}
// }} operator-
// operator*= {{
constexpr modint &operator*=(const modint &__x) noexcept {
value =
static_cast<value_type>(value * static_cast<mul_type>(__x.value) % mod);
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator*=(
_Tp __x) noexcept {
value = static_cast<value_type>(
value * mul_type((__x %= mod) < 0 ? __x + mod : __x) % mod);
return *this;
}
// }} operator*=
// operator* {{
constexpr modint operator*(const modint &__x) const noexcept {
return {static_cast<mul_type>(value) * __x.value % mod, direct_ctor_tag};
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator*(
_Tp __x) const noexcept {
__x %= mod;
if (__x < 0) __x += mod;
return {static_cast<mul_type>(value) * __x % mod, direct_ctor_tag};
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator*(_Tp __x, const modint &__y) noexcept {
__x %= mod;
if (__x < 0) __x += mod;
return {static_cast<mul_type>(__x) * __y.value % mod, direct_ctor_tag};
}
// }} operator*
protected:
static value_type _mem(value_type __x) {
static std::vector<value_type> __m{0, 1};
static value_type __i = (__m.reserve(storage), 1);
while (__i < __x) {
++__i;
__m.emplace_back(mod - mul_type(mod / __i) * __m[mod % __i] % mod);
}
return __m[__x];
}
static value_type _div(mul_type __r, value_type __x) noexcept {
assert(__x != value_type(0));
if (!__r) return 0;
std::make_signed_t<value_type> __v{};
bool __neg = __x < 0 ? __x = -__x, true : false;
if (static_cast<decltype(storage)>(__x) < storage)
__v = _mem(__x);
else {
value_type __y{mod}, __u{1}, __t;
while (__x)
__t = __y / __x, __y ^= __x ^= (__y -= __t * __x) ^= __x,
__v ^= __u ^= (__v -= __t * __u) ^= __u;
if (__y < 0) __neg ^= 1;
}
if (__neg)
__v = 0 < __v ? mod - __v : -__v;
else if (__v < 0)
__v += mod;
return __r == mul_type(1) ? static_cast<value_type>(__v)
: static_cast<value_type>(__r * __v % mod);
}
public:
// operator/= {{
constexpr modint &operator/=(const modint &__x) noexcept {
if (value) value = _div(value, __x.value);
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator/=(
_Tp __x) noexcept {
if (value) value = _div(value, __x %= mod);
return *this;
}
// }} operator/=
// operator/ {{
constexpr modint operator/(const modint &__x) const noexcept {
if (!value) return {};
return {_div(value, __x.value), direct_ctor_tag};
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator/(
_Tp __x) const noexcept {
if (!value) return {};
return {_div(value, __x %= mod), direct_ctor_tag};
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator/(_Tp __x, const modint &__y) noexcept {
if (!__x) return {};
if ((__x %= mod) < 0) __x += mod;
return {_div(__x, __y.value), direct_ctor_tag};
}
// }} operator/
constexpr modint inv() const noexcept { return _div(1, value); }
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> pow(
_Tp __e) const noexcept {
modint __r{1, direct_ctor_tag};
for (modint __b{__e < 0 ? __e = -__e, _div(1, value) : value,
direct_ctor_tag};
__e; __e >>= 1, __b *= __b)
if (__e & 1) __r *= __b;
return __r;
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint> pow(
modint __b, _Tp __e) noexcept {
if (__e < 0) {
__e = -__e;
__b.value = _div(1, __b.value);
}
modint __r{1, direct_ctor_tag};
for (; __e; __e >>= 1, __b *= __b)
if (__e & 1) __r *= __b;
return __r;
}
constexpr modint sqrt() const noexcept {
return {sqrt_mod(value, mod), direct_ctor_tag};
}
friend constexpr modint sqrt(const modint &__x) noexcept {
return {sqrt_mod(__x.value, mod), direct_ctor_tag};
}
template <class _Os>
friend _Os &operator<<(_Os &__os, const modint &__x) noexcept {
return __os << __x.value;
}
friend std::istream &operator>>(std::istream &__is, modint &__x) noexcept {
std::string __s;
__is >> __s;
bool __neg = false;
if (__s.front() == '-') {
__neg = true;
__s.erase(__s.begin());
}
__x = 0;
for (char __c : __s) __x = __x * 10 + (__c - '0');
if (__neg) __x = -__x;
return __is;
}
};
template <auto _Mod, unsigned _Storage>
typename modint<_Mod, _Storage>::mod_type modint<_Mod, _Storage>::mod =
_Mod > 0 ? _Mod : 0;
template <auto _Mod, unsigned _Storage>
unsigned modint<_Mod, _Storage>::storage = _Storage;
} // namespace _modint_impl
template <auto _Mod, unsigned _Storage = 0,
typename = std::enable_if_t<(_Mod > 0)>>
using modint = _modint_impl::modint<_Mod, _Storage>;
template <unsigned _Id = 0>
using modint_runtime = _modint_impl::modint<-(signed)_Id, 0>;
} // namespace workspace
#line 2 "Library\\src\\combinatorics\\factorial.hpp"
/**
* @file factorial.hpp
* @brief Factorial
* @date 2021-01-15
*
*
*/
#line 12 "Library\\src\\combinatorics\\factorial.hpp"
namespace workspace {
template <class _Tp> _Tp factorial(int32_t __x) noexcept {
if (__x < 0) return 0;
static std::vector<_Tp> __t{1};
static int32_t __i = (__t.reserve(0x1000000), 0);
while (__i < __x) {
++__i;
__t.emplace_back(__t.back() * _Tp(__i));
}
return __t[__x];
}
template <class _Tp> _Tp factorial_inverse(int32_t __x) noexcept {
if (__x < 0) return 0;
static std::vector<_Tp> __t{1};
static int32_t __i = (__t.reserve(0x1000000), 0);
while (__i < __x) {
++__i;
__t.emplace_back(__t.back() / _Tp(__i));
}
return __t[__x];
}
} // namespace workspace
#line 10 "Library\\src\\combinatorics\\binomial.hpp"
namespace workspace {
namespace _binom_impl {
struct _binom_table {
constexpr static int size = 132;
__uint128_t __b[size][size]{1};
constexpr _binom_table() noexcept {
for (int __i = 1; __i != size; ++__i)
for (int __j = 0; __j != __i; ++__j)
__b[__i][__j] += __b[__i - 1][__j],
__b[__i][__j + 1] += __b[__i - 1][__j];
}
constexpr auto operator()(int __x, int __y) const noexcept {
return __x < 0 || __x < __y ? 0 : (assert(__x < size), __b[__x][__y]);
}
};
constexpr _binom_table table;
} // namespace _binom_impl
/**
* @brief Binomial coefficient for integer args. Be careful with overflow.
*/
template <class _Tp> constexpr _Tp binomial(int32_t __x, int32_t __y) {
if constexpr (is_integral_ext<_Tp>::value)
return _binom_impl::table(__x, __y);
if (__y < 0 || __x < __y) return 0;
return factorial<_Tp>(__x) * factorial_inverse<_Tp>(__y) *
factorial_inverse<_Tp>(__x - __y);
}
/**
* @brief Catalan number.
*/
template <class _Tp> constexpr _Tp catalan(int32_t __x) {
return binomial<_Tp>(__x << 1, __x) - binomial<_Tp>(__x << 1, __x + 1);
}
} // namespace workspace
#line 28 "other-workspace\\yuki.cc"
namespace workspace {
using mint = modint<1000000007>;
auto binom = binomial<mint>;
void main() {
// start here!
int h, w;
cin >> h >> w;
--h, --w;
mint ans;
ans += binom(h + w - 2, h - 1);
ans *= 2 * (h + w - 1);
cout << ans << "\n";
}
} // namespace workspace