結果
問題 | No.1349 Subset Product Queries |
ユーザー | jell |
提出日時 | 2021-01-16 14:37:57 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
TLE
|
実行時間 | - |
コード長 | 51,937 bytes |
コンパイル時間 | 4,409 ms |
コンパイル使用メモリ | 283,164 KB |
実行使用メモリ | 149,456 KB |
最終ジャッジ日時 | 2024-11-27 16:36:59 |
合計ジャッジ時間 | 60,423 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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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 | 2 ms
13,632 KB |
testcase_01 | AC | 2 ms
137,724 KB |
testcase_02 | AC | 2 ms
13,640 KB |
testcase_03 | AC | 2 ms
138,000 KB |
testcase_04 | AC | 3 ms
13,636 KB |
testcase_05 | AC | 2 ms
137,280 KB |
testcase_06 | AC | 2 ms
13,636 KB |
testcase_07 | AC | 2 ms
137,024 KB |
testcase_08 | AC | 2 ms
13,632 KB |
testcase_09 | AC | 2 ms
140,420 KB |
testcase_10 | AC | 2 ms
13,640 KB |
testcase_11 | TLE | - |
testcase_12 | TLE | - |
testcase_13 | TLE | - |
testcase_14 | TLE | - |
testcase_15 | TLE | - |
testcase_16 | TLE | - |
testcase_17 | TLE | - |
testcase_18 | AC | 335 ms
52,104 KB |
testcase_19 | WA | - |
testcase_20 | TLE | - |
testcase_21 | TLE | - |
testcase_22 | TLE | - |
testcase_23 | TLE | - |
testcase_24 | TLE | - |
testcase_25 | TLE | - |
testcase_26 | TLE | - |
testcase_27 | TLE | - |
testcase_28 | TLE | - |
testcase_29 | TLE | - |
testcase_30 | TLE | - |
ソースコード
#line 1 "atcoder-workspace/177.cc" // #undef _GLIBCXX_DEBUG // #define NDEBUG #include <bits/extc++.h> #line 2 "Library/lib/alias" /** * @file alias * @brief Alias */ #line 13 "Library/lib/alias" #line 1 "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 _Tp __rotl(_Tp __x, int __s) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; const int __r = __s % _Nd; if (__r == 0) return __x; else if (__r > 0) return (__x << __r) | (__x >> ((_Nd - __r) % _Nd)); else return (__x >> -__r) | (__x << ((_Nd + __r) % _Nd)); // rotr(x, -r) } template <typename _Tp> constexpr _Tp __rotr(_Tp __x, int __s) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; const int __r = __s % _Nd; if (__r == 0) return __x; else if (__r > 0) return (__x >> __r) | (__x << ((_Nd - __r) % _Nd)); else return (__x << -__r) | (__x >> ((_Nd + __r) % _Nd)); // rotl(x, -r) } 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 __countl_one(_Tp __x) noexcept { if (__x == numeric_limits<_Tp>::max()) return numeric_limits<_Tp>::digits; return __countl_zero<_Tp>((_Tp)~__x); } 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 __countr_one(_Tp __x) noexcept { if (__x == numeric_limits<_Tp>::max()) return numeric_limits<_Tp>::digits; return __countr_zero((_Tp)~__x); } 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 bool __has_single_bit(_Tp __x) noexcept { return __popcount(__x) == 1; } 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 15 "Library/lib/alias" namespace workspace { constexpr 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 128bit integer is not available. #endif template <class T, class Comp = less<T>> using priority_queue = std::priority_queue<T, vector<T>, Comp>; template <class T> using stack = std::stack<T, vector<T>>; 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 2 "Library/lib/cxx20" /* * @file cxx20 * @brief C++20 Features */ #line 1 "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 _Tp __rotl(_Tp __x, int __s) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; const int __r = __s % _Nd; if (__r == 0) return __x; else if (__r > 0) return (__x << __r) | (__x >> ((_Nd - __r) % _Nd)); else return (__x >> -__r) | (__x << ((_Nd + __r) % _Nd)); // rotr(x, -r) } template <typename _Tp> constexpr _Tp __rotr(_Tp __x, int __s) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; const int __r = __s % _Nd; if (__r == 0) return __x; else if (__r > 0) return (__x >> __r) | (__x << ((_Nd - __r) % _Nd)); else return (__x << -__r) | (__x >> ((_Nd + __r) % _Nd)); // rotl(x, -r) } 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 __countl_one(_Tp __x) noexcept { if (__x == numeric_limits<_Tp>::max()) return numeric_limits<_Tp>::digits; return __countl_zero<_Tp>((_Tp)~__x); } 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 __countr_one(_Tp __x) noexcept { if (__x == numeric_limits<_Tp>::max()) return numeric_limits<_Tp>::digits; return __countr_zero((_Tp)~__x); } 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 bool __has_single_bit(_Tp __x) noexcept { return __popcount(__x) == 1; } 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 9 "Library/lib/cxx20" #if __cplusplus <= 201703L #include <algorithm> #include <vector> namespace std { /* * @fn erase_if * @brief Erase the elements of a container that do not satisfy the condition. * @param __cont Container. * @param __pred Predicate. * @return Number of the erased elements. */ template <typename _Tp, typename _Alloc, typename _Predicate> inline typename vector<_Tp, _Alloc>::size_type erase_if( vector<_Tp, _Alloc>& __cont, _Predicate __pred) { const auto __osz = __cont.size(); __cont.erase(remove_if(__cont.begin(), __cont.end(), __pred), __cont.end()); return __osz - __cont.size(); } /* * @fn erase * @brief Erase the elements of a container that are equal to the given value. * @param __cont Container. * @param __value Value. * @return Number of the erased elements. */ template <typename _Tp, typename _Alloc, typename _Up> inline typename vector<_Tp, _Alloc>::size_type erase( vector<_Tp, _Alloc>& __cont, const _Up& __value) { const auto __osz = __cont.size(); __cont.erase(remove(__cont.begin(), __cont.end(), __value), __cont.end()); return __osz - __cont.size(); } } // namespace std #endif #line 2 "Library/lib/direct" /* * @file direct * @brief Pragma Directive */ #ifdef ONLINE_JUDGE #pragma GCC optimize("O3") #pragma GCC target("avx,avx2") #pragma GCC optimize("unroll-loops") #endif #line 2 "Library/src/opt/binary_search.hpp" /* * @file binary_search.hpp * @brief Binary Search */ #line 12 "Library/src/opt/binary_search.hpp" namespace workspace { /* * @fn binary_search * @brief binary search on a discrete range. * @param ok pred(ok) is true * @param ng pred(ng) is false * @param pred the predicate * @return the closest point to (ng) where pred is true */ template <class Iter, class Pred> typename std::enable_if< std::is_convertible<decltype(std::declval<Pred>()(std::declval<Iter>())), bool>::value, Iter>::type binary_search(Iter ok, Iter ng, Pred pred) { assert(ok != ng); typename std::make_signed<decltype(ng - ok)>::type dist(ng - ok); while (1 < dist || dist < -1) { const Iter mid(ok + dist / 2); if (pred(mid)) ok = mid, dist -= dist / 2; else ng = mid, dist /= 2; } return ok; } /* * @fn binary_search * @brief binary search on the real number line. * @param ok pred(ok) is true * @param ng pred(ng) is false * @param eps the error tolerance * @param pred the predicate * @return the boundary point */ template <class Real, class Pred> typename std::enable_if< std::is_convertible<decltype(std::declval<Pred>()(std::declval<Real>())), bool>::value, Real>::type binary_search(Real ok, Real ng, const Real eps, Pred pred) { assert(ok != ng); for (auto loops = 0; loops != std::numeric_limits<Real>::digits && (ok + eps < ng || ng + eps < ok); ++loops) { const Real mid{(ok + ng) / 2}; (pred(mid) ? ok : ng) = mid; } return ok; } /* * @fn parallel_binary_search * @brief parallel binary search on discrete ranges. * @param ends a vector of pairs; pred(first) is true, pred(second) is false * @param pred the predicate * @return the closest points to (second) where pred is true */ template <class Array, class Iter = typename std::decay< decltype(std::get<0>(std::declval<Array>()[0]))>::type, class Pred> typename std::enable_if< std::is_convertible< decltype(std::declval<Pred>()(std::declval<std::vector<Iter>>())[0]), bool>::value, std::vector<Iter>>::type parallel_binary_search(Array ends, Pred pred) { std::vector<Iter> mids(std::size(ends)); for (;;) { bool all_found = true; for (size_t i{}; i != std::size(ends); ++i) { const Iter &ok = std::get<0>(ends[i]); const Iter &ng = std::get<1>(ends[i]); const Iter mid( ok + typename std::make_signed<decltype(ng - ok)>::type(ng - ok) / 2); if (mids[i] != mid) { all_found = false; mids[i] = mid; } } if (all_found) break; const auto res = pred(mids); for (size_t i{}; i != std::size(ends); ++i) { (res[i] ? std::get<0>(ends[i]) : std::get<1>(ends[i])) = mids[i]; } } return mids; } /* * @fn parallel_binary_search * @brief parallel binary search on the real number line. * @param ends a vector of pairs; pred(first) is true, pred(second) is false * @param eps the error tolerance * @param pred the predicate * @return the boundary points */ template <class Array, class Real = typename std::decay< decltype(std::get<0>(std::declval<Array>()[0]))>::type, class Pred> typename std::enable_if< std::is_convertible< decltype(std::declval<Pred>()(std::declval<std::vector<Real>>())[0]), bool>::value, std::vector<Real>>::type parallel_binary_search(Array ends, const Real eps, Pred pred) { std::vector<Real> mids(std::size(ends)); for (auto loops = 0; loops != std::numeric_limits<Real>::digits; ++loops) { bool all_found = true; for (size_t i{}; i != std::size(ends); ++i) { const Real ok = std::get<0>(ends[i]); const Real ng = std::get<1>(ends[i]); if (ok + eps < ng || ng + eps < ok) { all_found = false; mids[i] = (ok + ng) / 2; } } if (all_found) break; const auto res = pred(mids); for (size_t i{}; i != std::size(ends); ++i) { (res[i] ? std::get<0>(ends[i]) : std::get<1>(ends[i])) = mids[i]; } } return mids; } } // namespace workspace #line 2 "Library/src/opt/exponential_search.hpp" /* * @file exponential_search.hpp * @brief Exponential Search */ #line 9 "Library/src/opt/exponential_search.hpp" namespace workspace { /* * @fn exponential_search * @brief Exponential search on a discrete range. * @param range Range of search, exclusive * @param pred Predicate * @return Minimum non-negative integer where pred is false. */ template <class Index, class Pred> typename std::enable_if< std::is_convertible<decltype(std::declval<Pred>()(std::declval<Index>())), bool>::value, Index>::type exponential_search(Index range, Pred pred) { Index step(1); while (step < range && pred(step)) step <<= 1; if (range < step) step = range; return binary_search(Index(0), step, pred); } /* * @fn exponential_search * @brief Exponential search on the real number line. * @param range Range of search * @param eps Error tolerance * @param pred Predicate * @return Boundary point. */ template <class Real, class Pred> typename std::enable_if< std::is_convertible<decltype(std::declval<Pred>()(std::declval<Real>())), bool>::value, Real>::type exponential_search(Real range, Real const &eps, Pred pred) { Real step(1); while (step < range && pred(step)) step += step; if (range < step) step = range; return binary_search(Real(0), step, eps, pred); } } // namespace workspace #line 2 "Library/src/opt/trinary_search.hpp" /* * @file trinary_search.hpp * @brief Trinary Search */ #line 9 "Library/src/opt/trinary_search.hpp" #include <type_traits> namespace workspace { /* * @brief Trinary search on discrete range. * @param first Left end, inclusive * @param last Right end, exclusive * @param comp Compare function * @return Local minimal point. */ template <class Iter, class Comp> typename std::enable_if< std::is_convertible<decltype(std::declval<Comp>()(std::declval<Iter>(), std::declval<Iter>())), bool>::value, Iter>::type trinary_search(Iter first, Iter last, Comp comp) { assert(first < last); typename std::make_signed<decltype(last - first)>::type dist(last - first); while (2 < dist) { Iter left(first + dist / 3), right(first + dist * 2 / 3); if (comp(left, right)) last = right, dist = (dist + dist) / 3; else first = left, dist -= dist / 3; } if (1 < dist && comp(first + 1, first)) ++first; return first; } /* * @brief Trinary search on discrete range. * @param first Left end, inclusive * @param last Right end, exclusive * @param func Function * @return Local minimal point. */ template <class Iter, class Func> typename std::enable_if< std::is_same<decltype(std::declval<Func>()(std::declval<Iter>()), nullptr), std::nullptr_t>::value, Iter>::type trinary_search(Iter const &first, Iter const &last, Func func) { return trinary_search(first, last, [&](Iter const &__i, Iter const &__j) { return func(__i) < func(__j); }); } /* * @brief Trinary search on the real number line. * @param first Left end * @param last Right end * @param eps Error tolerance * @param comp Compare function * @return Local minimal point. */ template <class Real, class Comp> typename std::enable_if< std::is_convertible<decltype(std::declval<Comp>()(std::declval<Real>(), std::declval<Real>())), bool>::value, Real>::type trinary_search(Real first, Real last, Real const &eps, Comp comp) { assert(first < last); while (eps < last - first) { Real left{(first * 2 + last) / 3}, right{(first + last * 2) / 3}; if (comp(left, right)) last = right; else first = left; } return first; } /* * @brief Trinary search on the real number line. * @param first Left end * @param last Right end * @param eps Error tolerance * @param func Function * @return Local minimal point. */ template <class Real, class Func> typename std::enable_if< std::is_same<decltype(std::declval<Func>()(std::declval<Real>()), nullptr), std::nullptr_t>::value, Real>::type trinary_search(Real const &first, Real const &last, Real const &eps, Func func) { return trinary_search( first, last, eps, [&](Real const &__i, Real const &__j) { return func(__i) < func(__j); }); } } // 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/src/utils/cat.hpp" /** * @file cat.hpp * @brief Cat */ #line 9 "Library/src/utils/cat.hpp" namespace workspace { template <class C1, class C2> constexpr C1 &&cat(C1 &&__c1, C2 const &__c2) noexcept { __c1.insert(__c1.end(), std::begin(__c2), std::end(__c2)); return __c1; } } // 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 { /* * @fn chle * @brief Substitute y for x if comp(y, x) is true. * @param x Reference * @param y Const reference * @param comp Compare function * @return Whether or not x is updated */ template <class Tp, class Comp = std::less<Tp>> bool chle(Tp &x, const Tp &y, Comp comp = Comp()) { return comp(y, x) ? x = y, true : false; } /* * @fn chge * @brief Substitute y for x if comp(x, y) is true. * @param x Reference * @param y Const reference * @param comp Compare function * @return Whether or not x is updated */ template <class Tp, class Comp = std::less<Tp>> bool chge(Tp &x, const Tp &y, Comp comp = Comp()) { return comp(x, y) ? x = y, true : false; } } // 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 { /* * @class fixed_point * @brief Recursive calling of lambda expression. */ template <class lambda_type> class fixed_point { lambda_type func; public: /* * @param func 1st arg callable with the rest of args, and the return type * specified. */ fixed_point(lambda_type &&func) : func(std::move(func)) {} /* * @brief Recursively apply *this to 1st arg of func. * @param args Arguments of the recursive method. */ template <class... Args> auto operator()(Args &&... args) const { return func(*this, std::forward<Args>(args)...); } }; } // namespace workspace #line 2 "Library/src/utils/grid.hpp" /** * @file grid.hpp * @brief Grid * @date 2021-01-09 */ #line 10 "Library/src/utils/grid.hpp" namespace workspace { template <class Grid> Grid transpose(Grid const &grid) { Grid __t; for (auto &&__r : grid) { auto __i = std::begin(__t); for (auto &&__x : __r) { if (__i == std::end(__t)) __i = __t.insert(__t.end(), typename std::decay<decltype(__r)>::type{}); __i->insert(__i->end(), __x); ++__i; } } return __t; } // template <class _Tp, size_t _Row, size_t _Col> // std::array<std::array<_Tp, _Row>, _Col> transpose(_Tp (&__g)[_Row][_Col]) {} template <class Grid> Grid roll_ccw(Grid const &grid) { auto __t = transpose(grid); std::reverse(std::begin(__t), std::end(__t)); return __t; } template <class Grid> Grid roll_cw(Grid const &grid) { auto __t = grid; std::reverse(std::begin(__t), std::end(__t)); return transpose(__t); } } // namespace workspace #line 2 "Library/src/utils/hash.hpp" #line 8 "Library/src/utils/hash.hpp" #line 2 "Library/src/utils/sfinae.hpp" /** * @file sfinae.hpp * @brief SFINAE */ #line 11 "Library/src/utils/sfinae.hpp" #ifdef __SIZEOF_INT128__ #define __INT128_DEFINED__ 1 #else #define __INT128_DEFINED__ 0 #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; }; #endif } // namespace std namespace workspace { template <class type, template <class> class trait> using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type; template <class Container> using element_type = typename std::decay<decltype( *std::begin(std::declval<Container&>()))>::type; template <class T, class = std::nullptr_t> struct has_begin : std::false_type {}; template <class T> struct has_begin<T, decltype(std::begin(std::declval<T>()), nullptr)> : std::true_type {}; template <class T, class = int> struct mapped_of { using type = element_type<T>; }; template <class T> struct mapped_of<T, typename std::pair<int, typename T::mapped_type>::first_type> { using type = typename T::mapped_type; }; template <class T> using mapped_type = typename mapped_of<T>::type; template <class T, class = void> struct is_integral_ext : std::false_type {}; template <class T> struct is_integral_ext< T, typename std::enable_if<std::is_integral<T>::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 T> constexpr static bool is_integral_ext_v = is_integral_ext<T>::value; #endif template <typename T, typename = void> struct multiplicable_uint { using type = uint_least32_t; }; template <typename T> struct multiplicable_uint< T, typename std::enable_if<(2 < sizeof(T)) && (!__INT128_DEFINED__ || sizeof(T) <= 4)>::type> { using type = uint_least64_t; }; #if __INT128_DEFINED__ template <typename T> struct multiplicable_uint<T, typename std::enable_if<(4 < sizeof(T))>::type> { using type = __uint128_t; }; #endif template <typename T> struct multiplicable_int { using type = typename std::make_signed<typename multiplicable_uint<T>::type>::type; }; } // namespace workspace #line 10 "Library/src/utils/hash.hpp" namespace workspace { template <class T, class = void> struct hash : std::hash<T> {}; #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 internal { 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<typename std::decay<decltype(e)>::type>(is, e); else static_assert(has_begin<Tp>::value, "istream unsupported type."); } }; template <class Tp> struct istream_helper< Tp, decltype(std::declval<std::decay<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<__int128_t, std::nullptr_t> { istream_helper(std::istream &is, __int128_t &x) { std::string s; is >> s; bool negative = s.front() == '-' ? s.erase(s.begin()), true : false; x = 0; for (char e : s) x = x * 10 + e - '0'; if (negative) x = -x; } }; template <> struct istream_helper<__uint128_t, std::nullptr_t> { istream_helper(std::istream &is, __uint128_t &x) { std::string s; is >> s; bool negative = s.front() == '-' ? s.erase(s.begin()), true : false; x = 0; for (char e : s) x = x * 10 + e - '0'; if (negative) x = -x; } }; #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 internal /** * @brief A wrapper class for std::istream. */ class istream : public std::istream { public: /** * @brief Wrapped operator. */ template <typename Tp> istream &operator>>(Tp &x) { internal::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; } }; namespace internal { auto *const cin_ptr = (istream *)&std::cin; } auto &cin = *internal::cin_ptr; } // namespace workspace #line 2 "Library/src/utils/io/ostream.hpp" /* * @file ostream.hpp * @brief Output Stream */ #line 10 "Library/src/utils/io/ostream.hpp" namespace workspace { template <class T, class U> std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) { return os << p.first << ' ' << p.second; } template <class tuple_t, size_t index> struct tuple_os { static std::ostream &apply(std::ostream &os, const tuple_t &t) { tuple_os<tuple_t, index - 1>::apply(os, t); return os << ' ' << std::get<index>(t); } }; template <class tuple_t> struct tuple_os<tuple_t, 0> { static std::ostream &apply(std::ostream &os, const tuple_t &t) { return os << std::get<0>(t); } }; template <class tuple_t> struct tuple_os<tuple_t, SIZE_MAX> { static std::ostream &apply(std::ostream &os, const tuple_t &t) { return os; } }; template <class... T> std::ostream &operator<<(std::ostream &os, const std::tuple<T...> &t) { return tuple_os<std::tuple<T...>, std::tuple_size<std::tuple<T...>>::value - 1>::apply(os, t); } template <class Container, typename = decltype(std::begin(std::declval<Container>()))> typename std::enable_if< !std::is_same<typename std::decay<Container>::type, std::string>::value && !std::is_same<typename std::decay<Container>::type, char *>::value, std::ostream &>::type operator<<(std::ostream &os, const Container &cont) { bool head = true; for (auto &&e : cont) head ? head = 0 : (os << ' ', 0), os << e; return os; } } // namespace workspace #line 9 "Library/lib/utils" // #include "src/utils/io/read.hpp" #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 { /* * @fn io_setup * @brief Setup I/O. * @param precision Standard output precision */ void io_setup(int precision) { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(precision); #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 2 "Library/src/utils/make_vector.hpp" /* * @file make_vector.hpp * @brief Multi-dimensional Vector */ #if __cplusplus >= 201703L #include <tuple> #include <vector> namespace workspace { /* * @brief Make a multi-dimensional vector. * @tparam Tp type of the elements * @tparam N dimension * @tparam S integer type * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, size_t N, typename S> constexpr auto make_vector([[maybe_unused]] S* sizes, Tp const& init = Tp()) { static_assert(std::is_convertible_v<S, size_t>); if constexpr (N) return std::vector(*sizes, make_vector<Tp, N - 1, S>(std::next(sizes), init)); else return init; } /* * @brief Make a multi-dimensional vector. * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, size_t N, typename S> constexpr auto make_vector(const S (&sizes)[N], Tp const& init = Tp()) { return make_vector<Tp, N, S>((S*)sizes, init); } /* * @brief Make a multi-dimensional vector. * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, size_t N, typename S, size_t I = 0> constexpr auto make_vector([[maybe_unused]] std::array<S, N> const& sizes, Tp const& init = Tp()) { static_assert(std::is_convertible_v<S, size_t>); if constexpr (I == N) return init; else return std::vector(sizes[I], make_vector<Tp, N, S, I + 1>(sizes, init)); } /* * @brief Make a multi-dimensional vector. * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, size_t N = SIZE_MAX, size_t I = 0, class... Args> constexpr auto make_vector([[maybe_unused]] std::tuple<Args...> const& sizes, Tp const& init = Tp()) { using tuple_type = std::tuple<Args...>; if constexpr (I == std::tuple_size_v<tuple_type> || I == N) return init; else { static_assert( std::is_convertible_v<std::tuple_element_t<I, tuple_type>, size_t>); return std::vector(std::get<I>(sizes), make_vector<Tp, N, I + 1>(sizes, init)); } } /* * @brief Make a multi-dimensional vector. * @param sizes The size of each dimension * @param init The initial value */ template <typename Tp, class Fst, class Snd> constexpr auto make_vector(std::pair<Fst, Snd> const& sizes, Tp const& init = Tp()) { static_assert(std::is_convertible_v<Fst, size_t>); static_assert(std::is_convertible_v<Snd, size_t>); return make_vector({(size_t)sizes.first, (size_t)sizes.second}, init); } } // namespace workspace #endif #line 14 "Library/lib/utils" // #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 internal { template <class Container> class reversed { Container cont; public: constexpr reversed(Container &&cont) : cont(cont) {} constexpr auto begin() { return std::rbegin(cont); } constexpr auto end() { return std::rend(cont); } }; } // namespace internal template <class Container> constexpr auto reversed(Container &&cont) noexcept { return internal::reversed<Container>{std::forward<Container>(cont)}; } template <class Tp> constexpr auto reversed(std::initializer_list<Tp> &&cont) noexcept { return internal::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::bidirectional_iterator_tag; constexpr iterator(Index const &__i = Index()) noexcept : current(__i) {} constexpr bool operator==(iterator const &rhs) const noexcept { return current == rhs.current; } constexpr bool operator!=(iterator const &rhs) const noexcept { return current != rhs.current; } constexpr iterator &operator++() noexcept { ++current; return *this; } constexpr iterator &operator--() noexcept { --current; return *this; } 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()); } }; template <class... Args> constexpr auto rrange(Args &&... args) noexcept { return internal::reversed(range(std::forward<Args>(args)...)); } } // namespace workspace #endif #line 17 "Library/lib/utils" // #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 random_number_generator : uniform_distribution<Arithmetic> { using base = uniform_distribution<Arithmetic>; std::mt19937 engine; public: template <class... Args> random_number_generator(Args&&... args) : base(args...), engine(std::random_device{}()) {} auto operator()() { 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> void shuffle(RAIter const& __first, RAIter const& __last) { static std::mt19937 engine(std::random_device{}()); std::shuffle(__first, __last, engine); } } // 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 11 "atcoder-workspace/177.cc" signed main() { using namespace workspace; io_setup(15); /* given case_info.read(); //*/ /* unspecified case_info.total = -1; //*/ return case_info.iterate(); } // #include "lib/modular" #line 2 "Library/src/number_theory/ext_gcd.hpp" /* * @file ext_gcd * @brief Extended Euclidean Algorithm */ #line 9 "Library/src/number_theory/ext_gcd.hpp" #line 11 "Library/src/number_theory/ext_gcd.hpp" namespace workspace { /** * @param a Integer * @param b Integer * @return Pair of integers (x, y) s.t. ax + by = g = gcd(a, b), |x| < |b/g|, * |y| < |a/g|. * @note return (0, 0) if (a, b) = (0, 0) */ template <typename T1, typename T2> constexpr auto ext_gcd(T1 a, T2 b) { static_assert(is_integral_ext<T1>::value); static_assert(is_integral_ext<T2>::value); using result_type = typename std::make_signed<typename std::common_type<T1, T2>::type>::type; result_type p{1}, q{}, r{}, s{1}, t; while (b) { r ^= p ^= r ^= p -= (t = a / b) * r; s ^= q ^= s ^= q -= t * s; b ^= a ^= b ^= a %= b; } if (a < 0) p = -p, q = -q; return std::make_pair(p, q); } } // namespace workspace #line 28 "atcoder-workspace/177.cc" // #include "src/data_structure/disjoint_sparse_table.hpp" namespace workspace { template <class Semigroup> class disjoint_sparse_table { using container_type = std::vector<std::vector<Semigroup>>; container_type __dst; public: using value_type = Semigroup; using size_type = typename container_type::size_type; using const_reference = typename container_type::const_reference; public: disjoint_sparse_table() = default; /** * @brief Construct in O(n log(n)) time. * * @param __args Create a vector from. */ template <class... Args> disjoint_sparse_table(Args... __args) { __dst.emplace_back(__args...); const size_type size = __dst.front().size(); for (size_type __w = 2; __w < size; __w <<= 1) { typename container_type::value_type __t; __t.reserve(size); for (size_type __i = __w; __i < size; __i += __w << 1) { __t.emplace_back(__dst.front()[__i - 1]); for (size_type __k = 2; __k <= __w; ++__k) __t.emplace_back(__dst.front()[__i - __k] + __t.back()); __t.emplace_back(__dst.front()[__i]); for (size_type __k = 1; __k < __w && __i + __k < size; ++__k) __t.emplace_back(__t.back() + __dst.front()[__i + __k]); } __dst.emplace_back(::std::move(__t)); } } /** * @return The number of elements. */ size_type size() const { return __dst.empty() ? 0 : __dst.front().size(); } bool empty() const { return !size(); } /** * @param __first Left end, inclusive. * @param __last Right end, exclusive. * @return The sum of given range. */ std::pair<value_type, value_type> fold(size_type __first, size_type __last) { assert(__first < __last); --__last; if (__first == __last) return {__dst.front()[__first], value_type{}}; size_type __b = 31 - __builtin_clz(__first ^ __last); return {__dst[__b][__first ^ ((1 << __b) - 1)], __dst[__b][__last]}; } const_reference operator[](size_type __i) const { return __dst.front()[__i]; } }; void main() { // start here! int n, q; static int p; auto sol = [&](int a, int b) -> int { auto [s, t] = ext_gcd(a, p); const auto g = a * s + p * t; if (b % g) return -1; if (s < 0) s += p / g; (s *= b / g) %= p; return s; }; cin >> n >> q >> p; vector<int> a(n); cin >> a; int pre[5000][5000]; for (auto i : range(p)) { for (auto j : range(p)) { pre[i][j] = sol(i, j); } } using bset = bitset<5000>; struct semig { bset _t; bool sing = false; int a; bool id = false; semig(int _v) { sing = true; _t.set(_v); a = _v; } semig() : id(true) {} semig operator+(semig r) const { if (!sing) return r + *this; r.sing = false; auto tmp = r._t; assert(sing); for (auto x : range(p)) { if (r._t[x]) { tmp[(x * a) % p] = 1; } } tmp[a] = 1; swap(tmp, r._t); return r; } }; disjoint_sparse_table<semig> dst(begin(a), end(a)); while (q--) { int l, r, k; cin >> l >> r >> k; --l; auto [f, s] = dst.fold(l, r); bool suc = 0; if (s.id) { suc = f._t[k]; } else { suc = f._t[k] || s._t[k]; for (auto x : range(p)) { if (auto y = pre[x][k]; ~y && f._t[x] && s._t[y]) suc = 1; } } cout << (suc ? "Yes" : "No") << "\n"; } return; } } // namespace workspace