結果
問題 | No.8046 yukicoderの過去問 |
ユーザー | 👑 p-adic |
提出日時 | 2023-09-10 18:24:22 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
RE
|
実行時間 | - |
コード長 | 43,716 bytes |
コンパイル時間 | 4,741 ms |
コンパイル使用メモリ | 316,392 KB |
実行使用メモリ | 6,944 KB |
最終ジャッジ日時 | 2024-06-28 09:35:58 |
合計ジャッジ時間 | 5,934 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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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
6,812 KB |
testcase_01 | AC | 2 ms
6,816 KB |
testcase_02 | AC | 2 ms
6,812 KB |
testcase_03 | AC | 3 ms
6,940 KB |
testcase_04 | AC | 2 ms
6,940 KB |
testcase_05 | AC | 3 ms
6,940 KB |
testcase_06 | AC | 28 ms
6,940 KB |
testcase_07 | RE | - |
testcase_08 | RE | - |
ソースコード
#ifdef DEBUG #define _GLIBCXX_DEBUG #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ); signal( SIGABRT , &AlertAbort ) #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE ) #define CERR( MESSAGE ) cerr << MESSAGE << endl; #define COUT( ANSWER ) cout << "出力: " << ANSWER << endl #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック: " << ( MIN ) << ( ( MIN ) <= A ? "<=" : ">" ) << A << ( A <= ( MAX ) ? "<=" : ">" ) << ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) ) #define AUTO_CHECK bool auto_checked = true; AutoCheck( auto_checked ); if( auto_checked ){ return 0; }; #define START_WATCH( PROCESS_NAME ) StartWatch( PROCESS_NAME ) #define STOP_WATCH( HOW_MANY_TIMES ) StopWatch( HOW_MANY_TIMES ) #else #pragma GCC optimize ( "O3" ) #pragma GCC optimize( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE ) #define CERR( MESSAGE ) #define COUT( ANSWER ) cout << ANSWER << "\n" #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #define AUTO_CHECK #define START_WATCH( PROCESS_NAME ) #define STOP_WATCH( HOW_MANY_TIMES ) #endif // #define RANDOM_TEST #include <bits/stdc++.h> using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; #define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) ) #define TYPE_OF( VAR ) decay_t<decltype( VAR )> #define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE #define CIN( LL , A ) LL A; cin >> A #define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define GETLINE( A ) string A; getline( cin , A ) #define GETLINE_SEPARATE( A , SEPARATOR ) string A; getline( cin , A , SEPARATOR ) #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR >= FINAL ; VAR -- ) #define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end() #define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS ) #define QUIT goto END_MAIN #define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = 1; if constexpr( bound_T > 1 ){ SET_ASSERT( T , 1 , bound_T ); } #define START_MAIN REPEAT( T ){ if constexpr( bound_T > 1 ){ CERR( "testcase " << VARIABLE_FOR_REPEAT_T << ":" ); } #define FINISH_MAIN QUIT; } END_MAIN: CERR( "" ); #ifdef DEBUG inline void AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); } void AutoCheck( bool& auto_checked ); void StartWatch( const string& process_name = "nothing" ); void StopWatch( const int& how_many_times = 1 ); #endif #if defined( DEBUG ) && defined( RANDOM_TEST ) ll GetRand( const ll& Rand_min , const ll& Rand_max ); #define SET_ASSERT( A , MIN , MAX ) CERR( #A << " = " << ( A = GetRand( MIN , MAX ) ) ) #define RETURN( ANSWER ) if( ( ANSWER ) == guchoku ){ CERR( ( ANSWER ) << " == " << guchoku ); goto END_MAIN; } else { CERR( ( ANSWER ) << " != " << guchoku ); QUIT; } #else #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX ) #define RETURN( ANSWER ) COUT( ( ANSWER ) ); QUIT #endif // 算術的関数 template <typename T> inline T Absolute( const T& a ){ return a > 0 ? a : -a; } template <typename T> inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); } inline ll MIN( const ll& a , const ll& b ){ return min( a , b ); } inline ull MIN( const ull& a , const ull& b ){ return min( a , b ); } inline ll MAX( const ll& a , const ll& b ){ return max( a , b ); } inline ull MAX( const ull& a , const ull& b ){ return max( a , b ); } #define POWER( ANSWER , ARGUMENT , EXPONENT ) \ static_assert( ! is_same<TYPE_OF( ARGUMENT ),int>::value && ! is_same<TYPE_OF( ARGUMENT ),uint>::value ); \ TYPE_OF( ARGUMENT ) ANSWER{ 1 }; \ { \ TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT ); \ TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){ \ if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){ \ ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER; \ } \ ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER; \ EXPONENT_FOR_SQUARE_FOR_POWER /= 2; \ } \ } \ #define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO ) \ ll ANSWER{ 1 }; \ { \ ll ARGUMENT_FOR_SQUARE_FOR_POWER = ( ( MODULO ) + ( ( ARGUMENT ) % ( MODULO ) ) ) % ( MODULO ); \ TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){ \ if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){ \ ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \ } \ ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \ EXPONENT_FOR_SQUARE_FOR_POWER /= 2; \ } \ } \ #define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_INDEX , CONSTEXPR_LENGTH , MODULO ) \ static ll ANSWER[CONSTEXPR_LENGTH]; \ static ll ANSWER_INV[CONSTEXPR_LENGTH]; \ static ll INVERSE[CONSTEXPR_LENGTH]; \ { \ ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL; \ FOREQ( i , 1 , MAX_INDEX ){ \ ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \ } \ ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ FOREQ( i , 2 , MAX_INDEX ){ \ ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \ } \ } \ // 二分探索テンプレート // EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= TARGETの整数解を格納。 #define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \ static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \ ll ANSWER = MINIMUM; \ if( MINIMUM <= MAXIMUM ){ \ ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM; \ ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM; \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH; \ while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \ VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \ CERR( "二分探索中: " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << "=" << VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ); \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH INEQUALITY_FOR_CHECK 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_U = UPDATE_U; \ } else { \ VARIABLE_FOR_BINARY_SEARCH_L = UPDATE_L; \ } \ ANSWER = UPDATE_ANSWER; \ } \ CERR( "二分探索終了: " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << ( EXPRESSION > TARGET ? ">" : EXPRESSION < TARGET ? "<" : "=" ) << TARGET ); \ CERR( ( EXPRESSION DESIRED_INEQUALITY TARGET ? "二分探索成功" : "二分探索失敗" ) ); \ assert( EXPRESSION DESIRED_INEQUALITY TARGET ); \ } else { \ CERR( "二分探索失敗: " << MINIMUM << ">" << MAXIMUM ); \ assert( MINIMUM <= MAXIMUM ); \ } \ // 単調増加の時にEXPRESSION >= TARGETの最小解を格納。 #define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , >= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調増加の時にEXPRESSION <= TARGETの最大解を格納。 #define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , > , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調減少の時にEXPRESSION >= TARGETの最大解を格納。 #define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , < , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調減少の時にEXPRESSION <= TARGETの最小解を格納。 #define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , <= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。 template <typename T> inline typename set<T>::iterator MaximumLeq( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.upper_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; } // t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。 template <typename T> inline typename set<T>::iterator MaximumLt( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.lower_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; } // t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。 template <typename T> inline typename set<T>::iterator MinimumGeq( set<T>& S , const T& t ) { return S.lower_bound( t ); } // tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。 template <typename T> inline typename set<T>::iterator MinimumGt( set<T>& S , const T& t ) { return S.upper_bound( t ); } // データ構造用関数 template <typename T> inline T add( const T& t0 , const T& t1 ) { return t0 + t1; } template <typename T> inline const T& zero() { static const T z = 0; return z; } template <typename T> inline T add_inv( const T& t ) { return -t; } template <typename T> inline T multiply( const T& t0 , const T& t1 ) { return t0 * t1; } template <typename T> inline const T& one() { static const T o = 1; return o; } template <typename T> inline T id( const T& v ) { return v; } // グリッド問題用関数 int H , W , H_minus , W_minus , HW; inline pair<int,int> EnumHW( const int& v ) { return { v / W , v % W }; } inline int EnumHW_inv( const int& h , const int& w ) { return h * W + w; } const string direction[4] = {"U","R","D","L"}; // (i,j)->(k,h)の方向番号を取得 inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return i<k?2:i>k?0:j<h?1:j>h?3:(assert(false),-1);} // v->wの方向番号を取得 inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);return DirectionNumberOnGrid(i,j,k,h);} // 方向番号の反転U<->D、R<->L inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;} // 圧縮用 #define TE template #define TY typename #define US using #define ST static #define IN inline #define CL class #define PU public #define OP operator #define CE constexpr #define CO const #define NE noexcept #define RE return #define WH while #define VO void #define VE vector #define LI list #define BE begin #define EN end #define SZ size #define MO move #define TH this #define CRI CO int& #define CRUI CO uint& #define CRL CO ll& // 大きな素数 // inline CEXPR( ll , P , 998244353 ); inline CEXPR( ll , P2 , 1000000007 ); // データ構造使用畤のNの上限 // inline CEXPR( int , bound_N , 10 ); inline DEXPR( int , bound_N , 100000 , 100 ); // 0が5個 // inline CEXPR( int , bound_N , 1000000000 ); // 0が9個 // inline CEXPR( ll , bound_N , 1000000000000000000 ); // 0が18個 // データ構造使用畤のMの上限 // inline CEXPR( TYPE_OF( bound_N ) , bound_M , bound_N ); // inline CEXPR( int , bound_M , 10 ); inline DEXPR( int , bound_M , 100000 , 100 ); // 0が5個 // inline CEXPR( int , bound_M , 1000000000 ); // 0が9個 // inline CEXPR( ll , bound_M , 1000000000000000000 ); // 0が18個 // データ構造や壁配列使用畤のH,Wの上限 inline DEXPR( int , bound_H , 1000 , 10 ); // inline DEXPR( int , bound_H , 100000 , 10 ); // 0が5個 // inline CEXPR( int , bound_H , 1000000000 ); // 0が9個 inline CEXPR( int , bound_W , bound_H ); static_assert( ll( bound_H ) * bound_W < ll( 1 ) << 31 ); inline CEXPR( int , bound_HW , bound_H * bound_W ); // CEXPR( int , bound_HW , 100000 ); // 0が5個 // CEXPR( int , bound_HW , 1000000 ); // 0が6個 inline void SetEdgeOnGrid( const string& Si , const int& i , list<int> ( &e )[bound_HW] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back(v);}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back(v);}if(j>0){e[EnumHW_inv(i,j-1)].push_back(v);}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back(v);}}}} inline void SetWallOnGrid( const string& Si , const int& i , bool ( &non_wall )[bound_H+1][bound_W+1] , const char& walkable = '.' ){bool(&non_wall_i)[bound_W+1]=non_wall[i];FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]=='#'),false);}} // using path_type = int; // // using path_type = pair<int,ll>; // list<path_type> e[bound_M]; // bound_Mのデフォルト値は10^5 // // list<path_type> e[bound_HW]; // bound_HWのデフォルト値は10^6 // list<path_type> E( const int& i ) // { // list<path_type> answer = e[i]; // // 入力によらない処理 // return answer; // } US ull = unsigned long long;IN CEXPR(uint,P,998244353);TE <uint M,TY INT> IN CE INT& RS(INT& n)NE{RE n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n %= M;}TE <uint M> IN CE uint& RS(uint& n)NE{RE n %= M;}TE <uint M> IN CE ull& RS(ull& n)NE{RE n %= M;}TE <TY INT> IN CE INT& RSP(INT& n)NE{CE CO uint trunc = (1 << 23)- 1;INT n_u = n >> 23;n &= trunc;INT n_uq = (n_u / 7)/ 17;n_u -= n_uq * 119;n += n_u << 23;RE n < n_uq?n += P - n_uq:n -= n_uq;}TE <> IN CE ull& RS<P,ull>(ull& n)NE{CE CO ull Pull = P;CE CO ull Pull2 = (Pull - 1)* (Pull - 1);RE RSP(n > Pull2?n -= Pull2:n);}TE <uint M,TY INT> IN CE INT RS(INT&& n)NE{RE MO(RS<M>(n));}TE <uint M,TY INT> IN CE INT RS(CO INT& n)NE{RE RS<M>(INT(n));} #define SFINAE_FOR_MOD(DEFAULT)TY T,enable_if_t<is_constructible<uint,decay_t<T> >::value>* DEFAULT #define DC_OF_CM_FOR_MOD(FUNC)IN bool OP FUNC(CO Mod<M>& n)CO NE #define DC_OF_AR_FOR_MOD(FUNC)IN Mod<M> OP FUNC(CO Mod<M>& n)CO NE;TE <SFINAE_FOR_MOD(= nullptr)> IN Mod<M> OP FUNC(T&& n)CO NE; #define DF_OF_CM_FOR_MOD(FUNC)TE <uint M> IN bool Mod<M>::OP FUNC(CO Mod<M>& n)CO NE{RE m_n FUNC n.m_n;} #define DF_OF_AR_FOR_MOD(FUNC,FORMULA)TE <uint M> IN Mod<M> Mod<M>::OP FUNC(CO Mod<M>& n)CO NE{RE MO(Mod<M>(*TH)FUNC ## = n);}TE <uint M> TE <SFINAE_FOR_MOD()> IN Mod<M> Mod<M>::OP FUNC(T&& n)CO NE{RE FORMULA;}TE <uint M,SFINAE_FOR_MOD(= nullptr)> IN Mod<M> OP FUNC(T&& n0,CO Mod<M>& n1)NE{RE MO(Mod<M>(forward<T>(n0))FUNC ## = n1);} TE <uint M>CL Mod{PU:uint m_n;IN CE Mod()NE;IN CE Mod(CO Mod<M>& n)NE;IN CE Mod(Mod<M>& n)NE;IN CE Mod(Mod<M>&& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> IN CE Mod(CO T& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> IN CE Mod(T& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> IN CE Mod(T&& n)NE;IN CE Mod<M>& OP=(CO Mod<M>& n)NE;IN CE Mod<M>& OP=(Mod<M>&& n)NE;IN CE Mod<M>& OP+=(CO Mod<M>& n)NE;IN CE Mod<M>& OP-=(CO Mod<M>& n)NE;IN CE Mod<M>& OP*=(CO Mod<M>& n)NE;IN Mod<M>& OP/=(CO Mod<M>& n);IN CE Mod<M>& OP<<=(int n)NE;IN CE Mod<M>& OP>>=(int n)NE;IN CE Mod<M>& OP++()NE;IN CE Mod<M> OP++(int)NE;IN CE Mod<M>& OP--()NE;IN CE Mod<M> OP--(int)NE;DC_OF_CM_FOR_MOD(==);DC_OF_CM_FOR_MOD(!=);DC_OF_CM_FOR_MOD(<);DC_OF_CM_FOR_MOD(<=);DC_OF_CM_FOR_MOD(>);DC_OF_CM_FOR_MOD(>=);DC_OF_AR_FOR_MOD(+);DC_OF_AR_FOR_MOD(-);DC_OF_AR_FOR_MOD(*);DC_OF_AR_FOR_MOD(/);IN CE Mod<M> OP<<(int n)CO NE;IN CE Mod<M> OP>>(int n)CO NE;IN CE Mod<M> OP-()CO NE;IN CE Mod<M>& SignInvert()NE;IN CE Mod<M>& Double()NE;IN CE Mod<M>& Halve()NE;IN Mod<M>& Invert();TE <TY T> IN CE Mod<M>& PositivePW(T&& EX)NE;TE <TY T> IN CE Mod<M>& NonNegativePW(T&& EX)NE;TE <TY T> IN CE Mod<M>& PW(T&& EX);IN CE VO swap(Mod<M>& n)NE;IN CE CO uint& RP()CO NE;ST IN CE Mod<M> DeRP(CO uint& n)NE;ST IN CE uint& Normalise(uint& n)NE;ST IN CO Mod<M>& Inverse(CO uint& n)NE;ST IN CO Mod<M>& Factorial(CO uint& n)NE;ST IN CO Mod<M>& FactorialInverse(CO uint& n)NE;ST IN CO Mod<M>& zero()NE;ST IN CO Mod<M>& one()NE;TE <TY T> IN CE Mod<M>& Ref(T&& n)NE;}; #define SFINAE_FOR_MN(DEFAULT)TY T,enable_if_t<is_constructible<Mod<M>,decay_t<T> >::value>* DEFAULT #define DC_OF_AR_FOR_MN(FUNC)IN MN<M> OP FUNC(CO MN<M>& n)CO NE;TE <SFINAE_FOR_MOD(= nullptr)> IN MN<M> OP FUNC(T&& n)CO NE; #define DF_OF_CM_FOR_MN(FUNC)TE <uint M> IN bool MN<M>::OP FUNC(CO MN<M>& n)CO NE{RE m_n FUNC n.m_n;} #define DF_OF_AR_FOR_MN(FUNC,FORMULA)TE <uint M> IN MN<M> MN<M>::OP FUNC(CO MN<M>& n)CO NE{RE MO(MN<M>(*TH)FUNC ## = n);}TE <uint M> TE <SFINAE_FOR_MOD()> IN MN<M> MN<M>::OP FUNC(T&& n)CO NE{RE FORMULA;}TE <uint M,SFINAE_FOR_MOD(= nullptr)> IN MN<M> OP FUNC(T&& n0,CO MN<M>& n1)NE{RE MO(MN<M>(forward<T>(n0))FUNC ## = n1);} TE <uint M>CL MN :PU Mod<M>{PU:IN CE MN()NE;IN CE MN(CO MN<M>& n)NE;IN CE MN(MN<M>& n)NE;IN CE MN(MN<M>&& n)NE;TE <SFINAE_FOR_MN(= nullptr)> IN CE MN(CO T& n)NE;TE <SFINAE_FOR_MN(= nullptr)> IN CE MN(T&& n)NE;IN CE MN<M>& OP=(CO MN<M>& n)NE;IN CE MN<M>& OP=(MN<M>&& n)NE;IN CE MN<M>& OP+=(CO MN<M>& n)NE;IN CE MN<M>& OP-=(CO MN<M>& n)NE;IN CE MN<M>& OP*=(CO MN<M>& n)NE;IN MN<M>& OP/=(CO MN<M>& n);IN CE MN<M>& OP<<=(int n)NE;IN CE MN<M>& OP>>=(int n)NE;IN CE MN<M>& OP++()NE;IN CE MN<M> OP++(int)NE;IN CE MN<M>& OP--()NE;IN CE MN<M> OP--(int)NE;DC_OF_AR_FOR_MN(+);DC_OF_AR_FOR_MN(-);DC_OF_AR_FOR_MN(*);DC_OF_AR_FOR_MN(/);IN CE MN<M> OP<<(int n)CO NE;IN CE MN<M> OP>>(int n)CO NE;IN CE MN<M> OP-()CO NE;IN CE MN<M>& SignInvert()NE;IN CE MN<M>& Double()NE;IN CE MN<M>& Halve()NE;IN CE MN<M>& Invert();TE <TY T> IN CE MN<M>& PositivePW(T&& EX)NE;TE <TY T> IN CE MN<M>& NonNegativePW(T&& EX)NE;TE <TY T> IN CE MN<M>& PW(T&& EX);IN CE uint RP()CO NE;IN CE Mod<M> Reduce()CO NE;ST IN CE MN<M> DeRP(CO uint& n)NE;ST IN CO MN<M>& Formise(CO uint& n)NE;ST IN CO MN<M>& Inverse(CO uint& n)NE;ST IN CO MN<M>& Factorial(CO uint& n)NE;ST IN CO MN<M>& FactorialInverse(CO uint& n)NE;ST IN CO MN<M>& zero()NE;ST IN CO MN<M>& one()NE;ST IN CE uint Form(CO uint& n)NE;ST IN CE ull& Reduction(ull& n)NE;ST IN CE ull& ReducedMU(ull& n,CO uint& m)NE;ST IN CE uint MU(CO uint& n0,CO uint& n1)NE;ST IN CE uint BaseSquareTruncation(uint& n)NE;TE <TY T> IN CE MN<M>& Ref(T&& n)NE;};TE <uint M> IN CE MN<M> Twice(CO MN<M>& n)NE;TE <uint M> IN CE MN<M> Half(CO MN<M>& n)NE;TE <uint M> IN CE MN<M> Inverse(CO MN<M>& n);TE <uint M,TY T> IN CE MN<M> PW(CO MN<M>& n,CO T& EX);TE <TY T> IN CE MN<2> PW(CO MN<2>& n,CO T& p);TE <TY T> IN CE T Square(CO T& t);TE <> IN CE MN<2> Square<MN<2> >(CO MN<2>& t);TE <uint M> IN CE VO swap(MN<M>& n0,MN<M>& n1)NE;TE <uint M> IN string to_string(CO MN<M>& n)NE;TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO MN<M>& n); TE <uint M>CL COantsForMod{PU:COantsForMod()= delete;ST CE CO bool g_even = ((M & 1)== 0);ST CE CO uint g_memory_bound = 1000000;ST CE CO uint g_memory_LE = M < g_memory_bound?M:g_memory_bound;ST IN CE ull MNBasePW(ull&& EX)NE;ST CE uint g_M_minus = M - 1;ST CE uint g_M_minus_2 = M - 2;ST CE uint g_M_minus_2_neg = 2 - M;ST CE CO int g_MN_digit = 32;ST CE CO ull g_MN_base = ull(1)<< g_MN_digit;ST CE CO uint g_MN_base_minus = uint(g_MN_base - 1);ST CE CO uint g_MN_digit_half = (g_MN_digit + 1)>> 1;ST CE CO uint g_MN_base_sqrt_minus = (1 << g_MN_digit_half)- 1;ST CE CO uint g_MN_M_neg_inverse = uint((g_MN_base - MNBasePW((ull(1)<< (g_MN_digit - 1))- 1))& g_MN_base_minus);ST CE CO uint g_MN_base_mod = uint(g_MN_base % M);ST CE CO uint g_MN_base_square_mod = uint(((g_MN_base % M)* (g_MN_base % M))% M);};TE <uint M> IN CE ull COantsForMod<M>::MNBasePW(ull&& EX)NE{ull prod = 1;ull PW = M;WH(EX != 0){(EX & 1)== 1?(prod *= PW)&= g_MN_base_minus:prod;EX >>= 1;(PW *= PW)&= g_MN_base_minus;}RE prod;} #include <immintrin.h> #define SET_VE_32_128_FOR_SIMD(UINT,VE_NAME,SCALAR0,SCALAR1,SCALAR2,SCALAR3)CE CO UINT VE_NAME ## _copy[4] ={SCALAR0,SCALAR1,SCALAR2,SCALAR3};ST CO __m128i v_ ## VE_NAME = _mm_load_si128((__m128i*)VE_NAME ##_copy) #define SET_VE_64_128_FOR_SIMD(UINT,VE_NAME,SCALAR0,SCALAR1)CE CO UINT VE_NAME ## _copy[2] ={SCALAR0,SCALAR1};ST CO __m128i v_ ## VE_NAME = _mm_load_si128((__m128i*)VE_NAME ##_copy) #define SET_VE_64_256_FOR_SIMD(ULL,VE_NAME,SCALAR0,SCALAR1,SCALAR2,SCALAR3)CE CO ULL VE_NAME ## _copy[4] ={SCALAR0,SCALAR1,SCALAR2,SCALAR3};ST CO __m256i v_ ## VE_NAME = _mm256_load_si256((__m256i*)VE_NAME ##_copy) #define SET_CO_VE_32_128_FOR_SIMD(UINT,VE_NAME,SCALAR)SET_VE_32_128_FOR_SIMD(UINT,VE_NAME,SCALAR,SCALAR,SCALAR,SCALAR) #define SET_CO_VE_64_128_FOR_SIMD(ULL,VE_NAME,SCALAR)SET_VE_64_128_FOR_SIMD(ULL,VE_NAME,SCALAR,SCALAR) #define SET_CO_VE_64_256_FOR_SIMD(ULL,VE_NAME,SCALAR)SET_VE_64_256_FOR_SIMD(ULL,VE_NAME,SCALAR,SCALAR,SCALAR,SCALAR) TE <uint M>CL COantsForSIMDForMod{PU:COantsForSIMDForMod()= delete;ST IN CO __m128i& v_M()NE;ST IN CO __m128i& v_Mull()NE;ST IN CO __m128i& v_M_minus()NE;ST IN CO __m128i& v_M_neg_inverse()NE;ST IN CO __m128i& v_digitull()NE;};TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M,M);RE v_M;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_Mull()NE{SET_CO_VE_64_128_FOR_SIMD(ull,Mull,M);RE v_Mull;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M_minus()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M_minus,M - 1);RE v_M_minus;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M_neg_inverse()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M_neg_inverse,COantsForMod<M>::g_MN_M_neg_inverse);RE v_M_neg_inverse;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_digitull()NE{SET_CO_VE_64_128_FOR_SIMD(ull,digitull,COantsForMod<M>::g_MN_digit);RE v_digitull;}TE <uint M> IN __m128i& SIMD_RS_32_128(__m128i& v)NE{CO __m128i& v_M = COantsForSIMDForMod<M>::v_M();RE v -= v_M * _mm_cmpgt_epi32(v,v_M);}TE <uint M> IN __m128i& SIMD_RS_64_128(__m128i& v)NE{ull v_copy[2];_mm_store_si128((__m128i*)v_copy,v);for(uint i = 0;i < 2;i++){ull& v_copy_i = v_copy[i];v_copy_i = (v_copy_i < M?0:M);}RE v -= _mm_load_si128((__m128i*)v_copy);}TE <uint M> IN __m256i& SIMD_RS_64_256(__m256i& v)NE{ull v_copy[4];_mm256_store_si256((__m256i*)v_copy,v);for(uint i = 0;i < 4;i++){ull& v_copy_i = v_copy[i];v_copy_i = (v_copy_i < M?0:M);}RE v -= _mm256_load_si256((__m256i*)v_copy);}IN CE int SIMD_Shuffle(CRI a0,CRI a1,CRI a2,CRI a3)NE{RE (a0 << (0 << 1))+ (a1 << (1 << 1))+ (a2 << (2 << 1))+ (a3 << (3 << 1));}TE <uint M> IN VO SIMD_Addition_32_64(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& b0,CO Mod<M>& b1,Mod<M>& c0,Mod<M>& c1)NE{uint a_copy[4] ={a0.m_n,a1.m_n,0,0};uint b_copy[4] ={b0.m_n,b1.m_n,0,0};__m128i v_a = _mm_load_si128((__m128i*)a_copy);v_a += _mm_load_si128((__m128i*)b_copy);ST CO __m128i& v_M_minus = COantsForSIMDForMod<M>::v_M_minus();ST CO __m128i& v_M = COantsForSIMDForMod<M>::v_M();v_a += _mm_cmpgt_epi32(v_a,v_M_minus)& v_M;_mm_store_si128((__m128i*)a_copy,v_a);c0.m_n = MO(a_copy[0]);c1.m_n = MO(a_copy[1]);RE;}TE <uint M> IN VO SIMD_Addition_32_128(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& a2,CO Mod<M>& a3,CO Mod<M>& b0,CO Mod<M>& b1,CO Mod<M>& b2,CO Mod<M>& b3,Mod<M>& c0,Mod<M>& c1,Mod<M>& c2,Mod<M>& c3)NE{uint a_copy[4] ={a0.m_n,a1.m_n,a2.m_n,a3.m_n};uint b_copy[4] ={b0.m_n,b1.m_n,b2.m_n,b3.m_n};__m128i v_a = _mm_load_si128((__m128i*)a_copy)+ _mm_load_si128((__m128i*)b_copy);_mm_store_si128((__m128i*)a_copy,v_a);for(uint i = 0;i < 4;i++){b_copy[i] = a_copy[i] < M?0:M;}v_a -= _mm_load_si128((__m128i*)b_copy);_mm_store_si128((__m128i*)a_copy,v_a);c0.m_n = MO(a_copy[0]);c1.m_n = MO(a_copy[1]);c2.m_n = MO(a_copy[2]);c3.m_n = MO(a_copy[3]);RE;}TE <uint M> IN VO SIMD_Substracition_32_64(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& b0,CO Mod<M>& b1,Mod<M>& c0,Mod<M>& c1)NE{uint a_copy[4] ={a0.m_n,a1.m_n,0,0};uint b_copy[4] ={b0.m_n,b1.m_n,0,0};__m128i v_a = _mm_load_si128((__m128i*)a_copy);__m128i v_b = _mm_load_si128((__m128i*)b_copy);_mm_store_si128((__m128i*)a_copy,v_a);for(uint i = 0;i < 2;i++){b_copy[i] = a_copy[i] < b_copy[i]?M:0;}(v_a += _mm_load_si128((__m128i*)b_copy))-= v_b;_mm_store_si128((__m128i*)a_copy,v_a);c0.m_n = MO(a_copy[0]);c1.m_n = MO(a_copy[1]);RE;}TE <uint M> IN VO SIMD_Subtraction_32_128(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& a2,CO Mod<M>& a3,CO Mod<M>& b0,CO Mod<M>& b1,CO Mod<M>& b2,CO Mod<M>& b3,Mod<M>& c0,Mod<M>& c1,Mod<M>& c2,Mod<M>& c3)NE{uint a_copy[4] ={a0.m_n,a1.m_n,a2.m_n,a3.m_n};uint b_copy[4] ={b0.m_n,b1.m_n,b2.m_n,b3.m_n};__m128i v_a = _mm_load_si128((__m128i*)a_copy);__m128i v_b = _mm_load_si128((__m128i*)b_copy);_mm_store_si128((__m128i*)a_copy,v_a);for(uint i = 0;i < 4;i++){b_copy[i] = a_copy[i] < b_copy[i]?M:0;}(v_a += _mm_load_si128((__m128i*)b_copy))-= v_b;_mm_store_si128((__m128i*)a_copy,v_a);c0.m_n = MO(a_copy[0]);c1.m_n = MO(a_copy[1]);c2.m_n = MO(a_copy[2]);c3.m_n = MO(a_copy[3]);RE;} US MP = Mod<P>;US MNP = MN<P>;TE <uint M> IN CE uint MN<M>::Form(CO uint& n)NE{ull n_copy = n;RE uint(MO(Reduction(n_copy *= COantsForMod<M>::g_MN_base_square_mod)));}TE <uint M> IN CE ull& MN<M>::Reduction(ull& n)NE{ull n_sub = n & COantsForMod<M>::g_MN_base_minus;RE ((n += ((n_sub *= COantsForMod<M>::g_MN_M_neg_inverse)&= COantsForMod<M>::g_MN_base_minus)*= M)>>= COantsForMod<M>::g_MN_digit)< M?n:n -= M;}TE <uint M> IN CE ull& MN<M>::ReducedMU(ull& n,CO uint& m)NE{RE Reduction(n *= m);}TE <uint M> IN CE uint MN<M>::MU(CO uint& n0,CO uint& n1)NE{ull n0_copy = n0;RE uint(MO(ReducedMU(ReducedMU(n0_copy,n1),COantsForMod<M>::g_MN_base_square_mod)));}TE <uint M> IN CE uint MN<M>::BaseSquareTruncation(uint& n)NE{CO uint n_u = n >> COantsForMod<M>::g_MN_digit_half;n &= COantsForMod<M>::g_MN_base_sqrt_minus;RE n_u;}TE <uint M> IN CE MN<M>::MN()NE:Mod<M>(){static_assert(! COantsForMod<M>::g_even);}TE <uint M> IN CE MN<M>::MN(CO MN<M>& n)NE:Mod<M>(n){}TE <uint M> IN CE MN<M>::MN(MN<M>& n)NE:Mod<M>(n){}TE <uint M> IN CE MN<M>::MN(MN<M>&& n)NE:Mod<M>(MO(n)){}TE <uint M> TE <SFINAE_FOR_MN()> IN CE MN<M>::MN(CO T& n)NE:Mod<M>(n){static_assert(! COantsForMod<M>::g_even);Mod<M>::m_n = Form(Mod<M>::m_n);}TE <uint M> TE <SFINAE_FOR_MN()> IN CE MN<M>::MN(T&& n)NE:Mod<M>(forward<T>(n)){static_assert(! COantsForMod<M>::g_even);Mod<M>::m_n = Form(Mod<M>::m_n);}TE <uint M> IN CE MN<M>& MN<M>::OP=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP=(MN<M>&& n)NE{RE Ref(Mod<M>::OP=(MO(n)));}TE <uint M> IN CE MN<M>& MN<M>::OP+=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP+=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP-=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP-=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP*=(CO MN<M>& n)NE{ull m_n_copy = Mod<M>::m_n;RE Ref(Mod<M>::m_n = MO(ReducedMU(m_n_copy,n.m_n)));}TE <uint M> IN MN<M>& MN<M>::OP/=(CO MN<M>& n){RE OP*=(MN<M>(n).Invert());}TE <uint M> IN CE MN<M>& MN<M>::OP<<=(int n)NE{RE Ref(Mod<M>::OP<<=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP>>=(int n)NE{RE Ref(Mod<M>::OP>>=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP++()NE{RE Ref(Mod<M>::Normalise(Mod<M>::m_n += COantsForMod<M>::g_MN_base_mod));}TE <uint M> IN CE MN<M> MN<M>::OP++(int)NE{MN<M> n{*TH};OP++();RE n;}TE <uint M> IN CE MN<M>& MN<M>::OP--()NE{RE Ref(Mod<M>::m_n < COantsForMod<M>::g_MN_base_mod?((Mod<M>::m_n += M)-= COantsForMod<M>::g_MN_base_mod):Mod<M>::m_n -= COantsForMod<M>::g_MN_base_mod);}TE <uint M> IN CE MN<M> MN<M>::OP--(int)NE{MN<M> n{*TH};OP--();RE n;}DF_OF_AR_FOR_MN(+,MN<M>(forward<T>(n))+= *TH);DF_OF_AR_FOR_MN(-,MN<M>(forward<T>(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MN(*,MN<M>(forward<T>(n))*= *TH);DF_OF_AR_FOR_MN(/,MN<M>(forward<T>(n)).Invert()*= *TH);TE <uint M> IN CE MN<M> MN<M>::OP<<(int n)CO NE{RE MO(MN<M>(*TH)<<= n);}TE <uint M> IN CE MN<M> MN<M>::OP>>(int n)CO NE{RE MO(MN<M>(*TH)>>= n);}TE <uint M> IN CE MN<M> MN<M>::OP-()CO NE{RE MO(MN<M>(*TH).SignInvert());}TE <uint M> IN CE MN<M>& MN<M>::SignInvert()NE{RE Ref(Mod<M>::m_n > 0?Mod<M>::m_n = M - Mod<M>::m_n:Mod<M>::m_n);}TE <uint M> IN CE MN<M>& MN<M>::Double()NE{RE Ref(Mod<M>::Double());}TE <uint M> IN CE MN<M>& MN<M>::Halve()NE{RE Ref(Mod<M>::Halve());}TE <uint M> IN CE MN<M>& MN<M>::Invert(){assert(Mod<M>::m_n > 0);RE PositivePW(uint(COantsForMod<M>::g_M_minus_2));}TE <uint M> TE <TY T> IN CE MN<M>& MN<M>::PositivePW(T&& EX)NE{MN<M> PW{*TH};(--EX)%= COantsForMod<M>::g_M_minus_2;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <uint M> TE <TY T> IN CE MN<M>& MN<M>::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(Mod<M>::m_n = 1):PositivePW(forward<T>(EX));}TE <uint M> TE <TY T> IN CE MN<M>& MN<M>::PW(T&& EX){bool neg = EX < 0;assert(!(neg && Mod<M>::m_n == 0));RE neg?PositivePW(forward<T>(EX *= COantsForMod<M>::g_M_minus_2_neg)):NonNegativePW(forward<T>(EX));}TE <uint M> IN CE uint MN<M>::RP()CO NE{ull m_n_copy = Mod<M>::m_n;RE MO(Reduction(m_n_copy));}TE <uint M> IN CE Mod<M> MN<M>::Reduce()CO NE{ull m_n_copy = Mod<M>::m_n;RE Mod<M>::DeRP(MO(Reduction(m_n_copy)));}TE <uint M> IN CE MN<M> MN<M>::DeRP(CO uint& n)NE{RE MN<M>(Mod<M>::DeRP(n));}TE <uint M> IN CO MN<M>& MN<M>::Formise(CO uint& n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = DeRP(LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::Inverse(CO uint& n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>(Mod<M>::Inverse(LE_curr));LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::Factorial(CO uint& n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN<M> val_curr{one()};MN<M> val_last{one()};WH(LE_curr <= n){memory[LE_curr++] = val_curr *= ++val_last;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::FactorialInverse(CO uint& n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN<M> val_curr{one()};MN<M> val_last{one()};WH(LE_curr <= n){memory[LE_curr] = val_curr *= Inverse(LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::zero()NE{ST CE CO MN<M> z{};RE z;}TE <uint M> IN CO MN<M>& MN<M>::one()NE{ST CE CO MN<M> o{DeRP(1)};RE o;}TE <uint M> TE <TY T> IN CE MN<M>& MN<M>::Ref(T&& n)NE{RE *TH;}TE <uint M> IN CE MN<M> Twice(CO MN<M>& n)NE{RE MO(MN<M>(n).Double());}TE <uint M> IN CE MN<M> Half(CO MN<M>& n)NE{RE MO(MN<M>(n).Halve());}TE <uint M> IN CE MN<M> Inverse(CO MN<M>& n){RE MO(MN<M>(n).Invert());}TE <uint M,TY T> IN CE MN<M> PW(CO MN<M>& n,CO T& EX){RE MO(MN<M>(n).PW(T(EX)));}TE <uint M> IN CE VO swap(MN<M>& n0,MN<M>& n1)NE{n0.swap(n1);}TE <uint M> IN string to_string(CO MN<M>& n)NE{RE to_string(n.RP())+ " + MZ";}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO MN<M>& n){RE os << n.RP();} TE <uint M> IN CE Mod<M>::Mod()NE:m_n(){}TE <uint M> IN CE Mod<M>::Mod(CO Mod<M>& n)NE:m_n(n.m_n){}TE <uint M> IN CE Mod<M>::Mod(Mod<M>& n)NE:m_n(n.m_n){}TE <uint M> IN CE Mod<M>::Mod(Mod<M>&& n)NE:m_n(MO(n.m_n)){}TE <uint M> TE <SFINAE_FOR_MOD()> IN CE Mod<M>::Mod(CO T& n)NE:m_n(RS<M>(n)){}TE <uint M> TE <SFINAE_FOR_MOD()> IN CE Mod<M>::Mod(T& n)NE:m_n(RS<M>(decay_t<T>(n))){}TE <uint M> TE <SFINAE_FOR_MOD()> IN CE Mod<M>::Mod(T&& n)NE:m_n(RS<M>(forward<T>(n))){}TE <uint M> IN CE Mod<M>& Mod<M>::OP=(CO Mod<M>& n)NE{RE Ref(m_n = n.m_n);}TE <uint M> IN CE Mod<M>& Mod<M>::OP=(Mod<M>&& n)NE{RE Ref(m_n = MO(n.m_n));}TE <uint M> IN CE Mod<M>& Mod<M>::OP+=(CO Mod<M>& n)NE{RE Ref(Normalise(m_n += n.m_n));}TE <uint M> IN CE Mod<M>& Mod<M>::OP-=(CO Mod<M>& n)NE{RE Ref(m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n);}TE <uint M> IN CE Mod<M>& Mod<M>::OP*=(CO Mod<M>& n)NE{RE Ref(m_n = COantsForMod<M>::g_even?RS<M>(ull(m_n)* n.m_n):MN<M>::MU(m_n,n.m_n));}TE <> IN CE MP& MP::OP*=(CO MP& n)NE{ull m_n_copy = m_n;RE Ref(m_n = MO((m_n_copy *= n.m_n)< P?m_n_copy:RSP(m_n_copy)));}TE <uint M> IN Mod<M>& Mod<M>::OP/=(CO Mod<M>& n){RE OP*=(Mod<M>(n).Invert());}TE <uint M> IN CE Mod<M>& Mod<M>::OP<<=(int n)NE{WH(n-- > 0){Normalise(m_n <<= 1);}RE *TH;}TE <uint M> IN CE Mod<M>& Mod<M>::OP>>=(int n)NE{WH(n-- > 0){((m_n & 1)== 0?m_n:m_n += M)>>= 1;}RE *TH;}TE <uint M> IN CE Mod<M>& Mod<M>::OP++()NE{RE Ref(m_n < COantsForMod<M>::g_M_minus?++m_n:m_n = 0);}TE <uint M> IN CE Mod<M> Mod<M>::OP++(int)NE{Mod<M> n{*TH};OP++();RE n;}TE <uint M> IN CE Mod<M>& Mod<M>::OP--()NE{RE Ref(m_n == 0?m_n = COantsForMod<M>::g_M_minus:--m_n);}TE <uint M> IN CE Mod<M> Mod<M>::OP--(int)NE{Mod<M> n{*TH};OP--();RE n;}DF_OF_CM_FOR_MOD(==);DF_OF_CM_FOR_MOD(!=);DF_OF_CM_FOR_MOD(>);DF_OF_CM_FOR_MOD(>=);DF_OF_CM_FOR_MOD(<);DF_OF_CM_FOR_MOD(<=);DF_OF_AR_FOR_MOD(+,Mod<M>(forward<T>(n))+= *TH);DF_OF_AR_FOR_MOD(-,Mod<M>(forward<T>(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MOD(*,Mod<M>(forward<T>(n))*= *TH);DF_OF_AR_FOR_MOD(/,Mod<M>(forward<T>(n)).Invert()*= *TH);TE <uint M> IN CE Mod<M> Mod<M>::OP<<(int n)CO NE{RE MO(Mod<M>(*TH)<<= n);}TE <uint M> IN CE Mod<M> Mod<M>::OP>>(int n)CO NE{RE MO(Mod<M>(*TH)>>= n);}TE <uint M> IN CE Mod<M> Mod<M>::OP-()CO NE{RE MO(Mod<M>(*TH).SignInvert());}TE <uint M> IN CE Mod<M>& Mod<M>::SignInvert()NE{RE Ref(m_n > 0?m_n = M - m_n:m_n);}TE <uint M> IN CE Mod<M>& Mod<M>::Double()NE{RE Ref(Normalise(m_n <<= 1));}TE <uint M> IN CE Mod<M>& Mod<M>::Halve()NE{RE Ref(((m_n & 1)== 0?m_n:m_n += M)>>= 1);}TE <uint M> IN Mod<M>& Mod<M>::Invert(){assert(m_n > 0);uint m_n_neg;RE m_n < COantsForMod<M>::g_memory_LE?Ref(m_n = Inverse(m_n).m_n):(m_n_neg = M - m_n < COantsForMod<M>::g_memory_LE)?Ref(m_n = M - Inverse(m_n_neg).m_n):PositivePW(uint(COantsForMod<M>::g_M_minus_2));}TE <> IN Mod<2>& Mod<2>::Invert(){assert(m_n > 0);RE *TH;}TE <uint M> TE <TY T> IN CE Mod<M>& Mod<M>::PositivePW(T&& EX)NE{Mod<M> PW{*TH};EX--;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <> TE <TY T> IN CE Mod<2>& Mod<2>::PositivePW(T&& EX)NE{RE *TH;}TE <uint M> TE <TY T> IN CE Mod<M>& Mod<M>::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(m_n = 1):Ref(PositivePW(forward<T>(EX)));}TE <uint M> TE <TY T> IN CE Mod<M>& Mod<M>::PW(T&& EX){bool neg = EX < 0;assert(!(neg && m_n == 0));neg?EX *= COantsForMod<M>::g_M_minus_2_neg:EX;RE m_n == 0?*TH:(EX %= COantsForMod<M>::g_M_minus)== 0?Ref(m_n = 1):PositivePW(forward<T>(EX));}TE <uint M> IN CO Mod<M>& Mod<M>::Inverse(CO uint& n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr].m_n = M - MN<M>::MU(memory[M % LE_curr].m_n,M / LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::Factorial(CO uint& n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>::Factorial(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::FactorialInverse(CO uint& n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>::FactorialInverse(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE <uint M> IN CE VO Mod<M>::swap(Mod<M>& n)NE{std::swap(m_n,n.m_n);}TE <uint M> IN CE CO uint& Mod<M>::RP()CO NE{RE m_n;}TE <uint M> IN CE Mod<M> Mod<M>::DeRP(CO uint& n)NE{Mod<M> n_copy{};n_copy.m_n = n;RE n_copy;}TE <uint M> IN CE uint& Mod<M>::Normalise(uint& n)NE{RE n < M?n:n -= M;}TE <uint M> IN CO Mod<M>& Mod<M>::zero()NE{ST CE CO Mod<M> z{};RE z;}TE <uint M> IN CO Mod<M>& Mod<M>::one()NE{ST CE CO Mod<M> o{DeRP(1)};RE o;}TE <uint M> TE <TY T> IN CE Mod<M>& Mod<M>::Ref(T&& n)NE{RE *TH;}TE <uint M> IN CE Mod<M> Twice(CO Mod<M>& n)NE{RE MO(Mod<M>(n).Double());}TE <uint M> IN CE Mod<M> Half(CO Mod<M>& n)NE{RE MO(Mod<M>(n).Halve());}TE <uint M> IN Mod<M> Inverse(CO Mod<M>& n){RE MO(Mod<M>(n).Invert());}TE <uint M> IN CE Mod<M> Inverse_COrexpr(CO uint& n)NE{RE MO(Mod<M>::DeRP(RS<M>(n)).NonNegativePW(M - 2));}TE <uint M,TY T> IN CE Mod<M> PW(CO Mod<M>& n,CO T& EX){RE MO(Mod<M>(n).PW(T(EX)));}TE <uint M> IN CE VO swap(Mod<M>& n0,Mod<M>& n1)NE{n0.swap(n1);}TE <uint M> IN string to_string(CO Mod<M>& n)NE{RE to_string(n.RP())+ " + MZ";}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO Mod<M>& n){RE os << n.RP();} TE<int N>CL PWInverse_CE{PU:int m_val;CE PWInverse_CE();}; TE<int N>CE PWInverse_CE<N>::PWInverse_CE():m_val(1){WH(m_val < N){m_val <<= 1;}} TE <TY T,int N>CL BIT{PU:T m_fenwick[N + 1];IN BIT();BIT(CO T(& a)[N]);IN T Get(CRI i)CO;IN VO Set(CRI i,CO T& n);IN VO Set(CO T(& a)[N]);IN BIT<T,N>& OP+=(CO T(& a)[N]);VO Add(CRI i,CO T& n);T InitialSegmentSum(CRI i_final)CO;IN T IntervalSum(CRI i_start,CRI i_final)CO;int BinarySearch(CO T& n)CO;IN int BinarySearch(CRI i_start,CO T& n)CO;}; TE <TY T,int N> IN BIT<T,N>::BIT():m_fenwick(){static_assert(! is_same<T,int>::value);}TE <TY T,int N>BIT<T,N>::BIT(CO T(& a)[N]):m_fenwick(){static_assert(! is_same<T,int>::value);for(int j = 1;j <= N;j++){T& fenwick_j = m_fenwick[j];int i = j - 1;fenwick_j = a[i];int i_lim = j -(j & -j);WH(i != i_lim){fenwick_j += m_fenwick[i];i -=(i & -i);}}}TE <TY T,int N> IN T BIT<T,N>::Get(CRI i)CO{RE IntervalSum(i,i);}TE <TY T,int N> IN VO BIT<T,N>::Set(CRI i,CO T& n){Add(i,n - IntervalSum(i,i));}TE <TY T,int N> IN VO BIT<T,N>::Set(CO T(& a)[N]){BIT<T,N> a_copy{a};swap(m_fenwick,a_copy.m_fenwick);}TE <TY T,int N> IN BIT<T,N>& BIT<T,N>::OP+=(CO T(& a)[N]){for(int i = 0;i < N;i++){Add(i,a[i]);}RE *TH;}TE <TY T,int N>VO BIT<T,N>::Add(CRI i,CO T& n){int j = i + 1;WH(j <= N){m_fenwick[j] += n;j +=(j & -j);}RE;}TE <TY T,int N>T BIT<T,N>::InitialSegmentSum(CRI i_final)CO{T sum = 0;int j =(i_final < N?i_final:N - 1)+ 1;WH(j > 0){sum += m_fenwick[j];j -= j & -j;}RE sum;}TE <TY T,int N> IN T BIT<T,N>::IntervalSum(CRI i_start,CRI i_final)CO{RE InitialSegmentSum(i_final)- InitialSegmentSum(i_start - 1);}TE <TY T,int N>int BIT<T,N>::BinarySearch(CO T& n)CO{int j = 0;int PW = PWInverse_CE<N>().m_val;T sum{};T sum_next{};WH(PW > 0){int j_next = j | PW;if(j_next < N){sum_next += m_fenwick[j_next];if(sum_next < n){sum = sum_next;j = j_next;}else{sum_next = sum;}}PW >>= 1;}RE j;}TE <TY T,int N> IN int BIT<T,N>::BinarySearch(CRI i_start,CO T& n)CO{RE max(i_start,BinarySearch(InitialSegmentSum(i_start)+ n));} TE <TY T,int N>CL IntervalAddBIT{PU:BIT<T,N> m_bit_0;BIT<T,N> m_bit_1;IN IntervalAddBIT();IN IntervalAddBIT(CO T(&a)[N]);IN T Get(CRI i)CO;IN VO Set(CRI i,CO T& n);IN VO Set(CO T(&a)[N]);IN IntervalAddBIT<T,N>& OP+=(CO T(& a)[N]);IN VO Add(CRI i,CO T& n);IN VO IntervalAdd(CRI i_start,CRI i_final,CO T& n);IN T InitialSegmentSum(CRI i_final)CO;IN T IntervalSum(CRI i_start,CRI i_final)CO;}; TE <TY T,int N> IN IntervalAddBIT<T,N>::IntervalAddBIT():m_bit_0(),m_bit_1(){}TE <TY T,int N> IN IntervalAddBIT<T,N>::IntervalAddBIT(CO T(&a)[N]):m_bit_0(),m_bit_1(){OP+=(a);}TE <TY T,int N> IN T IntervalAddBIT<T,N>::Get(CRI i)CO{RE IntervalSum(i,i);}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Set(CRI i,CO T& n){Add(i,n - IntervalSum(i,i));}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Set(CO T(&a)[N]){IntervalAddBIT<T,N> a_copy{a};swap(m_bit_0,a_copy.m_bit_0);swap(m_bit_1,a_copy.m_bit_1);}TE <TY T,int N> IN IntervalAddBIT<T,N>& IntervalAddBIT<T,N>::OP+=(CO T(& a)[N]){for(int i = 0;i < N;i++){Add(i,a[i]);}RE *TH;}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Add(CRI i,CO T& n){IntervalAdd(i,i,n);}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::IntervalAdd(CRI i_start,CRI i_final,CO T& n){m_bit_0.Add(i_start,-(i_start - 1)* n);m_bit_0.Add(i_final + 1,i_final * n);m_bit_1.Add(i_start,n);m_bit_1.Add(i_final + 1,- n);}TE <TY T,int N> IN T IntervalAddBIT<T,N>::InitialSegmentSum(CRI i_final)CO{RE m_bit_0.InitialSegmentSum(i_final)+ i_final * m_bit_1.InitialSegmentSum(i_final);}TE <TY T,int N> IN T IntervalAddBIT<T,N>::IntervalSum(CRI i_start,CRI i_final)CO{RE InitialSegmentSum(i_final)- InitialSegmentSum(i_start - 1);} int main() { UNTIE; AUTO_CHECK; TEST_CASE_NUM( 1 ); START_MAIN; CIN( ll , K ); CIN( ll , N ); // // CIN_ASSERT( N , 1 , bound_N ); // 基本不要、上限のデフォルト値は10^5 // // CIN_ASSERT( M , 1 , bound_M ); // 基本不要、上限のデフォルト値は10^5 int x[N]; FOR( i , 0 , N ){ cin >> x[i]; } if( N < 1000 ){ ll dp[K+1]{}; dp[0] = 1; FOR( k , 0 , K ){ FOR( i , 0 , N ){ if( k + x[i] <= K ){ if( ( dp[k+x[i]] += dp[k] ) >= P2 ){ dp[k+x[i]] -= P2; } } } } RETURN( dp[K] ); } assert( x[0] + N - 1 == x[N-1] ); IntervalAddBIT<Mod<P2>,100001> bit{}; bit.Set( 0 , 1 ); FOR( i , 0 , K ){ bit.IntervalAdd( i + x[0] , i + x[N-1] , bit.Get( i ) ); } RETURN( bit.Get( K ) ); // CIN( string , S ); // CIN( string , T ); // cin >> H >> W; // // SET_ASSERT( H , 1 , bound_H ); // 基本不要、上限のデフォルト値は10^3 // // SET_ASSERT( W , 1 , bound_W ); // 基本不要、上限のデフォルト値は10^3 // H_minus = H - 1; // W_minus = W - 1; // HW = H * W; // // assert( HW <= bound_HW ); // 基本不要、上限のデフォルト値は10^6 // string S[H]; // // bool non_wall[bound_H+1][bound_W+1]={}; // FOR( i , 0 , H ){ // cin >> S[i]; // // SetEdgeOnGrid( S[i] , i , e ); // eの宣言のコメントアウト必要 // // SetWallOnGrid( S[i] , i , non_wall ); // } // // (i,j)->(k,h)の方向番号を取得: DirectionNumberOnGrid( i , j , k , h ); // // v->wの方向番号を取得: DirectionNumberOnGrid( v , w ); // // 方向番号の反転U<->D、R<->L: ReverseDirectionNumberOnGrid( n ); // ll A[N]; // // ll B[N]; // // ll A[bound_N]; // 基本不要、長さのデフォルト値は10^5 // // ll B[bound_N]; // 基本不要、長さのデフォルト値は10^5 // FOR( i , 0 , N ){ // cin >> A[i]; // // cin >> B[i]; // } // FOR( i , 0 , M ){ // CIN_ASSERT( ui , 1 , N ); // CIN_ASSERT( vi , 1 , N ); // ui--; // vi--; // e[ui].push_back( vi ); // e[vi].push_back( ui ); // } // CIN( int , Q ); // // DEXPR( int , bound_Q , 100000 , 100 ); // 基本不要 // // CIN_ASSERT( Q , 1 , bound_Q ); // 基本不要 // tuple<int,int,int> query[Q]; // FOR( q , 0 , Q ){ // CIN( int , type ); // if( type == 1 ){ // CIN( int , x ); // CIN( int , y ); // // query[q] = { type , x , y }; // } else if( type == 2 ){ // CIN( int , x ); // CIN( int , y ); // // query[q] = { type , x , y }; // } else { // CIN( int , x ); // CIN( int , y ); // // query[q] = { type , x , y }; // } // } // // ll guchoku = Guchoku(); // ll answer = 0; // FOR( i , 0 , N ){ // answer += A[i]; // } // // COUT( ( answer ) ); // RETURN( answer ); FINISH_MAIN; }