#ifndef INCLUDE_MODE #define INCLUDE_MODE // #define REACTIVE // #define USE_GETLINE /* #define SUBMIT_ONLY */ #define DEBUG_OUTPUT #define SAMPLE_CHECK G #endif #ifdef INCLUDE_MAIN VO Solve() { CIN( int , N , M , K ); RETURN( Answer( N , M , K ) ); } REPEAT_MAIN(1); #else /* INCLUDE_MAIN */ #ifdef INCLUDE_SUB /* COMPAREに使用。圧縮時は削除する。*/ MP Naive( int N , int M , int K , const bool& debug_output = true ) { MP answer{}; vector lbound( N , 1 ) , ubound( N , M ) , index = lbound; while( true ){ MexSet S{ N + K }; FOR( i , 0 , N ){ S.insert( index[i] ); } MP temp{ 1 }; FOREQ( k , 1 , K ){ S.insert( k - 1 ); temp *= S.mex(); } answer += temp; if( !NextLoopEq( lbound , ubound , index ) ){ break; } } return answer; } /* COMPAREに使用。圧縮時は削除する。*/ MP Answer( ll N , ll M , ll K , const bool& debug_output = true ) { vector dp1( N + 1 , vector( M + 1 ) ); vector dp2( N + 1 , vector( M + 1 , vector( M + 1 ) ) ); FOREQ( r , 1 , M ){ dp1[1][r] = 1; FOREQ( k , 1 , K ){ dp1[1][r] *= k == r ? r + 1 : k; } dp2[1][r][r] = dp1[1][r]; } if( debug_output ){ CERR( 1 , ":" , dp1[1] ); } FOR( n , 1 , N ){ FOR( r , n , M ){ FOREQ( l , r + 2 , M ){ dp2[n+1][l][l] += dp1[n][r] * ( ( MP{ l + 1 } / l ) ^ ( l <= K ? 1 : 0 ) ); } } FOREQ( r , n + 1 , M ){ dp1[n+1][r] = dp2[n+1][r][r]; } FOR( l , 1 , M ){ FOR( r , max( l , n ) , min( l + n , M ) ){ dp1[n+1][r+1] += dp2[n+1][l][r+1] = dp2[n][l][r] * ( ( MP{ r + 2 } / ( r + 1 ) ) ^ max( 0LL , min( K , r + 1 ) - l + 1 ) ); } } if( debug_output ){ CERR( n + 1 , ":" , dp1[n+1] ); } } static SecondStirlingNumberCalculator sn{}; MP answer{}; FOREQ( n , 1 , N ){ FOREQ( r , 1 , M ){ answer += dp1[n][r] * sn.CountSurjectiveMap( N , n ); } } return answer; } /* 圧縮時は中身だけ削除する。*/ IN VO Experiment() { /* // 1変数 ../Contest/Template/Experiment/OneVariable.txt */ /* // 2変数 ../Contest/Template/Experiment/TwoVariable.txt */ /* // 3変数 ../Contest/Template/Experiment/ThreeVariable.txt */ CEXPR( int , bound , 10 ); int N_min = 1 , N_max = bound; vector>> naive3( N_max - N_min + 1 ); FOREQ( N , N_min , N_max ){ int M_min = 1 , M_max = bound; naive3[N-N_min].resize( M_max - M_min + 1 ); FOREQ( M , M_min , M_max ){ int K_min = 1 , K_max = bound; naive3[N-N_min][M-M_min].resize( K_max - K_min + 1 ); FOREQ( K , K_min , K_max ){ naive3[N-N_min][M-M_min][K-K_min] = Naive( N , M , K , false ); } CERRNS( "(N,M)=(",N,",",M,"),K∈[",K_min,"--",K_max,"]: " , naive3[N-N_min][M-M_min] , "\n" ); } } CERRNS( "Inline: " ); FOREQ( N , N_min , N_max ){ CERRNS( naive3[N-N_min] , " \n"[N==N_max] ); } } /* 圧縮時は中身だけ削除する。*/ IN VO SmallTest() { /* // 数 ../Contest/Template/SmallTest/Number.txt */ /* // 配列 ../Contest/Template/SmallTest/Array.txt */ /* // 順列 ../Contest/Template/SmallTest/Permutation.txt */ /* // 文字列 ../Contest/Template/SmallTest/String.txt */ /* // グリッド ../Contest/Template/SmallTest/Grid.txt */ /* // グラフ ../Contest/Template/SmallTest/Graph.txt */ /* // 重み付きグラフ ../Contest/Template/SmallTest/WeightedGraph.txt */ /* // 区間クエリ ../Contest/Template/SmallTest/IntervalQuery.txt */ CEXPR( int , bound , 10 ); int N_min = 1 , N_max = bound; FOREQ( N , N_min , N_max ){ int M_min = 1 , M_max = bound; FOREQ( M , M_min , M_max ){ int K_min = 1 , K_max = bound; FOREQ( K , K_min , K_max ){ COMPARE( N , M , K ); } } } } /* 圧縮時は中身だけ削除する。*/ IN VO RandomTest( const int& test_case_num ) { /* // 数 ../Contest/Template/SmallTest/Number.txt */ /* // 配列 ../Contest/Template/SmallTest/Array.txt */ /* // 順列 ../Contest/Template/SmallTest/Permutation.txt */ /* // 文字列 ../Contest/Template/SmallTest/String.txt */ /* // グリッド ../Contest/Template/SmallTest/Grid.txt */ /* // グラフ ../Contest/Template/SmallTest/Graph.txt */ /* // 重み付きグラフ ../Contest/Template/SmallTest/WeightedGraph.txt */ /* // 区間クエリ ../Contest/Template/SmallTest/IntervalQuery.txt */ /* // 多種クエリ ../Contest/Template/SmallTest/MultiTypeQuery.txt */ REPEAT( test_case_num ){ } } #define INCLUDE_MAIN #include __FILE__ #else /* INCLUDE_SUB */ #ifdef INCLUDE_LIBRARY /* VVV 常設でないライブラリは以下に挿入する。*/ /* // BFS ../Contest/Template/Library/BFS.txt */ /* // BIT ../Contest/Template/Library/BIT.txt */ /* // CoordinateCompress ../Contest/Template/Library/CoordinateCompress.txt */ /* // DFS ../Contest/Template/Library/DFS.txt */ /* // DifferenceSequence ../Contest/Template/Library/DifferenceSequence.txt */ /* // Dijkstra ../Contest/Template/Library/Dijkstra.txt */ /* // Divisor ../Contest/Template/Library/Divisor.txt */ /* // Knapsack ../Contest/Template/Library/Knapsack.txt */ /* // Matrix ../Contest/Template/Library/Matrix.txt */ /* // Set ../Contest/Template/Library/Set.txt */ /* // Polynomial ../Contest/Template/Library/Polynomial.txt */ /* // SqrtDecomposition ../Contest/Template/Library/SqrtDecomposition.txt */ /* // UnionFind ../Contest/Template/Library/UnionFind.txt */ #ifdef DEBUG #include "c:/Users/user/Documents/Programming/Mathematics/SetTheory/Mex/Debug/a_Body.hpp" #else CL MexSet{PU:int m_QuerySZ;VE m_in;int m_mex;IN MexSet(CRI QuerySZ);IN VO insert(CRI i);IN CRI mex()CO NE;}; IN MexSet::MexSet(CRI QuerySZ):m_QuerySZ(QuerySZ),m_in(m_QuerySZ + 1),m_mex(0){}IN VO MexSet::insert(CRI i){AS(i >= 0);if(i < m_QuerySZ){m_in[i]= true;WH(m_in[m_mex]){m_mex++;}}}IN CRI MexSet::mex()CO NE{RE m_mex;} #endif #ifdef DEBUG #include "c:/Users/user/Documents/Programming/Mathematics/Combinatorial/StirlingNumber/SecondKind/a_Body.hpp" #else TE CL SecondStirlingNumberCalculator{PU:T m_val[le][le];CE SecondStirlingNumberCalculator();CE CO T(&OP[](CRI i)CO)[le];CE T CountDisjointCover(CRI N,CRI i)CO;CE T CountDisjointSubset(CRI N,CRI i)CO;IN T CountDisjointCoverSequence(CRI N,CRI i)CO;IN T CountDisjointSubsetSequence(CRI N,CRI i)CO;IN T CountDisjointCover(CRI N,CRI n,CRI i)CO;IN T CountDisjointCoverSequence(CRI N,CRI n,CRI i)CO;IN T CountSurjectiveMap(CRI N,CRI i)CO;}; TE CE SecondStirlingNumberCalculator::SecondStirlingNumberCalculator():m_val(){m_val[0][0]= 1;for(int i = 1;i < le;i++){auto& m_val_i = m_val[i];CO auto& m_val_i_minus = m_val[i - 1];for(int j = 1;j < i;j++){((m_val_i[j]= m_val_i_minus[j])*= j)+= m_val_i_minus[j - 1];}m_val_i[i]= 1;}}TE CE CO T(&SecondStirlingNumberCalculator::OP[](CRI i)CO)[le]{AS(i < le);RE m_val[i];}TE CE T SecondStirlingNumberCalculator::CountDisjointCover(CRI N,CRI i)CO{AS(N < le);RE i <= N?m_val[N][i]:T();}TE CE T SecondStirlingNumberCalculator::CountDisjointSubset(CRI N,CRI i)CO{AS(N < le);RE i < N?m_val[N][i]+ m_val[N][i+1]:i == N?m_val[N][i]:T();}TE IN T SecondStirlingNumberCalculator::CountDisjointCoverSequence(CRI N,CRI i)CO{RE CountDisjointCover(N,i)* T::Factorial(i);}TE IN T SecondStirlingNumberCalculator::CountDisjointSubsetSequence(CRI N,CRI i)CO{RE CountDisjointSubset(N,i)* T::Factorial(i);}TE IN T SecondStirlingNumberCalculator::CountDisjointCover(CRI N,CRI n,CRI i)CO{RE CountDisjointCover(n,i)* T::Combination(N,n);}TE IN T SecondStirlingNumberCalculator::CountDisjointCoverSequence(CRI N,CRI n,CRI i)CO{RE CountDisjointCoverSequence(n,i)* T::Combination(N,n);}TE IN T SecondStirlingNumberCalculator::CountSurjectiveMap(CRI N,CRI i)CO{AS(N < le);RE i <= N?m_val[N][i]* T::Factorial(i):T();} #endif /* AAA 常設でないライブラリは以上に挿入する。*/ #define INCLUDE_SUB #include __FILE__ #else /* INCLUDE_LIBRARY */ #ifdef DEBUG #define _GLIBCXX_DEBUG #else #pragma GCC optimize ( "O3" ) #pragma GCC optimize ( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if CE( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN #define FINISH_MAIN REPEAT( test_case_num ){ if CE( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } } #define DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE1 ) #define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) ) #ifdef USE_GETLINE #define SET_SEPARATE( SEPARATOR , ... ) VariadicGetline( cin , SEPARATOR , __VA_ARGS__ ) #define SET( ... ) SET_SEPARATE( '\n' , __VA_ARGS__ ) #define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; SET_SEPARATE( SEPARATOR , __VA_ARGS__ ) #define GETLINE( ... ) GETLINE_SEPARATE( '\n' , __VA_ARGS__ ) #else #define SET( ... ) VariadicCin( cin , __VA_ARGS__ ) #define CIN( LL , ... ) LL __VA_ARGS__; SET( __VA_ARGS__ ) #define SET_A( I , N , ... ) VariadicResize( N + I , __VA_ARGS__ ); FOR( VARIABLE_FOR_SET_A , 0 , N ){ VariadicSet( cin , VARIABLE_FOR_SET_A + I , __VA_ARGS__ ); } #define CIN_A( LL , I , N , ... ) VE __VA_ARGS__; SET_A( I , N , __VA_ARGS__ ) #define CIN_AA( LL , I0 , N0 , I1 , N1 , VAR ) VE> VAR( N0 + I0 ); FOR( VARIABLE_FOR_CIN_AA , 0 , N0 ){ SET_A( I1 , N1 , VAR[VARIABLE_FOR_CIN_AA + I0] ); } #endif #define SET_ASSERT( A , MIN , MAX ) SET( A ); ASSERT( A , MIN , MAX ) #define SOLVE_ONLY #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL #define COUTNS( ... ) VariadicCoutNonSep( cout , __VA_ARGS__ ) #define CERR( ... ) #define CERRNS( ... ) #define COUT_A( I , N , A ) CoutArray( cout , I , N , A ) << ENDL #define CERR_A( I , N , A ) #endif #ifdef REACTIVE #ifdef DEBUG #define RSET( A , ... ) A = __VA_ARGS__ #else #define RSET( A , ... ) SET( A ) #endif #define RCIN( LL , A , ... ) LL A; RSET( A , __VA_ARGS__ ) #define ENDL endl #else #define ENDL "\n" #endif #include using namespace std; #define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) ) #define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now(); double loop_average_time = 0.0 , loop_start_time = 0.0 , current_time = 0.0; int loop_count = 0 #define CURRENT_TIME ( current_time = static_cast( chrono::duration_cast( chrono::system_clock::now() - watch ).count() / 1000.0 ) ) #define CHECK_WATCH( TL_MS ) ( CURRENT_TIME , loop_count == 0 ? loop_start_time = current_time : loop_average_time = ( current_time - loop_start_time ) / loop_count , ++loop_count , current_time < TL_MS - loop_average_time * 2 - 100.0 ) #define CEXPR( LL , BOUND , VALUE ) CE LL BOUND = VALUE #define SET_A_ASSERT( I , N , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A + I] , MIN , MAX ); } #define SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_AA0 , 0 , N0 ){ FOR( VARIABLE_FOR_SET_AA1 , 0 , N1 ){ SET_ASSERT( A[VARIABLE_FOR_SET_AA0 + I0][VARIABLE_FOR_SET_AA1 + I1] , MIN , MAX ); } } #define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define CIN_A_ASSERT( I , N , A , MIN , MAX ) vector A( N + I ); SET_A_ASSERT( I , N , A , MIN , MAX ) #define CIN_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) vector A( N0 + I0 , vector( N1 + I1 ) ); SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) #define OUTPUT_ARRAY( C , I , N , A ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , I , N ){ C << A[VARIABLE_FOR_OUTPUT_ARRAY] << " \n"[VARIABLE_FOR_OUTPUT_ARRAY==(N)-1]; } #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( decldecay_t( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define FOREQ( VAR , INITIAL , FINAL ) for( decldecay_t( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define FOREQINV( VAR , INITIAL , FINAL ) for( decldecay_t( INITIAL ) VAR = INITIAL ; VAR + 1 > FINAL ; VAR -- ) #define ITR( ARRAY ) auto begin_ ## ARRAY = ARRAY .BE() , itr_ ## ARRAY = begin_ ## ARRAY , end_ ## ARRAY = ARRAY .EN() #define FOR_ITR( ARRAY ) for( ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ ) #define RUN( ARRAY , ... ) for( auto&& __VA_ARGS__ : ARRAY ) #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 ); cerr << fixed << setprecision( DECIMAL_DIGITS ) #define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); RE #define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ , false ); auto answer = Answer( __VA_ARGS__ , false ); bool match = naive == answer; CERR( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ RE; } /* 圧縮用 */ #define TE template #define TY typename #define US using #define ST static #define AS assert #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 LE length #define PW Power #define MO move #define TH this #define CRI CO int& #define CRUI CO uint& #define CRL CO ll& #define VI virtual #define IS basic_istream #define OS basic_ostream #define ST_AS static_assert #define reMO_CO remove_const #define is_COructible_v is_constructible_v #define rBE rbegin /* 型のエイリアス */ #define decldecay_t(VAR)decay_t TE US ret_t = decltype(declval()(declval()...)); TE US inner_t = TY T::type; US uint = unsigned int; US ll = long long; US ull = unsigned long long; US ld = long double; US lld = __float128; TE US T2 = pair; TE US T3 = tuple; TE US T4 = tuple; US path = pair; /* VVV 常設ライブラリは以下に挿入する。*/ #ifdef DEBUG #include "C:/Users/user/Documents/Programming/Contest/Template/Local/a_Body.hpp" #else /* BinarySearch (2KB)*/ /* EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CONST_TARGETの整数解を格納。*/ #define BS(AN,MINIMUM,MAXIMUM,EXPRESSION,DESIRED_INEQUALITY,CO_TARGET,INEQUALITY_FOR_CHECK,UPDATE_U,UPDATE_L,UPDATE_AN)ST_AS(! is_same::value && ! is_same::value);ll AN = MINIMUM;{ll AN ## _L = MINIMUM;ll AN ## _R = MAXIMUM;AN = UPDATE_AN;ll EXPRESSION_BS;CO ll CO_TARGET_BS =(CO_TARGET);ll DIFFERENCE_BS;WH(AN ## _L < AN ## _R){DIFFERENCE_BS =(EXPRESSION_BS =(EXPRESSION))- CO_TARGET_BS;if(DIFFERENCE_BS INEQUALITY_FOR_CHECK 0){AN ## _R = UPDATE_U;}else{AN ## _L = UPDATE_L;}AN = UPDATE_AN;}if(AN ## _L > AN ## _R || !((EXPRESSION)DESIRED_INEQUALITY CO_TARGET_BS)){AN = MAXIMUM + 1;}} /* 単調増加の時にEXPRESSION >= CONST_TARGETの最小解を格納。*/ #define BS1(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,>=,CO_TARGET,>=,AN,AN + 1,(AN ## _L + AN ## _R)/ 2) /* 単調増加の時にEXPRESSION <= CONST_TARGETの最大解を格納。*/ #define BS2(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,<=,CO_TARGET,>,AN - 1,AN,(AN ## _L + 1 + AN ## _R)/ 2) /* 単調減少の時にEXPRESSION >= CONST_TARGETの最大解を格納。*/ #define BS3(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,>=,CO_TARGET,<,AN - 1,AN,(AN ## _L + 1 + AN ## _R)/ 2) /* 単調減少の時にEXPRESSION <= CONST_TARGETの最小解を格納。*/ #define BS4(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,<=,CO_TARGET,<=,AN,AN + 1,(AN ## _L + AN ## _R)/ 2) /* TwoPoitnterApproach (2KB)*/ /* VAR_TPAは尺取り法用の変数名の接頭辞で、実際の変数名ではなく、_Lと_Rと_infoがつく。 ANSWER ## _temp = {VAR_TPA ## _L,VAR_TPA ## _R,VPA_TPA ## _info}を {INIT,INIT,INFO_init}で初期化する。VPA_TPA ## _infoは区間和など。 ANSWER ## _tempがCONTINUE_CONDITIONを満たす限り、ANSWER ## _tempが条件ON_CONDITIONを満たすか否かを判定し、それがtrueになるか VAR_TAR ## _LがVAR_TAR ## _Rに追い付くまでVAR_TPA ## _LとVPA_TPA ## _infoの更新操作UPDATE_Lを繰り返し、その後VAR_TPA ## _RとVPA_TPA ## _infoの更新操作UPDATE_Rを行う。（マクロとコンマの制約上、関数オブジェクトを用いる） ON_CONDITIONがtrueとなる極大閉区間とその時点でのinfoをANSWERに格納する。例えば長さNの非負整数値配列Aで極大な正値区間とそこでの総和を取得したい場合 auto update_L = [&]( int& i_L , auto& i_info ){ i_info -= A[i_L++]; }; auto update_R = [&]( int& i_R , auto& i_info ){ if( ++i_R < N ){ i_info += A[i_R]; } }; TPA( interval , i , 0 , i_R < N , update_L( i_L , i_info ) , update_R( i_R , i_info ) , A[i_L] > 0 && A[i_R] > 0 , ll( A[0] ) ); とすればtuple値配列intervalに{左端,右端,総和}の列が格納される。 VAR_TPA ## _infoもintervalにコピーされるので、setやvectorなどのコピーのコストが大きいデータを用いてon,off判定する時はTPAより前に宣言して使う。*/ #define TPA(AN,VAR_TPA,INIT,CONTINUE_CONDITION,UPDATE_L,UPDATE_R,ON_CONDITION,INFO_init)VE> AN{};{auto init_TPA = INIT;decldecay_t(AN.front())AN ## _temp ={init_TPA,init_TPA,INFO_init};auto AN ## _prev = AN ## _temp;auto& VAR_TPA ## _L = get<0>(AN ## _temp);auto& VAR_TPA ## _R = get<1>(AN ## _temp);auto& VAR_TPA ## _info = get<2>(AN ## _temp);bool on_TPA_prev = false;WH(true){bool continuing = CONTINUE_CONDITION;bool on_TPA = continuing &&(ON_CONDITION);if(on_TPA_prev && ! on_TPA){AN.push_back(AN ## _prev);}if(continuing){if(on_TPA || VAR_TPA ## _L == VAR_TPA ## _R){AN ## _prev = AN ## _temp;UPDATE_R;}else{UPDATE_L;}}else{break;}on_TPA_prev = on_TPA;}} /* Random (1KB)*/ ll GetRand(CRI Rand_min,CRI Rand_max){AS(Rand_min <= Rand_max);ll AN = time(NULL);RE AN * rand()%(Rand_max + 1 - Rand_min)+ Rand_min;} /* Set (1KB)*/ #define DC_OF_HASH(...)struct hash<__VA_ARGS__>{IN size_t OP()(CO __VA_ARGS__& n)CO;}; CL is_ordered{PU:is_ordered()= delete;TE ST CE auto Check(CO T& t)-> decltype(t < t,true_type());ST CE false_type Check(...);TE ST CE CO bool value = is_same_v< decltype(Check(declval())),true_type >;}; TE US Set = conditional_t>,unordered_set,conditional_t,set,VO>>; /* Tuple (5KB)*/ #define DF_OF_AR_FOR_TUPLE(OPR)TE TY V> IN auto OP OPR ## =(V& t0,CO V& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);RE t0;}TE IN tuple& OP OPR ## =(tuple& t0,CO tuple& t1){get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);RE t0;}TE IN tuple& OP OPR ## =(tuple& t0,CO tuple& t1){get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);get<3>(t0)OPR ## = get<3>(t1);RE t0;}TE TY V> IN auto OP OPR ## =(V& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;RE t0;}TE IN tuple& OP OPR ## =(tuple& t0,CO ARG& t1){get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;RE t0;}TE IN tuple& OP OPR ## =(tuple& t0,CO ARG& t1){get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;get<3>(t0)OPR ## = t1;RE t0;}TE TY V,TY...ARGS,TY ARG> IN auto OP OPR(CO V& t0,CO ARG& t1)-> decldecay_t((get<0>(t0),t0)){auto t = t0;RE MO(t OPR ## = t1);} #define DF_OF_INCREMENT_FOR_TUPLE(INCR)TE TY V> IN auto OP INCR(V& t)-> decltype((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);RE t;}TE IN tuple& OP INCR(tuple& t){INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);RE t;}TE IN tuple& OP INCR(tuple& t){INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);INCR get<3>(t);RE t;} TE IN IS& OP>>(IS& is,tuple& arg){RE is >> get<0>(arg);}TE TY V> IN auto OP>>(IS& is,V& arg)-> decltype((get<0>(arg),is))&{RE is >> get<0>(arg)>> get<1>(arg);}TE IN IS& OP>>(IS& is,tuple& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg);}TE IN IS& OP>>(IS& is,tuple& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg)>> get<3>(arg);}TE IN OS& OP<<(OS& os,CO tuple& arg){RE os << get<0>(arg);}TE TY V> IN auto OP<<(OS& os,CO V& arg)-> decltype((get<0>(arg),os))&{RE os << get<0>(arg)<< " " << get<1>(arg);}TE IN OS& OP<<(OS& os,CO tuple& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg);}TE IN OS& OP<<(OS& os,CO tuple& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg)<< " " << get<3>(arg);}DF_OF_AR_FOR_TUPLE(+);TE TY V> IN auto OP-(CO V& t)-> decltype(get<0>(t),t){RE{-get<0>(t),-get<1>(t)};}TE IN tuple OP-(CO tuple& t){RE{-get<0>(t),-get<1>(t),-get<2>(t)};}TE IN tuple OP-(CO tuple& t){RE{-get<0>(t),-get<1>(t),-get<2>(t),-get<3>(t)};}DF_OF_AR_FOR_TUPLE(-);DF_OF_AR_FOR_TUPLE(*);DF_OF_AR_FOR_TUPLE(/);DF_OF_AR_FOR_TUPLE(%);DF_OF_INCREMENT_FOR_TUPLE(++);DF_OF_INCREMENT_FOR_TUPLE(--); #define DF_OF_HASH_FOR_TUPLE(PAIR)TE IN size_t hash>::OP()(CO PAIR& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash h0;ST CO hash h1;RE(h0(get<0>(n))* seed)^ h1(get<1>(n));} TE DC_OF_HASH(tuple);TE DC_OF_HASH(pair);TE DC_OF_HASH(tuple);TE DC_OF_HASH(tuple);TE DC_OF_HASH(tuple); TE IN size_t hash>::OP()(CO tuple& n)CO{ST CO hash h;RE h(get<0>(n));}DF_OF_HASH_FOR_TUPLE(pair);DF_OF_HASH_FOR_TUPLE(tuple);TE IN size_t hash>::OP()(CO tuple& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash> h01;ST CO hash h2;RE(h01({get<0>(n),get<1>(n)})* seed)^ h2(get<2>(n));}TE IN size_t hash>::OP()(CO tuple& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash> h01;ST CO hash> h23;RE(h01({get<0>(n),get<1>(n)})* seed)^ h23({get<2>(n),get<3>(n)});} /* Vector (2KB)*/ #define DF_OF_COUT_FOR_VE(V)TE IN OS& OP<<(OS& os,CO V& arg){auto BE = arg.BE(),EN = arg.EN();auto IT = BE;WH(IT != EN){(IT == BE?os:os << " ")<< *IT;IT++;}RE os;} #define DF_OF_AR_FOR_VE(V,OPR)TE IN V& OP OPR ## =(V& a,CO T& t){for(auto& s:a){s OPR ## = t;}RE a;}TE IN V& OP OPR ## =(V& a0,CO V& a1){AS(a0.SZ()<= a1.SZ());auto IT0 = a0.BE(),EN0 = a0.EN();auto IT1 = a1.BE();WH(IT0 != EN0){*(IT0++)OPR ## = *(IT1++);}RE a0;}TE IN V OP OPR(V a,CO U& u){RE MO(a OPR ## = u);} #define DF_OF_INCREMENT_FOR_VE(V,INCR)TE IN V& OP INCR(V& a){for(auto& i:a){INCR i;}RE a;} #define DF_OF_ARS_FOR_VE(V)DF_OF_AR_FOR_VE(V,+);DF_OF_AR_FOR_VE(V,-);DF_OF_AR_FOR_VE(V,*);DF_OF_AR_FOR_VE(V,/);DF_OF_AR_FOR_VE(V,%);DF_OF_INCREMENT_FOR_VE(V,++);DF_OF_INCREMENT_FOR_VE(V,--);TE IN V OP*(CO T& scalar,V v){for(auto& t:v){t *= scalar;}RE MO(v);} DF_OF_COUT_FOR_VE(VE);DF_OF_COUT_FOR_VE(LI);DF_OF_ARS_FOR_VE(VE);DF_OF_ARS_FOR_VE(LI);IN VO VariadicResize(CRI SZ){}TE IN VO VariadicResize(CRI SZ,Arg& arg,ARGS&... args){arg.resize(SZ);VariadicResize(SZ,args...);}TE IN auto Get(V& a){RE[&](CRI i = 0)-> CO decldecay_t(a[0])&{RE a[i];};}TE IN VE id(CRI SZ){VE AN(SZ);FOR(i,0,SZ){AN[i]= i;}RE AN;}TE VO Sort(VE& a,CO bool& reversed = false){if(reversed){ST auto comp =[](CO T& t0,CO T& t1){RE t1 < t0;};sort(a.BE(),a.EN(),comp);}else{sort(a.BE(),a.EN());}}TE IN VE IndexSort(CO VE& a,CO bool& reversed = false){auto index = id(a.SZ());if(reversed){sort(index.BE(),index.EN(),[&](CRI i,CRI j){RE a[j]< a[i];});}else{sort(index.BE(),index.EN(),[&](CRI i,CRI j){RE a[i]< a[j];});}RE index;}TE IN U Sum(CO VE& a){U AN{};for(auto& x:a){AN += x;}RE AN;}TE IN U Product(CO VE& a){U AN{};for(auto& x:a){AN *= x;}RE AN;} /* Map (1KB)*/ #define DF_OF_AR_FOR_MAP(MAP,OPR)TE IN MAP& OP OPR ## =(MAP& a,CO pair& v){a[v.first]OPR ## = v.second;RE a;}TE IN MAP& OP OPR ## =(MAP& a0,CO MAP& a1){for(auto&[t,u]:a1){a0[t]OPR ## = u;}RE a0;}TE IN MAP OP OPR(MAP a,CO ARG& arg){RE MO(a OPR ## = arg);} #define DF_OF_ARS_FOR_MAP(MAP)DF_OF_AR_FOR_MAP(MAP,+);DF_OF_AR_FOR_MAP(MAP,-);DF_OF_AR_FOR_MAP(MAP,*);DF_OF_AR_FOR_MAP(MAP,/);DF_OF_AR_FOR_MAP(MAP,%); TE US Map = conditional_t>,unordered_map,conditional_t,map,VO>>; DF_OF_ARS_FOR_MAP(map);DF_OF_ARS_FOR_MAP(unordered_map); /* StdStream (2KB)*/ TE IN IS& VariadicCin(IS& is){RE is;}TE IN IS& VariadicCin(IS& is,Arg& arg,ARGS&... args){RE VariadicCin(is >> arg,args...);}TE IN IS& VariadicSet(IS& is,CRI i){RE is;}TE IN IS& VariadicSet(IS& is,CRI i,Arg& arg,ARGS&... args){RE VariadicSet(is >> arg[i],i,args...);}TE IN IS& VariadicGetline(IS& is,CO char& separator){RE is;}TE IN IS& VariadicGetline(IS& is,CO char& separator,Arg& arg,ARGS&... args){RE VariadicGetline(getline(is,arg,separator),separator,args...);}TE IN OS& VariadicCout(OS& os,Arg&& arg){RE os << forward(arg);}TE IN OS& VariadicCout(OS& os,Arg1&& arg1,Arg2&& arg2,ARGS&&... args){RE VariadicCout(os << forward(arg1)<< " ",forward(arg2),forward(args)...);}TE IN OS& VariadicCoutNonSep(OS& os,Arg&& arg){RE os << forward(arg);}TE IN OS& VariadicCoutNonSep(OS& os,Arg1&& arg1,Arg2&& arg2,ARGS&&... args){RE VariadicCoutNonSep(os << forward(arg1),forward(arg2),forward(args)...);}TE IN OS& CoutArray(OS& os,CRI i_start,CRI i_ulim,ARRAY&& a){for(int i = i_start;i < i_ulim;i++){(i == i_start?os:(os << " "))<< a[i];}RE os;} /* Module (6KB)*/ #define DC_OF_CPOINT(POINT)IN CO U& POINT()CO NE #define DC_OF_POINT(POINT)IN U& POINT()NE #define DF_OF_CPOINT(POINT)TE IN CO U& VirtualPointedSet::POINT()CO NE{RE Point();} #define DF_OF_POINT(POINT)TE IN U& VirtualPointedSet::POINT()NE{RE Point();} TE CL UnderlyingSet{PU:US type = U;};TE CL VirtualPointedSet:VI PU UnderlyingSet{PU:VI CO U& Point()CO NE = 0;VI U& Point()NE = 0;DC_OF_CPOINT(Unit);DC_OF_CPOINT(Zero);DC_OF_CPOINT(One);DC_OF_CPOINT(Infty);DC_OF_POINT(init);DC_OF_POINT(root);};TE CL PointedSet:VI PU VirtualPointedSet{PU:U m_b_U;IN PointedSet(U b_u = U());IN CO U& Point()CO NE;IN U& Point()NE;};TE CL VirtualNSet:VI PU UnderlyingSet{PU:VI U Transfer(CO U& u)= 0;IN U Inverse(CO U& u);};TE CL AbstractNSet:VI PU VirtualNSet{PU:F_U m_f_U;IN AbstractNSet(F_U f_U);IN AbstractNSet& OP=(CO AbstractNSet&)NE;IN U Transfer(CO U& u);};TE CL VirtualMagma:VI PU UnderlyingSet{PU:VI U Product(U u0,CO U& u1)= 0;IN U Sum(U u0,CO U& u1);};TE CL AdditiveMagma:VI PU VirtualMagma{PU:IN U Product(U u0,CO U& u1);};TE CL MultiplicativeMagma:VI PU VirtualMagma{PU:IN U Product(U u0,CO U& u1);};TE CL AbstractMagma:VI PU VirtualMagma{PU:M_U m_m_U;IN AbstractMagma(M_U m_U);IN AbstractMagma& OP=(CO AbstractMagma&)NE;IN U Product(U u0,CO U& u1);}; TE IN PointedSet::PointedSet(U b_U):m_b_U(MO(b_U)){}TE IN CO U& PointedSet::Point()CO NE{RE m_b_U;}TE IN U& PointedSet::Point()NE{RE m_b_U;}DF_OF_CPOINT(Unit);DF_OF_CPOINT(Zero);DF_OF_CPOINT(One);DF_OF_CPOINT(Infty);DF_OF_POINT(init);DF_OF_POINT(root);TE IN AbstractNSet::AbstractNSet(F_U f_U):m_f_U(MO(f_U)){ST_AS(is_invocable_r_v);}TE IN AbstractNSet& AbstractNSet::operator=(CO AbstractNSet&)NE{RE *TH;}TE IN U AbstractNSet::Transfer(CO U& u){RE m_f_U(u);}TE IN U VirtualNSet::Inverse(CO U& u){RE Transfer(u);}TE IN AbstractMagma::AbstractMagma(M_U m_U):m_m_U(MO(m_U)){ST_AS(is_invocable_r_v);}TE IN AbstractMagma& AbstractMagma::OP=(CO AbstractMagma&)NE{RE *TH;}TE IN U AdditiveMagma::Product(U u0,CO U& u1){RE MO(u0 += u1);}TE IN U MultiplicativeMagma::Product(U u0,CO U& u1){RE MO(u0 *= u1);}TE IN U AbstractMagma::Product(U u0,CO U& u1){RE m_m_U(MO(u0),u1);}TE IN U VirtualMagma::Sum(U u0,CO U& u1){RE Product(MO(u0),u1);} TE CL VirtualMonoid:VI PU VirtualMagma,VI PU VirtualPointedSet{};TE CL AdditiveMonoid:VI PU VirtualMonoid,PU AdditiveMagma,PU PointedSet{};TE CL MultiplicativeMonoid:VI PU VirtualMonoid,PU MultiplicativeMagma,PU PointedSet{PU:IN MultiplicativeMonoid(U e_U);};TE CL AbstractMonoid:VI PU VirtualMonoid,PU AbstractMagma,PU PointedSet{PU:IN AbstractMonoid(M_U m_U,U e_U);}; TE IN MultiplicativeMonoid::MultiplicativeMonoid(U e_U):PointedSet(MO(e_U)){}TE IN AbstractMonoid::AbstractMonoid(M_U m_U,U e_U):AbstractMagma(MO(m_U)),PointedSet(MO(e_U)){} TE CL VirtualGroup:VI PU VirtualMonoid,VI PU VirtualPointedSet,VI PU VirtualNSet{};TE CL AdditiveGroup:VI PU VirtualGroup,PU AdditiveMonoid{PU:IN U Transfer(CO U& u);};TE CL AbstractGroup:VI PU VirtualGroup,PU AbstractMonoid,PU AbstractNSet{PU:IN AbstractGroup(M_U m_U,U e_U,I_U i_U);}; TE IN AbstractGroup::AbstractGroup(M_U m_U,U e_U,I_U i_U):AbstractMonoid(MO(m_U),MO(e_U)),AbstractNSet(MO(i_U)){}TE IN U AdditiveGroup::Transfer(CO U& u){RE -u;} TE CL VirtualRSet:VI PU UnderlyingSet{PU:VI U Action(CO R& r,U u)= 0;IN U PW(U u,CO R& r);IN U ScalarProduct(CO R& r,U u);};TE CL RegularRSet:VI PU VirtualRSet,PU MAGMA{PU:IN RegularRSet(MAGMA magma);IN U Action(CO U& r,U u);};TE RegularRSet(MAGMA magma)-> RegularRSet,MAGMA>;TE CL AbstractRSet:VI PU VirtualRSet{PU:O_U m_o_U;IN AbstractRSet(CO R& dummy0,CO U& dummy1,O_U o_U);IN AbstractRSet& OP=(CO AbstractRSet&)NE;IN U Action(CO R& r,U u);};TE CL AbstractModule:PU AbstractRSet,PU GROUP{PU:IN AbstractModule(CO R& dummy,O_U o_U,GROUP M);};TE AbstractModule(CO R& dummy,O_U o_U,GROUP M)-> AbstractModule,O_U,GROUP>;TE CL Module:VI PU VirtualRSet,PU AdditiveGroup{PU:IN U Action(CO R& r,U u);}; TE IN RegularRSet::RegularRSet(MAGMA magma):MAGMA(MO(magma)){}TE IN AbstractRSet::AbstractRSet(CO R& dummy0,CO U& dummy1,O_U o_U):m_o_U(MO(o_U)){ST_AS(is_invocable_r_v);}TE IN AbstractModule::AbstractModule(CO R& dummy,O_U o_U,GROUP M):AbstractRSet(dummy,M.One(),MO(o_U)),GROUP(MO(M)){ST_AS(is_same_v>);}TE IN AbstractRSet& AbstractRSet::OP=(CO AbstractRSet&)NE{RE *TH;}TE IN U RegularRSet::Action(CO U& r,U u){RE TH->Product(r,MO(u));}TE IN U AbstractRSet::Action(CO R& r,U u){RE m_o_U(r,MO(u));}TE IN U Module::Action(CO R& r,U u){RE MO(u *= r);}TE IN U VirtualRSet::PW(U u,CO R& r){RE Action(r,MO(u));}TE IN U VirtualRSet::ScalarProduct(CO R& r,U u){RE Action(r,MO(u));} /* Graph (5KB)*/ TE CL VirtualGraph:VI PU UnderlyingSet{PU:VI R1 Enumeration(CRI i)= 0;IN R2 Enumeration_inv(CO T& t);TE IN R2 Enumeration_inv(CO PATH& p);IN VO Reset();VI CRI SZ()CO NE = 0;VI E& edge()NE = 0;VI ret_t Edge(CO T& t)= 0;TE IN ret_t Edge(CO PATH& p);ST IN CO T& Vertex(CO T& t)NE;TE ST IN CO T& Vertex(CO PATH& e)NE;VI R2 Enumeration_inv_Body(CO T& t)= 0;};TE CL EdgeImplimentation:VI PU VirtualGraph{PU:int m_SZ;E m_edge;IN EdgeImplimentation(CRI SZ,E edge);IN CRI SZ()CO NE;IN E& edge()NE;IN ret_t Edge(CO T& t);};TE CL Graph:PU EdgeImplimentation{PU:IN Graph(CRI SZ,E edge);IN CRI Enumeration(CRI i);TE IN Graph GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CRI t);};TE CL EnumerationGraph:PU EdgeImplimentation,ret_t,E>{PU:Enum_T m_enum_T;Enum_T_inv m_enum_T_inv;IN EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge);IN ret_t Enumeration(CRI i);TE IN EnumerationGraph GetGraph(F edge)CO;IN ret_t Enumeration_inv_Body(CO T& t);};TE EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge)-> EnumerationGraph()(0)),Enum_T,Enum_T_inv,E>;TE CL MemorisationGraph:PU EdgeImplimentation{PU:int m_LE;VE m_memory;Map m_memory_inv;IN MemorisationGraph(CRI SZ,CO T& dummy,E edge);IN T Enumeration(CRI i);IN VO Reset();TE IN MemorisationGraph GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CO T& t);}; TE IN EdgeImplimentation::EdgeImplimentation(CRI SZ,E edge):m_SZ(SZ),m_edge(MO(edge)){ST_AS(is_COructible_v && is_COructible_v && is_invocable_v);}TE IN Graph::Graph(CRI SZ,E edge):EdgeImplimentation(SZ,MO(edge)){}TE IN EnumerationGraph::EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge):EdgeImplimentation,ret_t,E>(SZ,MO(edge)),m_enum_T(MO(enum_T)),m_enum_T_inv(MO(enum_T_inv)){}TE IN MemorisationGraph::MemorisationGraph(CRI SZ,CO T& dummy,E edge):EdgeImplimentation(SZ,MO(edge)),m_LE(),m_memory(),m_memory_inv(){ST_AS(is_invocable_v);}TE IN CRI Graph::Enumeration(CRI i){RE i;}TE IN ret_t EnumerationGraph::Enumeration(CRI i){RE m_enum_T(i);}TE IN T MemorisationGraph::Enumeration(CRI i){AS(0 <= i && i < m_LE);RE m_memory[i];}TE IN R2 VirtualGraph::Enumeration_inv(CO T& t){RE Enumeration_inv_Body(t);}TE TE IN R2 VirtualGraph::Enumeration_inv(CO PATH& p){RE Enumeration_inv_Body(get<0>(p));}TE