#ifndef INCLUDE_MODE #define INCLUDE_MODE /* #define SUBMIT_ONLY */ #define DEBUG_OUTPUT #define SAMPLE_CHECK A #endif #ifdef INCLUDE_MAIN VO Solve() { CEXPR( int , digit , 20 ); // CEXPR( int , amb , ( 1 << digit ) - 1 ); // CEXPR( int , B , P >> digit ); // MP temp = 1; // vector embed( B + 1 , temp ); // FOREQ( i , 1 , B << digit ){ // temp *= i; // if( ( i & amb ) == 0 ){ // embed[i>>digit] = temp; // } // } // RETURN( embed ); int embed[] = {1,467742124,703158536,849331177,183632821,786787592,708945888,623860151,442444797,339076928,916211838,827641482,982515753,303461550,466748179,669060208,789885751,915736046,189957301,934038903,728735046,774755699,649374308,602288735,492352484,958678776,943233257,148504501,352124178,569334038,927469492,343841688,432351202,700916755,170721982,8283809,875807278,931632987,330722936,603566523,391470976,157944106,826756015,278928878,178606531,522053153,175494307,16217485,310769109,430912024,970167731,302127847,960178710,607169580,211863227,918097328,664502958,598427325,415194799,38321157,375608821,557298612,497769749,114695383,77784134,629192790,339438380,348348875,713806860,526342541,671850855,414726935,844082152,412454739,351143550,868784407,834684152,186057224,996072584,619190001,24770542,765280770,513490122,468949120,867194196,866447292,937135640,560788103,308335177,703539315,252044620,119916775,298069903,43651994,148641017,730387621,856452172,74265901,626807500,980602375,42825068,348086475,162321900,207340584,151258454,461547160,320321845,361026143,882876292,842563318,257705870,158156446,292795459,984763947,917068833,811332379,782439665,944504775,298167161,141501910,155584237,149720256,71954352,666430555,580966229,884747116,616367471,918981127,310328833,724405658,383796145,256700166,487819118,642491144,181867555,524937737,222137750,445244561,79921588,253457448,405659726,260707689,740044210,654653354,229885020,230551611,616689587,939003921,565960348,904184966,133298693,859220865,186139683,765071679,247651638,451157944,929341123,503724944,768266737,142218056,910573117,274579400,151387843,212671109,815271666,406331931,154251304,642676789,570372925,976277122,442985463,928799971,817581666,797627351,100113334,877639265,541537097,434482347,300960222,270085755,481153328,236088097,686884498,323505794,897572220,900787550,277507290,157634146,892066519,616420589,46056764,697140618,592483685,896871487,896388868,106444279,115102765,191484323,62322499,434613622,426026852,378184205,194359325,415197585,965735328,598860936,653751428,942602959,475099103,642401460,77868208,464952529,549976420,705774928,635299526,704085554,809044086,670938184,799176916,58985566,402328281,182103192,921913660,674272214,428301920,520916749,127424638,296779896,166780239,19634060,95873539,708947606,532272305,980167862,7015847,370183454,45567119,866949818,374428494,25583689,351370758,835388325,232690098,42002598,17055285,985022727,214528454,122907290,793349516,609331634,87133548,248246624,448572380,502875867,183097664,536117329,170926160,381772251,37038194,374439881,94285547,880631489,452052533,739811514,675382782,587926712,179133902,694266603,338843576,281485671,813341519,616512705,222785194,382494725,471654428,961907947,442140830,702296161,548575377,388901073,19119024,545916498,947169254,801677200,377657430,634980290,246239186,13175103,239754689,656729178,364003283,646568868,584909084,690387116,452007054,131381944,908149670,807287523,802277179,745423153,893994782,197548253,376096720,105840336,687751559,170787791,928507410,620382696,446955151,139665212,882526402,494793004,107171423,753993075,467588754,207595897,269813018,941027990,856873596,717085190,245280646,792026805,548741735,523767341,637697735,261200153,89666563,344573088,15832984,558492246,825051585,923222974,826620400,558080789,657328927,991078225,706029275,738905108,401212366,980043233,895405022,597894231,636951913,947342478,786075225,395095090,188433847,121279219,860403973,396099425,240442489,521535558,280382318,58023116,735594008,8696133,477645338,223630480,816606673,680021043,362424474,181667447,504295826,332167472,766361494,992840497,417671938,376941230,11880047,275790726,106186450,150546053,966438917,431896075,158021876,734833661,328332504,632143386,962477966,638741189,728804571,753715698,20536106,45105841,271673172,982138522,604809222,199722980,211807634,478008419,194715230,246865373,316443541,869035744,202922168,245262975,136244583,650969410,566222746,55188168,495968583,571946805,188658038,353720239,830419870,669127165,86710835,810103736,630008035,764354348,209246227,277861984,725469211,151404581,894191013,775554083,634671016,170299187,471849450,575347258,505276194,636730506,40086858,386228700,789875034,998219457,359035788,843760715,864829665,794240359,241486050,48334220,583177582,714653706,617669563,132782021,779225352,333301287,520569296,508276228,689073648,573645847,200419842,911561316,310562870,204959007,879280837,762843188,103128368,133300147,648946778,287218789,662474952,587555465,105622721,648151526,517033362,729251452,850555187,708613432,874408867,345608416,690718720,10813958,42384375,882264058,825490058,252850511,652942840,202604098,277615259,862885671,582470925,190843016,534488148,187675153,911660635,377262012,642854978,359397276,712333871,580131409,841639861,925383257,213683380,25291651,974815450,32032244,119030165,443676106,555727293,170519648,171131074,839941962,789829593,140975543,845347712,303299112,530420097,857005350,249174130,224087061,311280308,404814306,567648772,7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auto fact = [&]( const int& i ){ MP a = embed[i>>digit]; FOREQ( j , ( ( i >> digit ) << digit ) + 1 , i ){ a *= j; } return a; }; CIN( int , N , M ); SetMin( M , N - M ); if( M == 0 ){ RETURN( 1 ); } if( N - M < ll( P ) && ll( P ) <= N ){ RETURN( 0 ); } N %= ll( P ); M %= ll( P ); RETURN( fact( N ) / ( fact( M ) * fact( N - M ) ) ); } REPEAT_MAIN(1); #else /* INCLUDE_MAIN */ #ifdef INCLUDE_SUB /* 圧縮時は中身だけ削除する。*/ IN VO Experiment() { } /* 圧縮時は中身だけ削除する。*/ IN VO SmallTest() { CERR( "全てのケースを確認しました。" ); } /* 圧縮時は中身だけ削除する。*/ IN VO RandomTest( const int& test_case_num ) { REPEAT( test_case_num ){ } CERR( "全てのケースを確認しました。" ); } #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。*/ /* 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 DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE1 ) #define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) ) #define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , test_case_num_bound , BOUND ); int test_case_num = 1; if CE( test_case_num_bound > 1 ){ FINISH_MAIN #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__ ) #define FINISH_MAIN GETLINE( test_case_num_str ); test_case_num = stoi( test_case_num_str ); ASSERT( test_case_num , 1 , test_case_num_bound ); } REPEAT( test_case_num ){ Solve(); } } #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 , VE( N1 + I1 ) ); FOR( VARIABLE_FOR_CIN_AA , 0 , N0 ){ SET_A( I1 , N1 , VAR[VARIABLE_FOR_CIN_AA + I0] ); } #define FINISH_MAIN SET_ASSERT( test_case_num , 1 , test_case_num_bound ); } REPEAT( test_case_num ){ Solve(); } } #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 ) #define WHAT( ... ) #define TLE( CONDITION ) if( !( CONDITION ) ){ ll TLE_VAR = 1; while( TLE_VAR != 0 ){ ( TLE_VAR += 2 ) %= int( 1e9 ); } cerr << TLE_VAR << endl; } #define MLE( CONDITION ) if( !( CONDITION ) ){ vector> MLE_VAR{}; REPEAT( 1e6 ){ MLE_VAR.push_back( vector( 1e6 ) ); } cerr << MLE_VAR << endl; } #define OLE( CONDITION ) if( !( CONDITION ) ){ REPEAT( 1e8 ){ cerr << "OLE\n"; } } #endif #ifdef REACTIVE #ifndef DEBUG #define LOCAL( ... ) #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 = loop_average_time , current_time = loop_start_time; int loop_count = current_time; assert( 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 PR1( A1 , ... ) A1 #define PR2( A1 , A2 , ... ) A2 #define PR3( A1 , A2 , A3 , ... ) A3 #define FOR_( VAR , INITIAL , FINAL , UPPER , COMP , INCR ) for( decldecay_t( UPPER ) VAR = INITIAL ; VAR COMP FINAL ; VAR INCR ) #define FOR( VAR , INITIAL , ... ) FOR_( VAR , INITIAL , PR1( __VA_ARGS__ ) , PR1( __VA_ARGS__ ) , < , PR3( __VA_ARGS__ , += PR2( __VA_ARGS__ , ? ) , ++ ) ) #define FOREQ( VAR , INITIAL , ... ) FOR_( VAR , INITIAL , PR1( __VA_ARGS__ ) , PR1( __VA_ARGS__ ) , <= , PR3( __VA_ARGS__ , += PR2( __VA_ARGS__ , ? ) , ++ ) ) #define FOREQINV( VAR , INITIAL , ... ) FOR_( VAR , INITIAL , PR1( __VA_ARGS__ ) , INITIAL , + 1 > , PR3( __VA_ARGS__ , -= PR2( __VA_ARGS__ , ? ) , -- ) ) #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 , 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 ){ CERR( "出力の不一致が検出されました。" ); RE; } #define CHECK( ... ) auto answer = Answer( __VA_ARGS__ , false ); CERR( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Answer == " , answer ) /* 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; /* 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 /* Random (1KB)*/ ll GetRand(CRL Rand_min,CRL Rand_max){AS(Rand_min <= Rand_max);ll AN = time(NULL);RE AN * rand()%(Rand_max + 1 - Rand_min)+ Rand_min;} /* Set (2KB)*/ #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>>; #define DF_OF_POP_FOR_SET(SET)TE IN T pop_max(SET& S){AS(!S.empty());auto IT = --S.EN();T AN = *IT;S.erase(IT);RE AN;}TE IN T pop_min(SET& S){AS(!S.empty());auto IT = S.BE();T AN = *IT;S.erase(IT);RE AN;}TE IN SET& OP<<=(SET& S,T t){S.insert(MO(t));RE S;}TE IN SET& OP<<=(SET& S,U&& u){S.insert(T{forward(u)});RE S;}TE IN SET& OP>>=(SET& S,CO T& t){auto IT = S.find(t);if(IT != S.EN()){S.erase(IT);}RE S;}TE IN SET& OP>>=(SET& S,CO U& u){RE S >>= T{u};}TE IN CO T& Get(CO SET& S,int i){auto BE = S.BE(),EN = S.EN();auto& IT = i < 0?(++i,--EN):BE;WH(i > 0 && IT != EN){--i;++IT;}WH(i < 0 && IT != BE){++i;--IT;}AS(i == 0);RE *IT;} #define DF_OF_UNION_FOR_SET(SET)TE IN SET& OP|=(SET& S0,SET S1){S0.merge(MO(S1));RE S0;}TE IN SET OP|(SET S0,SET S1){RE MO(S0.SZ()< S1.SZ()?S1 |= MO(S0):S0 |= MO(S1));} TE IN TY SET::const_iterator MaximumLeq(CO SET& S,CO T& t){auto IT = S.upper_bound(t);RE IT == S.BE()?S.EN():--IT;}TE IN TY SET::const_iterator MaximumLt(CO SET& S,CO T& t){auto IT = S.lower_bound(t);RE IT == S.BE()?S.EN():--IT;}TE IN TY SET::const_iterator MinimumGeq(CO SET& S,CO T& t){RE S.lower_bound(t);}TE IN TY SET::const_iterator MinimumGt(CO SET& S,CO T& t){RE S.upper_bound(t);}TE IN VO EraseBack(SET& S,ITERATOR& IT){IT = S.erase(IT);}TE IN VO EraseFront(SET& S,ITERATOR& IT){IT = S.erase(IT);IT == S.BE()?IT = S.EN():--IT;}TE TY SET,TY T,TY...Args> IN bool In(CO T& t,CO SET& S){RE S.count(t)== 1;}DF_OF_POP_FOR_SET(set);DF_OF_POP_FOR_SET(unordered_set);DF_OF_POP_FOR_SET(multiset);DF_OF_POP_FOR_SET(unordered_multiset);DF_OF_UNION_FOR_SET(set);DF_OF_UNION_FOR_SET(unordered_set);DF_OF_UNION_FOR_SET(multiset);DF_OF_UNION_FOR_SET(unordered_multiset);DF_OF_UNION_FOR_SET(VE);DF_OF_UNION_FOR_SET(LI); /* Tuple (6KB)*/ #define DF_OF_AR_FOR_TUPLE(OPR)TE TY PAIR> IN auto OP OPR ## =(PAIR& t0,CO PAIR& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);RE t0;}TE TY TUPLE> IN auto OP OPR ## =(TUPLE& t0,CO TUPLE& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);RE t0;}TE TY TUPLE> IN auto OP OPR ## =(TUPLE& t0,CO TUPLE& t1)-> decltype((get<0>(t0),t0))&{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 PAIR> IN auto OP OPR ## =(PAIR& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;RE t0;}TE TY TUPLE> IN auto OP OPR ## =(TUPLE& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;RE t0;}TE TY TUPLE> IN auto OP OPR ## =(TUPLE& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;get<3>(t0)OPR ## = t1;RE t0;}TE TY TUPLE,TY...ARGS,TY ARG> IN auto OP OPR(CO TUPLE& 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 PAIR> IN auto OP INCR(PAIR& t)-> decltype((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);RE t;}TE TY TUPLE> IN auto OP INCR(TUPLE& t)-> decltype((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);RE t;}TE TY TUPLE> IN auto OP INCR(TUPLE& t)-> decltype((get<0>(t),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)-> decldecay_t((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(--); TE CL TupleAccessIndex{};TE CL Tuple:PU tuple{PU:IN Tuple(Types&&... args);TE IN Tuple(Args&&... args);TE IN auto& OP[](CO TupleAccessIndex& i)NE;TE IN CO auto& OP[](CO TupleAccessIndex& i)CO NE;};TE CL tuple_size>:PU tuple_size>{};TE CL tuple_element>:PU tuple_element>{}; TE US Pair = Tuple;TE US T2 = Pair;TE US T3 = Tuple;TE US T4 = Tuple; CE TupleAccessIndex<0> O{};CE TupleAccessIndex<1> I{};CE TupleAccessIndex<2> II{};CE TupleAccessIndex<3> III{}; TE IN Tuple::Tuple(Types&&... args):tuple(MO(args)...){}TE TE IN Tuple::Tuple(Args&&... args):tuple(forward(args)...){}TE TE IN auto& Tuple::OP[](CO TupleAccessIndex& i)NE{RE get(*TH);}TE TE IN CO auto& Tuple::OP[](CO TupleAccessIndex& i)CO NE{RE get(*TH);}TE TY PAIR,TY INT> T2 cast(CO PAIR& t){RE{get<0>(t),get<1>(t)};}TE T3 cast(CO tuple& t){RE{get<0>(t),get<1>(t),get<2>(t)};}TE T4 cast(CO tuple& t){RE{get<0>(t),get<1>(t),get<2>(t),get<3>(t)};} #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 (3KB)*/ #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;} DF_OF_COUT_FOR_VE(VE);DF_OF_COUT_FOR_VE(LI);DF_OF_COUT_FOR_VE(set);DF_OF_COUT_FOR_VE(unordered_set);DF_OF_COUT_FOR_VE(multiset);IN VO VariadicResize(CRI SZ){}TE IN VO VariadicResize(CRI SZ,Arg& arg,ARGS&... args){arg.resize(SZ);VariadicResize(SZ,args...);} #define DF_OF_AR_FOR_VE(V,OPR)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 T& t){for(auto& x:a){x OPR## = t;}RE a;}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_SHIFT_FOR_VE(V)TE IN V& OP<<=(V& a,T t){a.push_back(MO(t));RE a;}TE IN V& OP<<=(V& a,U&& u){RE a <<= T{forward(u)};}TE IN T pop(V& a){AS(!a.empty());T AN = MO(a.back());a.pop_back();RE AN;} #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-(V a){RE MO(a *= T(-1));}TE IN V OP*(CO T& t,V v){RE MO(v *= t);}DF_OF_SHIFT_FOR_VE(V); DF_OF_ARS_FOR_VE(VE);DF_OF_ARS_FOR_VE(LI);DF_OF_SHIFT_FOR_VE(basic_string); 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(int i = 0;i < SZ;i++){AN[i]= i;}RE AN;}TE IN VO Sort(V& a,CO bool& reversed = false){US T = decldecay_t(a[0]);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 VO Sort(V0& a,V1& b,CO bool& reversed = false){CO int SZ = a.SZ();AS(SZ == int(b.SZ()));VE> v(SZ);for(int i = 0;i < SZ;i++){v[i]={MO(a[i]),MO(b[i])};}Sort(v,reversed);for(int i = 0;i < SZ;i++){a[i]= MO(v[i].first);b[i]= MO(v[i].second);}}TE IN pair,VE> IndexSort(CO V& a,CO bool& reversed = false){CO int SZ = a.SZ();auto index = id(SZ),ord = index;sort(index.BE(),index.EN(),[&](CRI i,CRI j){CO pair ti{a[i],i},tj{a[j],j};RE reversed?tj < ti:ti < tj;});for(int i = 0;i < SZ;i++){ord[index[i]]= i;}RE{MO(index),MO(ord)};}TE IN int len(CO V& a){RE a.SZ();}TE IN VO Reverse(V& a){CO int SZ = len(a),half = SZ / 2;for(int i = 0;i < half;i++){swap(a[i],a[SZ-1-i]);}};TE IN V Reversed(V a){Reverse(a);RE MO(a);}TE TY V,TY T> IN V cast(CO V& a){V AN{};for(auto& x:a){AN <<= a;}} /* 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;} /* DynamicModulo (9KB)*/ CEXPR(uint,P,998244353); #define RP Represent #define DeRP Derepresent TE CE INT1 Residue(INT1 n,CO INT2& M)NE{RE MO(n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n < M?n:n %= M);} TE IN INT ModularInverse(CO INT& base,ll c){AS(base > 0);ll a[2]={0,1 % base};INT b[2]={base,INT((c %= base)< 0?c += base:c)};WH(b[1]!= 0){CO INT q = b[0]/ b[1];(a[0]-= q * a[1]% base)< 0?a[0]+= base:a[0];b[0]-= q * b[1];swap(a[0],a[1]);swap(b[0],b[1]);}AS(b[0]== 1 &&(a[0]* c - 1)% base == 0);RE a[0];} TE CL DMods;TE CL COantsForDMods{PU:COantsForDMods()= delete;ST uint g_M;ST CE CO uint g_memory_bound = 2e6;ST uint g_memory_le;ST uint g_M_minus;ST bool g_M_is_prime;}; TE uint COantsForDMods::g_M = P;TE uint COantsForDMods::g_memory_le = g_memory_bound;TE uint COantsForDMods::g_M_minus = P-1;TE bool COantsForDMods::g_M_is_prime = true; #define SFINAE_FOR_DMOD enable_if_t>>* #define DC_OF_CM_FOR_DMOD(OPR)IN bool OP OPR(CO DMods& n)CO NE #define DC_OF_AR_FOR_DMOD(OPR,EX)IN DMods OP OPR(DMods n)CO EX; #define DF_OF_CM_FOR_DMOD(OPR)TE IN bool DMods::OP OPR(CO DMods& n)CO NE{RE m_n OPR n.m_n;} #define DF_OF_AR_FOR_DMOD(OPR,EX,LEFT,OPR2)TE IN DMods DMods::OP OPR(DMods n)CO EX{RE MO(LEFT OPR2 ## = *TH);}TE IN DMods OP OPR(T n0,CO DMods& n1)EX{RE MO(DMods(MO(n0))OPR ## = n1);} TE CL DMods{PU:uint m_n;IN DMods()NE;IN DMods(CO DMods& n)NE;IN DMods(DMods&& n)NE;TE IN DMods(T n)NE;IN DMods& OP=(DMods n)NE;IN DMods& OP+=(CO DMods& n)NE;IN DMods& OP-=(CO DMods& n)NE;IN DMods& OP*=(CO DMods& n)NE;IN DMods& OP/=(DMods n);IN DMods& OP^=(ll EX);IN DMods& OP<<=(ll n);IN DMods& OP>>=(ll n);IN DMods& OP++()NE;IN DMods OP++(int)NE;IN DMods& OP--()NE;IN DMods OP--(int)NE;DC_OF_CM_FOR_DMOD(==);DC_OF_CM_FOR_DMOD(!=);DC_OF_CM_FOR_DMOD(<);DC_OF_CM_FOR_DMOD(<=);DC_OF_CM_FOR_DMOD(>);DC_OF_CM_FOR_DMOD(>=);DC_OF_AR_FOR_DMOD(+,NE);DC_OF_AR_FOR_DMOD(-,NE);DC_OF_AR_FOR_DMOD(*,NE);DC_OF_AR_FOR_DMOD(/,);IN DMods OP^(ll EX)CO;IN DMods OP<<(ll n)CO;IN DMods OP>>(ll n)CO;IN DMods OP-()CO NE;IN VO swap(DMods& n)NE;IN CRUI RP()CO NE;ST IN DMods DeRP(uint n)NE;ST IN CO DMods& Factorial(CRL n);ST IN CO DMods& FactorialInverse(CRL n);ST IN DMods Combination(CRL n,CRL i);ST IN CO DMods& zero()NE;ST IN CO DMods& one()NE;ST IN CRUI GetModulo()NE;ST IN VO SetModulo(CRUI M,CO bool& M_is_prime = false)NE;IN DMods& SignInvert()NE;IN DMods& Invert();IN DMods& PPW(ll EX)NE;IN DMods& NNPW(ll EX)NE;ST IN CO DMods& Inverse(CRI n);ST IN CO DMods& TwoPower(CRI n);ST IN CO DMods& TwoPowerInverse(CRI n);US COants = COantsForDMods;}; US DMod = DMods<0>; TE IN DMods::DMods()NE:m_n(){}TE IN DMods::DMods(CO DMods& n)NE:m_n(n.m_n){}TE IN DMods::DMods(DMods&& n)NE:m_n(MO(n.m_n)){}TE TE IN DMods::DMods(T n)NE:m_n(Residue(MO(n),COants::g_M)){}TE IN DMods& DMods::OP=(DMods n)NE{m_n = MO(n.m_n);RE *TH;}TE IN DMods& DMods::OP+=(CO DMods& n)NE{(m_n += n.m_n)< COants::g_M?m_n:m_n -= COants::g_M;RE *TH;}TE IN DMods& DMods::OP-=(CO DMods& n)NE{m_n < n.m_n?(m_n += COants::g_M)-= n.m_n:m_n -= n.m_n;RE *TH;}TE IN DMods& DMods::OP*=(CO DMods& n)NE{m_n = Residue(MO(ull(m_n)* n.m_n),COants::g_M);RE *TH;}TE IN DMods& DMods::OP/=(DMods n){RE OP*=(n.Invert());}TE IN DMods& DMods::PPW(ll EX)NE{DMods pw{*TH};EX--;WH(EX != 0){(EX & 1)== 1?*TH *= pw:*TH;EX >>= 1;pw *= pw;}RE *TH;}TE IN DMods& DMods::NNPW(ll EX)NE{RE EX == 0?(m_n = 1,*TH):PPW(MO(EX));}TE IN DMods& DMods::OP^=(ll EX){if(EX < 0){m_n = ModularInverse(COants::g_M,MO(m_n));EX *= -1;}RE NNPW(MO(EX));}TE IN DMods& DMods::OP<<=(ll n){RE *TH *=(n < 0 && -n < int(COants::g_memory_le))?TwoPowerInverse(- int(n)):(n >= 0 && n < int(COants::g_memory_le))?TwoPower(int(n)):DMods(2)^= MO(n);}TE IN DMods& DMods::OP>>=(ll n){RE *TH <<= MO(n *= -1);}TE IN DMods& DMods::OP++()NE{m_n < COants::g_M_minus?++m_n:m_n = 0;RE *TH;}TE IN DMods DMods::OP++(int)NE{DMods n{*TH};OP++();RE n;}TE IN DMods& DMods::OP--()NE{m_n == 0?m_n = COants::g_M_minus:--m_n;RE *TH;}TE IN DMods DMods::OP--(int)NE{DMods n{*TH};OP--();RE n;}DF_OF_CM_FOR_DMOD(==);DF_OF_CM_FOR_DMOD(!=);DF_OF_CM_FOR_DMOD(>);DF_OF_CM_FOR_DMOD(>=);DF_OF_CM_FOR_DMOD(<);DF_OF_CM_FOR_DMOD(<=);DF_OF_AR_FOR_DMOD(+,NE,n,+);DF_OF_AR_FOR_DMOD(-,NE,n.SignInvert(),+);DF_OF_AR_FOR_DMOD(*,NE,n,*);DF_OF_AR_FOR_DMOD(/,,n.Invert(),*);TE IN DMods DMods::OP^(ll EX)CO{RE MO(DMods(*TH)^= MO(EX));}TE IN DMods DMods::OP<<(ll n)CO{RE MO(DMods(*TH)<<= MO(n));}TE IN DMods