#ifndef INCLUDE_MODE #define INCLUDE_MODE /* #define SUBMIT_ONLY */ #define DEBUG_OUTPUT #endif #ifdef INCLUDE_MAIN VO Solve() { using MOD = DynamicMod; MOD::SetModulo( 998243353 ); vector factor = {443,2253371}; CIN( int , T , Tau ); FOREQ( t , 1 , Tau ){ CIN( int , N , M ); if( t == T ){ COUT( -1 ); } else { auto [a,val] = CombinationFactorialValuative( M , N , factor ); FOR( i , 0 , 2 ){ a *= PowerMemorisation( MOD::Derepresent( factor[i] ) , val[i] ); } COUT( a ); } } } 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。*/ #ifdef DEBUG #include "c:/Users/user/Documents/Programming/Mathematics/Combinatorial/Combination/a_Body.hpp" #else // - intやllの時はオーバーフローしうることに注意。 // - Modは法pが素数でないと/の計算が合わないことに注意。 // - DyamicModはSetModuloでis_prime=trueを渡した時のみ/がメモ化再帰でO(1)で計算され、 // 一般には/がユークリッドの互除法でO(log_2 n)で計算されることに注意。 // CombinationCumulativeProduct(n,m) 均しO(1)(nごとに合計O(min(m,n-m))) // CombinationCumulativeProductValuative(n,m,factor) 均しO(L)(前計算O(log n)、nごとに合計O(min(m,n-m)(L+log min(m,n-m)))) // CombinationFactorial(n,m) O(1)(前計算O(n)、n<=20) // CombinationFactorialValuative(n,m,factor) O(L)(前計算O(n(L+log n))) TE RET CombinationCumulativeProductRecursion(CO INT& n,CO INT& m,CO bool& reset){ST Map> memory{};auto& memory_n = memory[n];if(memory_n.empty()){memory_n.push_back(1);}INT SZ;WH((SZ = memory_n.SZ())<= m){memory_n.push_back(memory_n.back()*(n - SZ + 1)/ SZ);}if(reset){RET AN = memory_n[m];memory.erase(n);RE AN;}RE memory_n[m];}TE IN RET CombinationCumulativeProduct(CO INT1& n,INT2 m,CO bool& reset){CO INT1 m_copy = MO(m);RE m < 0 || n < m_copy?CombinationCumulativeProductRecursion(n,INT1{0},reset)- 1:CombinationCumulativeProductRecursion(n,min(m_copy,n - m_copy),reset);}TE IN pair> CombinationCumulativeProductValuativeRecursion(CO INT& n,CO INT& m,CO VEC& factor,CO bool& reset){ST CO int L = factor.SZ();AS(L == int(factor.SZ()));ST Map,VE>>> memory{};if(n < m){if(reset){memory.erase(n);}RE{MOD{0},VE(L)};}auto&[comb,EX]= memory[n];if(comb.empty()){comb.push_back(1);EX.push_back(VE(L));}INT SZ;WH((SZ = comb.SZ())<= m){MOD c = comb.back();VE e = EX.back();for(int num = 0;num < 2;num++){INT r = num == 0?n - SZ + 1:SZ;for(int i = 0;i < L;i++){auto& p = factor[i];WH(r % p == 0){r /= p;num == 0?++e[i]:--e[i];}}num == 0?c *= r:c /= r;}comb.push_back(MO(c));EX.push_back(MO(e));}if(reset){pair> AN{MO(comb[m]),MO(EX[m])};memory.erase(n);RE AN;}RE{comb[m],EX[m]};}TE IN pair> CombinationCumulativeProductValuative(CO INT1& n,INT2 m,CO VEC& factor,CO bool& reset){CO INT1 m_copy = MO(m);RE CombinationCumulativeProductValuativeRecursion(n,m < 0 || n < m_copy?n + 1:min(m_copy,n - m_copy),factor,reset);}TE INT CombinationFactorialRecursion(CO INT& n,CO INT& m){ST VE factorial{1};INT SZ;WH((SZ = factorial.SZ())<= n){factorial.push_back(factorial.back()* SZ);}RE factorial[n]/ factorial[m]/ factorial[n-m];}TE IN INT1 CombinationFactorial(CO INT1& n,INT2 m){AS(((is_same_v || is_same_v)&& n <= 12)||((is_same_v || is_same_v)&& n <= 20));CO INT1 m_copy = MO(m);RE m < 0 || n < m_copy?INT1(0):CombinationFactorialRecursion(n,m_copy);}TE pair> CombinationFactorialValuativeRecursion(CO INT1& n,CO VE& m,CO VEC& factor){ST CO int L = factor.SZ();AS(L == int(factor.SZ()));if(m.empty()){RE{MOD{1},VE(L)};}CO INT1 sum = Sum(m);if(n < sum || Min(m)< 0){RE{MOD{0},VE(L)};}ST VE factorial{1};ST VE factorial_inv{1};ST VE EX(1,VE(L));INT1 SZ;WH((SZ = factorial.SZ())<= n){VE e = EX.back();for(int i = 0;i < L;i++){auto& p = factor[i];WH(SZ % p == 0){SZ /= p;e[i]++;}}factorial.push_back(factorial.back()* SZ);factorial_inv.push_back(factorial_inv.back()/ SZ);EX.push_back(MO(e));}MOD f = factorial[n];VE e = EX[n];CO int M = m.SZ();for(int j = 0;j <= M;j++){CO int k = j < M?INT1(m[j]):n - sum;f *= factorial_inv[k];auto& denom = EX[k];for(int i = 0;i < L;i++){e[i]-= denom[i];}}RE{MO(f),MO(e)};}TE IN pair> CombinationFactorialValuative(CO INT1& n,CO VE m,CO VEC& factor){RE CombinationFactorialValuativeRecursion(n,m,factor);}TE IN pair> CombinationFactorialValuative(CO INT1& n,INT2 m,CO VEC& factor){RE CombinationFactorialValuativeRecursion(n,VE{MO(m)},factor);} // PrimeEnumeration: // val_limit = 316 ≒ sqrt(1e5) -> length = 65 // val_limit = 448 ≒ sqrt(2e5) -> length = 86 // val_limit = 1e5 -> length = 9592 // val_limit = 1e6 -> length = 78498 // nの素因数分解:PrimeFactorisation(CO PE/LD& pe,CO INT& n) O(√n/log n)/O(log n) // nの素羃への分解:PrimePowerFactorisation(CO PE/LD& pe,CO int& n) O(√n/log n)/O(log n) TE CL PrimeEnumeration{PU:bool m_is_composite[val_limit];int m_val[le_max];int m_le;CE PrimeEnumeration();IN CRI OP[](CRI i)CO;CE CRI Get(CRI i)CO;CE CO bool& IsComposite(CRI n)CO;CE CRI length()CO NE;}; TE CE PrimeEnumeration::PrimeEnumeration():m_is_composite(),m_val(),m_le(0){for(int i = 2;i < val_limit;i++){if(! m_is_composite[i]){for(ll j = ll(i)* i;j < val_limit;j += i){m_is_composite[j]= true;}m_val[m_le++]= i;if(m_le >= le_max){break;}}}}TE IN CRI PrimeEnumeration::OP[](CRI i)CO{AS(0 <= i && i < m_le);RE m_val[i];}TE CE CRI PrimeEnumeration::Get(CRI i)CO{RE m_val[i];}TE CE CO bool& PrimeEnumeration::IsComposite(CRI n)CO{RE m_is_composite[n];}TE CE CRI PrimeEnumeration::length()CO NE{RE m_le;} CL HeapPrimeEnumeration{PU:int m_val_limit;VE m_is_composite;VE m_val;int m_le;IN HeapPrimeEnumeration(CRI val_limit);IN CRI OP[](CRI i)CO;IN CRI Get(CRI i)CO;IN bool IsComposite(CRI n)CO;IN CRI length()CO NE;}; IN HeapPrimeEnumeration::HeapPrimeEnumeration(CRI val_limit):m_val_limit(val_limit),m_is_composite(m_val_limit),m_val(),m_le(0){for(int i = 2;i < m_val_limit;i++){if(! m_is_composite[i]){for(ll j = ll(i)* i;j < val_limit;j += i){m_is_composite[j]= true;}m_val.push_back(i);}}m_le = m_val.SZ();}IN CRI HeapPrimeEnumeration::OP[](CRI i)CO{AS(0 <= i && i < m_le);RE m_val[i];}IN CRI HeapPrimeEnumeration::Get(CRI i)CO{RE OP[](i);}IN bool HeapPrimeEnumeration::IsComposite(CRI n)CO{AS(0 <= n && n < m_val_limit);RE m_is_composite[n];}IN CRI HeapPrimeEnumeration::length()CO NE{RE m_le;} TE auto CheckPE(CO PE& pe)-> decltype(pe.IsComposite(0),true_type());TE false_type CheckPE(...);TE CE bool IsPE = decltype(CheckPE(declval()))(); TE CL LeastDivisor{PU:int m_val[val_limit];CE LeastDivisor()NE;IN CRI OP[](CRI i)CO;CE CRI Get(CRI i)CO;CE int length()CO NE;}; TE CE LeastDivisor::LeastDivisor()NE:m_val{}{for(int d = 2;d < val_limit;d++){if(m_val[d]== 0){for(int n = d;n < val_limit;n += d){m_val[n]== 0?m_val[n]= d:d;}}}}TE IN CRI LeastDivisor::OP[](CRI i)CO{AS(0 <= i && i < val_limit);RE m_val[i];}TE CE CRI LeastDivisor::Get(CRI i)CO{RE m_val[i];}TE CE int LeastDivisor::length()CO NE{RE val_limit;} CL HeapLeastDivisor{PU:int m_val_limit;VE m_val;IN HeapLeastDivisor(CRI val_limit)NE;IN CRI OP[](CRI i)CO;IN CRI Get(CRI i)CO;IN CRI length()CO NE;}; IN HeapLeastDivisor::HeapLeastDivisor(CRI val_limit)NE:m_val_limit(val_limit),m_val(m_val_limit){for(int d = 2;d < m_val_limit;d++){if(m_val[d]== 0){for(int n = d;n < m_val_limit;n += d){m_val[n]== 0?m_val[n]= d:d;}}}}IN CRI HeapLeastDivisor::OP[](CRI i)CO{AS(0 <= i && i < m_val_limit);RE m_val[i];}IN CRI HeapLeastDivisor::Get(CRI i)CO{RE m_val[i];}IN CRI HeapLeastDivisor::length()CO NE{RE m_val_limit;} TE auto PrimeFactorisation(CO PE& pe,INT n)-> enable_if_t,pair,VE>>{AS(n > 0);VE P{};VE E{};CRI le = pe.length();for(int i = 0;i < le;i++){auto& p = pe[i];if(n % p == 0){int e = 1;WH((n /= p)% p == 0){e++;}P.push_back(p);E.push_back(e);}else if(n / p < p){break;}}if(n != 1){P.push_back(n);E.push_back(1);}RE{MO(P),MO(E)};}TE auto PrimeFactorisation(CO LD& ld,int n)-> enable_if_t,pair,VE>>{AS(n > 0);VE P{};VE E{};if(n > 1){P.push_back(ld[n]);E.push_back(1);n /= ld[n];}WH(n > 1){if(P.back()!= ld[n]){P.push_back(ld[n]);E.push_back(1);}else{E.back()++;}n /= ld[n];}RE{MO(P),MO(E)};}TE auto PrimePowerFactorisation(CO PE& pe,INT n)-> enable_if_t,tuple,VE,VE>>{AS(n > 0);VE P{};VE E{};VE Q{};CRI le = pe.length();for(int i = 0;i < le;i++){auto& p = pe[i];if(n % p == 0){int e = 1;INT q = p;WH((n /= p)% p == 0){e++;q *= p;}P.push_back(p);E.push_back(e);Q.push_back(q);}else if(n / p < p){break;}}if(n != 1){P.push_back(n);E.push_back(1);Q.push_back(n);}RE{MO(P),MO(E),MO(Q)};}TE auto PrimePowerFactorisation(CO LD& ld,int n)-> enable_if_t,tuple,VE,VE>>{AS(n > 0);VE P{};VE E{};VE Q{};if(n > 1){P.push_back(ld[n]);E.push_back(1);Q.push_back(ld[n]);n /= ld[n];}WH(n > 1){if(P.back()!= ld[n]){P.push_back(ld[n]);E.push_back(1);Q.push_back(ld[n]);}else{Q.back()*= ld[n];E.back()++;}n /= ld[n];}RE{MO(P),MO(E),MO(Q)};}TE bool IsPrime(CO PE& pe,CO INT& n){auto& L = pe.length();for(int i = 0;i < L && pe[i]* INT(pe[i])<= n;i++){if(n % pe[i]== 0){RE false;}}RE n > 1;} #endif #ifdef DEBUG #include "c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/DynamicModulo/Debug/a_Body.hpp" #else 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 CL DynamicMods;TE CL COantsForDynamicMods{PU:COantsForDynamicMods()= 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 COantsForDynamicMods::g_M = 0;TE uint COantsForDynamicMods::g_memory_le = 0;TE uint COantsForDynamicMods::g_M_minus = -1;TE bool COantsForDynamicMods::g_M_is_prime = false; #define SFINAE_FOR_DMOD enable_if_t>>* #define DC_OF_CM_FOR_DYNAMIC_MOD(OPR)IN bool OP OPR(CO DynamicMods& n)CO NE #define DC_OF_AR_FOR_DYNAMIC_MOD(OPR,EX)IN DynamicMods OP OPR(DynamicMods n)CO EX; #define DF_OF_CM_FOR_DYNAMIC_MOD(OPR)TE IN bool DynamicMods::OP OPR(CO DynamicMods& n)CO NE{RE m_n OPR n.m_n;} #define DF_OF_AR_FOR_DYNAMIC_MOD(OPR,EX,LEFT,OPR2)TE IN DynamicMods DynamicMods::OP OPR(DynamicMods n)CO EX{RE MO(LEFT OPR2 ## = *TH);}TE IN DynamicMods OP OPR(T n0,CO DynamicMods& n1)EX{RE MO(DynamicMods(MO(n0))OPR ## = n1);} TE CL DynamicMods{PU:uint m_n;IN DynamicMods()NE;IN DynamicMods(CO DynamicMods& n)NE;IN DynamicMods(DynamicMods&& n)NE;TE IN DynamicMods(T n)NE;IN DynamicMods& OP=(DynamicMods n)NE;IN DynamicMods& OP+=(CO DynamicMods& n)NE;IN DynamicMods& OP-=(CO DynamicMods& n)NE;IN DynamicMods& OP*=(CO DynamicMods& n)NE;IN DynamicMods& OP/=(DynamicMods n);IN DynamicMods& OP^=(ll EX);IN DynamicMods& OP<<=(ll n);IN DynamicMods& OP>>=(ll n);IN DynamicMods& OP++()NE;IN DynamicMods OP++(int)NE;IN DynamicMods& OP--()NE;IN DynamicMods OP--(int)NE;DC_OF_CM_FOR_DYNAMIC_MOD(==);DC_OF_CM_FOR_DYNAMIC_MOD(!=);DC_OF_CM_FOR_DYNAMIC_MOD(<);DC_OF_CM_FOR_DYNAMIC_MOD(<=);DC_OF_CM_FOR_DYNAMIC_MOD(>);DC_OF_CM_FOR_DYNAMIC_MOD(>=);DC_OF_AR_FOR_DYNAMIC_MOD(+,NE);DC_OF_AR_FOR_DYNAMIC_MOD(-,NE);DC_OF_AR_FOR_DYNAMIC_MOD(*,NE);DC_OF_AR_FOR_DYNAMIC_MOD(/,);IN DynamicMods OP^(ll EX)CO;IN DynamicMods OP<<(ll n)CO;IN DynamicMods OP>>(ll n)CO;IN DynamicMods OP-()CO NE;IN VO swap(DynamicMods& n)NE;IN CRUI RP()CO NE;ST IN DynamicMods DeRP(uint n)NE;ST IN CO DynamicMods& Factorial(CRL n);ST IN CO DynamicMods& FactorialInverse(CRL n);ST IN DynamicMods Combination(CRL n,CRL i);ST IN CO DynamicMods& zero()NE;ST IN CO DynamicMods& one()NE;ST IN CRUI GetModulo()NE;ST IN VO SetModulo(CRUI M,CO bool& M_is_prime = false)NE;IN DynamicMods& SignInvert()NE;IN DynamicMods& Invert();IN DynamicMods& PPW(ll EX)NE;IN DynamicMods& NNPW(ll EX)NE;ST IN CO DynamicMods& Inverse(CRI n);ST IN CO DynamicMods& TwoPower(CRI n);ST IN CO DynamicMods& TwoPowerInverse(CRI n);US COants = COantsForDynamicMods;}; US DynamicMod = DynamicMods<0>; TE IN DynamicMods::DynamicMods()NE:m_n(){}TE IN DynamicMods::DynamicMods(CO DynamicMods& n)NE:m_n(n.m_n){}TE IN DynamicMods::DynamicMods(DynamicMods&& n)NE:m_n(MO(n.m_n)){}TE TE IN DynamicMods::DynamicMods(T n)NE:m_n(Residue(MO(n),COants::g_M)){}TE IN DynamicMods& DynamicMods::OP=(DynamicMods n)NE{m_n = MO(n.m_n);RE *TH;}TE IN DynamicMods& DynamicMods::OP+=(CO DynamicMods& n)NE{(m_n += n.m_n)< COants::g_M?m_n:m_n -= COants::g_M;RE *TH;}TE IN DynamicMods& DynamicMods::OP-=(CO DynamicMods& n)NE{m_n < n.m_n?(m_n += COants::g_M)-= n.m_n:m_n -= n.m_n;RE *TH;}TE IN DynamicMods& DynamicMods::OP*=(CO DynamicMods& n)NE{m_n = Residue(MO(ull(m_n)* n.m_n),COants::g_M);RE *TH;}TE IN DynamicMods& DynamicMods::OP/=(DynamicMods n){RE OP*=(n.Invert());}TE IN DynamicMods& DynamicMods::PPW(ll EX)NE{DynamicMods pw{*TH};EX--;WH(EX != 0){(EX & 1)== 1?*TH *= pw:*TH;EX >>= 1;pw *= pw;}RE *TH;}TE IN DynamicMods& DynamicMods::NNPW(ll EX)NE{RE EX == 0?(m_n = 1,*TH):PPW(MO(EX));}TE IN DynamicMods& DynamicMods::OP^=(ll EX){if(EX < 0){m_n = ModularInverse(COants::g_M,MO(m_n));EX *= -1;}RE NNPW(MO(EX));}TE IN DynamicMods& DynamicMods::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)):DynamicMods(2)^= MO(n);}TE IN DynamicMods& DynamicMods::OP>>=(ll n){RE *TH <<= MO(n *= -1);}TE IN DynamicMods& DynamicMods::OP++()NE{m_n < COants::g_M_minus?++m_n:m_n = 0;RE *TH;}TE IN DynamicMods DynamicMods::OP++(int)NE{DynamicMods n{*TH};OP++();RE n;}TE IN DynamicMods& DynamicMods::OP--()NE{m_n == 0?m_n = COants::g_M_minus:--m_n;RE *TH;}TE IN DynamicMods DynamicMods::OP--(int)NE{DynamicMods n{*TH};OP--();RE n;}DF_OF_CM_FOR_DYNAMIC_MOD(==);DF_OF_CM_FOR_DYNAMIC_MOD(!=);DF_OF_CM_FOR_DYNAMIC_MOD(>);DF_OF_CM_FOR_DYNAMIC_MOD(>=);DF_OF_CM_FOR_DYNAMIC_MOD(<);DF_OF_CM_FOR_DYNAMIC_MOD(<=);DF_OF_AR_FOR_DYNAMIC_MOD(+,NE,n,+);DF_OF_AR_FOR_DYNAMIC_MOD(-,NE,n.SignInvert(),+);DF_OF_AR_FOR_DYNAMIC_MOD(*,NE,n,*);DF_OF_AR_FOR_DYNAMIC_MOD(/,,n.Invert(),*);TE IN DynamicMods DynamicMods::OP^(ll EX)CO{RE MO(DynamicMods(*TH)^= MO(EX));}TE IN DynamicMods DynamicMods::OP<<(ll n)CO{RE MO(DynamicMods(*TH)<<= MO(n));}TE IN DynamicMods DynamicMods::OP>>(ll n)CO{RE MO(DynamicMods(*TH)>>= MO(n));}TE IN DynamicMods DynamicMods::OP-()CO NE{RE MO(DynamicMods(*TH).SignInvert());}TE IN DynamicMods& DynamicMods::SignInvert()NE{m_n > 0?m_n = COants::g_M - m_n:m_n;RE *TH;}TE IN DynamicMods& DynamicMods::Invert(){m_n = COants::g_M_is_prime && m_n < COants::g_memory_le?Inverse(int(m_n)).m_n:ModularInverse(COants::g_M,MO(m_n));RE *TH;}TE IN VO DynamicMods::swap(DynamicMods& n)NE{std::swap(m_n,n.m_n);}TE IN CO DynamicMods& DynamicMods::Inverse(CRI n){if(COants::g_M == 1){RE zero();}AS(COants::g_M_is_prime && 0 < n && n < int(COants::g_memory_le));ST VE> memory ={zero(),one()};ST int le_curr = 2;WH(le_curr <= n){memory.push_back(DeRP(COants::g_M - memory[COants::g_M % le_curr].m_n * ull(COants::g_M / le_curr)% COants::g_M));le_curr++;}RE memory[n];}TE IN CO DynamicMods& DynamicMods::TwoPower(CRI n){if(COants::g_M == 1){RE zero();}AS(0 <= n && n < int(COants::g_memory_le));ST VE> memory ={one()};ST int le_curr = 1;WH(le_curr <= n){memory.push_back(memory.back()+ memory.back());le_curr++;}RE memory[n];}TE IN CO DynamicMods& DynamicMods::TwoPowerInverse(CRI n){if(COants::g_M == 1){RE zero();}AS(0 <= n && n < int(COants::g_memory_le));ST VE> memory ={one()};ST int le_curr = 1;WH(le_curr <= n){auto& m = memory.back().m_n;memory.push_back(DeRP(((m & 1)== 0?m:m + COants::g_M)>> 1));le_curr++;}RE memory[n];}TE IN CO DynamicMods& DynamicMods::Factorial(CRL n){AS(0 <= n);if(ll(COants::g_M)<= n){RE zero();}ST VE> memory ={one(),one()};ST int le_curr = 2;WH(le_curr <= n && memory.back().m_n != 0){memory.push_back(memory.back()* DeRP(le_curr));le_curr++;}RE le_curr <= n?memory.back():memory[n];}TE IN CO DynamicMods& DynamicMods::FactorialInverse(CRL n){AS(0 <= n && n < COants::g_M);ST VE> memory ={one(),one()};ST int le_curr = 2;WH(le_curr <= n){memory.push_back(memory[le_curr - 1]* Inverse(le_curr));le_curr++;}RE memory[n];}TE IN DynamicMods DynamicMods::Combination(CRL n,CRL i){RE 0 <= i && i <= n?Factorial(n)* FactorialInverse(i)* FactorialInverse(n - i):zero();}TE IN CRUI DynamicMods::RP()CO NE{RE m_n;}TE IN DynamicMods DynamicMods::DeRP(uint n)NE{DynamicMods n_copy{};n_copy.m_n = MO(n);RE n_copy;}TE IN CO DynamicMods& DynamicMods::zero()NE{ST CO DynamicMods z{};RE z;}TE IN CO DynamicMods& DynamicMods::one()NE{ST CO DynamicMods o{1};RE o;}TE IN CRUI DynamicMods::GetModulo()NE{RE COants::g_M;}TE IN VO DynamicMods::SetModulo(CRUI M,CO bool& M_is_prime)NE{COants::g_M = M;COants::g_memory_le = M < COants::g_memory_bound?M:COants::g_memory_bound;;COants::g_M_minus = M - 1;COants::g_M_is_prime = M_is_prime;}TE IN DynamicMods Inverse(CO DynamicMods& n){RE MO(DynamicMods(n).Invert());}TE IN DynamicMods Power(DynamicMods n,ll EX){RE MO(n ^= MO(EX));}TE IN VO swap(DynamicMods& n0,DynamicMods& n1)NE{n0.swap(n1);}TE IN IS& OP>>(IS& is,DynamicMods& n){ll m;is >> m;n = m;RE is;}TE IN OS& OP<<(OS& os,CO DynamicMods& n){RE os << n.RP();} TE INT1 GCD(CO INT1& b_0,CO INT2& b_1){INT1 a_0 = b_0 < 0?-b_0:b_0;INT1 a_1 = b_1 < 0?-b_1:b_1;WH(a_1 != 0){swap(a_0 %= a_1,a_1);}RE a_0;}TE IN INT1 LCM(CO INT1& b_0,CO INT2& b_1){RE(b_0 == 0 && b_1 == 0)?0:(b_0 / GCD(b_0,b_1))* b_1;} #ifndef DF_OF_HASH_FOR_MOD #define DF_OF_HASH_FOR_MOD(MOD)IN size_t hash::OP()(CO MOD& n)CO{ST CO hash h;RE h(n.RP());} #endif TE DC_OF_HASH(DynamicMods); TE DF_OF_HASH_FOR_MOD( DynamicMods ); #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 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 ); 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){S.erase(t);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);} #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 = decltype(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);} /* 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;} /* ConstexprModulo (7KB)*/ CEXPR(uint,P,998244353); #define RP Represent #define DeRP Derepresent TE CE INT Residue(INT n)NE{RE MO(n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n < INT(M)?n:n %= M);}TE CE INT& ResidueP(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 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 Mod;TE CL COantsForMod{PU:COantsForMod()= delete;ST CE CO uint g_memory_bound = 2e6;ST CE CO uint g_memory_le = M < g_memory_bound?M:g_memory_bound;ST CE uint g_M_minus = M - 1;ST CE int g_order = M - 1;ST CE int g_order_minus = g_order - 1;}; #define SFINAE_FOR_MOD enable_if_t>>* #define DC_OF_CM_FOR_MOD(OPR)CE bool OP OPR(CO Mod& n)CO NE #define DC_OF_AR_FOR_MOD(OPR,EX)CE Mod OP OPR(Mod n)CO EX; #define DF_OF_CM_FOR_MOD(OPR)TE CE bool Mod::OP OPR(CO Mod& n)CO NE{RE m_n OPR n.m_n;} #define DF_OF_AR_FOR_MOD(OPR,EX,LEFT,OPR2)TE CE Mod Mod::OP OPR(Mod n)CO EX{RE MO(LEFT OPR2 ## = *TH);}TE CE Mod OP OPR(T n0,CO Mod& n1)EX{RE MO(Mod(MO(n0))OPR ## = n1);} TE CL Mod{PU:uint m_n;CE Mod()NE;CE Mod(CO Mod& n)NE;CE Mod(Mod&& n)NE;TE CE Mod(T n)NE;CE Mod& OP=(Mod n)NE;CE Mod& OP+=(CO Mod& n)NE;CE Mod& OP-=(CO Mod& n)NE;CE Mod& OP*=(CO Mod& n)NE;IN Mod& OP/=(Mod n);CE Mod& OP^=(ll EX);CE Mod& OP<<=(ll n);CE Mod& OP>>=(ll n);CE Mod& OP++()NE;CE Mod OP++(int)NE;CE Mod& OP--()NE;CE Mod 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(+,NE);DC_OF_AR_FOR_MOD(-,NE);DC_OF_AR_FOR_MOD(*,NE);DC_OF_AR_FOR_MOD(/,);CE Mod OP^(ll EX)CO;CE Mod OP<<(ll n)CO;CE Mod OP>>(ll n)CO;CE Mod OP-()CO NE;CE VO swap(Mod& n)NE;CE CRUI RP()CO NE;ST CE Mod DeRP(uint n)NE;ST IN CO Mod& Factorial(CRL n);ST IN CO Mod& FactorialInverse(CRL n);ST IN Mod Combination(CRL n,CRL i);ST IN CO Mod& zero()NE;ST IN CO Mod& one()NE;ST CE uint GetModulo()NE;CE Mod& SignInvert()NE;IN Mod& Invert();CE Mod& PPW(ll EX)NE;CE Mod& NNPW(ll EX)NE;ST IN CO Mod& Inverse(CRI n);ST IN CO Mod& TwoPower(CRI n);ST IN CO Mod& TwoPowerInverse(CRI n);US COants = COantsForMod;}; US MP = Mod

; TE CE Mod::Mod()NE:m_n(){}TE CE Mod::Mod(CO Mod& n)NE:m_n(n.m_n){}TE CE Mod::Mod(Mod&& n)NE:m_n(MO(n.m_n)){}TE TE CE Mod::Mod(T n)NE:m_n(Residue(MO(n))){}TE CE Mod& Mod::OP=(Mod n)NE{m_n = MO(n.m_n);RE *TH;}TE CE Mod& Mod::OP+=(CO Mod& n)NE{(m_n += n.m_n)< M?m_n:m_n -= M;RE *TH;}TE CE Mod& Mod::OP-=(CO Mod& n)NE{m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n;RE *TH;}TE CE Mod& Mod::OP*=(CO Mod& n)NE{m_n = MO(ull(m_n)* n.m_n)% M;RE *TH;}TE <> CE MP& MP::OP*=(CO MP& n)NE{ull m_n_copy = m_n;m_n = MO((m_n_copy *= n.m_n)< P?m_n_copy:ResidueP(m_n_copy));RE *TH;}TE IN Mod& Mod::OP/=(Mod n){RE OP*=(n.Invert());}TE CE Mod& Mod::PPW(ll EX)NE{Mod pw{*TH};EX--;WH(EX != 0){(EX & 1)== 1?*TH *= pw:*TH;EX >>= 1;pw *= pw;}RE *TH;}TE CE Mod& Mod::NNPW(ll EX)NE{RE EX == 0?(m_n = 1,*TH):PPW(MO(EX));}TE CE Mod& Mod::OP^=(ll EX){if(EX < 0){m_n = ModularInverse(M,MO(m_n));EX *= -1;}RE NNPW(MO(EX));}TE CE Mod& Mod::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)):Mod(2)^= MO(n);}TE CE Mod& Mod::OP>>=(ll n){RE *TH <<= MO(n *= -1);}TE CE Mod& Mod::OP++()NE{m_n < COants::g_M_minus?++m_n:m_n = 0;RE *TH;}TE CE Mod Mod::OP++(int)NE{Mod n{*TH};OP++();RE n;}TE CE Mod& Mod::OP--()NE{m_n == 0?m_n = COants::g_M_minus:--m_n;RE *TH;}TE CE Mod Mod::OP--(int)NE{Mod 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(+,NE,n,+);DF_OF_AR_FOR_MOD(-,NE,n.SignInvert(),+);DF_OF_AR_FOR_MOD(*,NE,n,*);DF_OF_AR_FOR_MOD(/,,n.Invert(),*);TE CE Mod Mod::OP^(ll EX)CO{RE MO(Mod(*TH)^= MO(EX));}TE CE Mod Mod::OP<<(ll n)CO{RE MO(Mod(*TH)<<= MO(n));}TE CE Mod Mod::OP>>(ll n)CO{RE MO(Mod(*TH)>>= MO(n));}TE CE Mod Mod::OP-()CO NE{RE MO(Mod(*TH).SignInvert());}TE CE Mod& Mod::SignInvert()NE{m_n > 0?m_n = M - m_n:m_n;RE *TH;}TE IN Mod& Mod::Invert(){m_n = m_n < COants::g_memory_le?Inverse(int(m_n)).m_n:ModularInverse(M,MO(m_n));RE *TH;}TE CE VO Mod::swap(Mod& n)NE{std::swap(m_n,n.m_n);}TE IN CO Mod& Mod::Inverse(CRI n){AS(0 < n && n < int(COants::g_memory_le));ST VE> memory ={zero(),one()};ST int le_curr = 2;WH(le_curr <= n){memory.push_back(DeRP(M - memory[M % le_curr].m_n * ull(M / le_curr)% M));le_curr++;}RE memory[n];}TE IN CO Mod& Mod::TwoPower(CRI n){AS(0 <= n && n < int(COants::g_memory_le));ST VE> memory ={one()};ST int le_curr = 1;WH(le_curr <= n){memory.push_back(memory.back()+ memory.back());le_curr++;}RE memory[n];}TE IN CO Mod& Mod::TwoPowerInverse(CRI n){AS(0 <= n && n < int(COants::g_memory_le));ST VE> memory ={one()};ST int le_curr = 1;WH(le_curr <= n){auto& m = memory.back().m_n;memory.push_back(DeRP(((m & 1)== 0?m:m + M)>> 1));le_curr++;}RE memory[n];}TE IN CO Mod& Mod::Factorial(CRL n){AS(n >= 0);if(ll(M)<= n){RE zero();}ST VE> memory ={one(),one()};ST int le_curr = 2;WH(le_curr <= n){memory.push_back(memory[le_curr - 1]* le_curr);le_curr++;}RE memory[n];}TE IN CO Mod& Mod::FactorialInverse(CRL n){AS(0 <= n && n < ll(M));ST VE> memory ={one(),one()};ST int le_curr = 2;WH(le_curr <= n){memory.push_back(memory[le_curr - 1]* Inverse(le_curr));le_curr++;}RE memory[n];}TE IN Mod Mod::Combination(CRL n,CRL i){RE 0 <= i && i <= n?Factorial(n)* FactorialInverse(i)* FactorialInverse(n - i):zero();}TE CE CRUI Mod::RP()CO NE{RE m_n;}TE CE Mod Mod::DeRP(uint n)NE{Mod n_copy{};n_copy.m_n = MO(n);RE n_copy;}TE IN CO Mod& Mod::zero()NE{ST CE CO Mod z{};RE z;}TE IN CO Mod& Mod::one()NE{ST CE CO Mod o{1};RE o;}TE CE uint Mod::GetModulo()NE{RE M;}TE IN Mod Inverse(CO Mod& n){RE MO(Mod(n).Invert());}TE CE Mod Power(Mod n,ll EX){RE MO(n ^= MO(EX));}TE CE VO swap(Mod& n0,Mod& n1)NE{n0.swap(n1);}TE IN string to_string(CO Mod& n)NE{RE to_string(n.RP())+ " + " + to_string(M)+ "Z";}TE IN IS& OP>>(IS& is,Mod& n){ll m;is >> m;n = m;RE is;}TE IN OS& OP<<(OS& os,CO Mod& n){RE os << n.RP();} #define DF_OF_HASH_FOR_MOD(MOD)IN size_t hash::OP()(CO MOD& n)CO{ST CO hash h;RE h(n.RP());} TE DC_OF_HASH(Mod);TE DF_OF_HASH_FOR_MOD(Mod); /* Iteration (3KB) */ #define SPECIALSATION_OF_AR_PROGRESSION_SUM(TYPE)TE <> IN TYPE ArithmeticProgressionSum(CO TYPE& l,CO TYPE& r,CO TYPE& d){RE SpecialisedArithmeticProgressionSum(l,r,d);} TE TY V,TY OPR> T LeftConnectiveProd(T t,CO V& f,OPR opr){for(auto& u:f){t = opr(MO(t),u);}RE MO(t);}TE TY V> IN T Sum(T t,CO V& f){RE LeftConnectiveProd(MO(t),f,[](T t0,CO U& u1){RE MO(t0 += u1);});}TE TY V> IN T Sum(CO V& f){RE Sum(T{},f);}TE TY V> IN T Prod(T t,CO V& f){RE LeftConnectiveProd(MO(t),f,[](T t0,CO U& u1){RE MO(t0 *= u1);});}TE TY V> IN T Prod(CO V& f){RE Prod(T{1},f);}TE IN T& SetMax(T& t){RE t;}TE IN T& SetMax(T& t0,CO U& u1,CO Args&... args){RE SetMax(t0 < u1?t0 = u1:t0,args...);}TE IN T& SetMin(T& t){RE t;}TE IN T& SetMin(T& t0,CO U& u1,CO Args&... args){RE SetMin(u1 < t0?t0 = u1:t0,args...);}TE TY V> IN CO T& Max(CO V& f){RE *max_element(f.BE(),f.EN());}TE IN T Max(T t0,CO U& t1,CO Args&... args){RE MO(SetMax(t0,t1,args...));}TE TY V> IN CO T& Min(CO V& f){RE *min_element(f.BE(),f.EN());}TE IN T Min(T t0,CO U& t1,CO Args&... args){RE MO(SetMin(t0,t1,args...));}TE T Power(CO T& t,CO UINT& EX,T init = 1){RE EX > 1?Power(t * t,EX >> 1,MO(EX & 1?init *= t:init)):MO(EX > 0?init *= t:(AS(EX == 0),init));}TE IN T PowerMemorisation(CO T& t,CRI EX){AS(EX >= 0);ST Map> memory{};auto& AN = memory[t];if(AN.empty()){AN.push_back(1);}WH(int(AN.SZ())<= EX){AN.push_back(AN.back()* t);}RE AN[EX];}TE IN INT ArithmeticProgressionSum(CO INT& l,CO INT& r,CO INT& d = 1){RE(l + r)*(r - l + 1)/ 2;}TE IN INT SpecialisedArithmeticProgressionSum(CO INT& l,CO INT& r,CO INT& d){AS(l - 1 <= r);CO INT c =(r - l)/ d;RE l - 1 == r?0:(c & 1)== 0?(c + 1)*(l + d *(c >> 1)):((c + 1)>> 1)*((l << 1)+ d * c);} SPECIALSATION_OF_AR_PROGRESSION_SUM(int); SPECIALSATION_OF_AR_PROGRESSION_SUM(uint); SPECIALSATION_OF_AR_PROGRESSION_SUM(ll); SPECIALSATION_OF_AR_PROGRESSION_SUM(ull); TE IN INT ArithmeticProgressionSum(CO INT& r){RE ArithmeticProgressionSum(INT{},r);}TE IN T GeometricProgressionSum(T rate,UINT EX_max,CO T& init = 1){T rate_minus = rate - 1;RE rate_minus == 0?init * ++EX_max:(Power(MO(rate),MO(++EX_max))- 1)/ MO(rate_minus)* init;}TE T GeometricProgressionLinearCombinationSum(VE rate,VE EX_max,CO VE& init){CO int SZ = init.SZ();AS(int(rate.SZ())== SZ && int(EX_max.SZ())== SZ);T AN{};for(int i = 0;i < SZ;i++){AN += GeometricProgressionSum(MO(rate[i]),MO(EX_max[i]),init[i]);}RE AN;} /* Sqrt (1KB) */ TE INT RoundDownSqrt(CO INT& n){ST_AS(is_same_v || is_same_v || is_same_v || is_same_v);AS(n >= 0);if(n <= 1){RE n;}CE INT r_max = is_same_v?46341:is_same_v?65536:is_same_v?3037000500:4294967296;INT l = 1,r = min(r_max,n);WH(l < r - 1){CO INT m =(l + r)>> 1;(m <= n / m?l:r)= m;}RE l;}TE INT RoundUpSqrt(CO INT& n){ST_AS(is_same_v || is_same_v || is_same_v || is_same_v);AS(n >= 0);if(n <= 2){RE n;}CE INT r_max = is_same_v?46341:is_same_v?65536:is_same_v?3037000500:4294967296;CO INT n_minus = n - 1;INT l = 1,r = min(r_max,n);WH(l + 1 < r){CO INT m =(l + r)>> 1;(m <= n_minus / m?l:r)= m;}RE r;}TE bool IsSquare(CO INT& n){CO INT r = RoundDownSqrt(n);RE n == r * r;} /* Loop (1KB)*/ TE bool NextLoop(CRI SZ,CO VE& lower_bound,CO VE& upper_limit,VE& index){int depth = 0;WH(depth < SZ){if(++index[depth]< upper_limit[depth]){break;}index[depth]= lower_bound[depth];depth++;}RE depth < SZ;}TE bool NextLoop(CO VE& lower_bound,CO VE& upper_limit,VE& index){RE NextLoop(index.SZ(),lower_bound,upper_limit,index);}TE bool NextLoopEq(CRI SZ,CO VE& lower_bound,CO VE& upper_bound,VE& index){int depth = 0;WH(depth < SZ){if(++index[depth]<= upper_bound[depth]){break;}index[depth]= lower_bound[depth];depth++;}RE depth < SZ;}TE bool NextLoopEq(CO VE& lower_bound,CO VE& upper_bound,VE& index){RE NextLoopEq(index.SZ(),lower_bound,upper_bound,index);} /* string (1KB)*/ TE IN char IntToChar(CO INT& i,CO char& c = 'a'){RE c + i;}TE IN INT CharToInt(CO char& i){RE i -(i < 'a'?'A':'a');}TE string ArrayToString(CO VE& A,CO char& c = 'a'){CO int N = A.SZ();string S(N,c);for(int i = 0;i < N;i++){S[i]= IntToChar(A[i],c);}RE S;}TE VE StringToArray(CO string& S){CO int N = S.SZ();VE A(N);for(int i = 0;i < N;i++){A[i]= CharToInt(S[i]);}RE A;}TE string ArrayToParenthesisString(CO VE& A){CO int N = A.SZ();string S(N,'(');for(int i = 0;i < N;i++){AS(0 <= A[i]&& A[i]<= 1);S[i]= "()"[A[i]];}RE S;}TE VE ParenthesisStringToArray(CO string& S){CO int N = S.SZ();VE A(N);for(int i = 0;i < N;i++){A[i]= S[i]- '(';}RE A;} #endif /* AAA 常設ライブラリは以上に挿入する。*/ #define INCLUDE_LIBRARY #include __FILE__ #endif /* INCLUDE_LIBRARY */ #endif /* INCLUDE_SUB */ #endif /* INCLUDE_MAIN */