#ifndef INCLUDE_MODE
#define INCLUDE_MODE
/* #define SUBMIT_ONLY */
#define DEBUG_OUTPUT
#endif
#ifdef INCLUDE_MAIN
VO Solve()
{
CEXPR( int , p , 998243353 );
using MOD = Mod
;
vector factor = {443,2253371};
int euler = ( factor[0] - 1 ) * ( factor[1] - 1 );
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 , euler );
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
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 = false){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,CRI euler,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:euler == -1?c /= r:c *= Power(MOD{r},euler - 1);}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,CRI euler,CO bool& reset = false){CO INT1 m_copy = MO(m);RE CombinationCumulativeProductValuativeRecursion(n,m < 0 || n < m_copy?n + 1:min(m_copy,n - m_copy),factor,euler,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,CRI euler){ST CO int L = factor.SZ();AS(L == int(factor.SZ()));if(m.empty()){RE{MOD{1},VE(L)};}CO INT1 sum = Sum(INT1(0),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(euler == -1?factorial_inv.back()/ SZ:factorial_inv.back()* Power(MOD{SZ},euler - 1));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,CRI euler){RE CombinationFactorialValuativeRecursion(n,m,factor,euler);}TE IN pair> CombinationFactorialValuative(CO INT1& n,INT2 m,CO VEC& factor,CRI euler){RE CombinationFactorialValuativeRecursion(n,VE{MO(m)},factor,euler);}
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 tuple,VE> EulerFunction_Body(PF pf,CO INT& n){auto[P,E]= pf(n);INT AN = n;for(auto& p:P){AN -= AN / p;}RE{AN,MO(P),MO(E)};}TE IN tuple,VE> EulerFunction(CO PE& pe,CO INT& n){RE EulerFunction_Body([&](CRI i){RE PrimeFactorisation(pe,i);},n);}TE VE TotalEulerFunction(CO PE& pe,CO INT& n_max){VE AN(n_max + 1);for(INT n = 1;n <= n_max;n++){AN[n]= n;}auto quotient = AN;CRI le = pe.length();for(int i = 0;i < le;i++){auto& p_i = pe[i];INT n = 0;WH((n += p_i)<= n_max){INT& AN_n = AN[n];INT& quotient_n = quotient[n];AN_n -= AN_n / p_i;WH((quotient_n /= p_i)% p_i == 0){}}}for(INT n = le == 0?2:pe[le - 1];n <= n_max;n++){CO INT& quotient_n = quotient[n];if(quotient_n != 1){INT& AN_n = AN[n];AN_n -= AN_n / quotient_n;}}RE AN;}
#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