#ifdef INCLUDE_MAIN ATT inline void Solve() { CIN( uint , N , M ); if( N == 0 ){ RETURN( "0 1" ); } const MNP& zero = PO::CO_zero(); const MNP& one = PO::CO_one(); const MNP two = one + one; TRPO x{ 3 * N + 2 , PO( 1 , one ) }; TRPO R{ 3 * N + 1 }; FOR( i , 0 , M ){ cin >> R[i]; } R /= x * x - one; R = Integral( R ); TRPO eR{ Exp( R ) }; TRPO G{ 2 * N + 2 , eR * x }; Shift( G , one ); assert( G.SZ() <= 2 * N + 2 ); G = MoeviusComposition( 3 * N + 2 , G , -two , zero , one , one ); assert( G.SZ() <= 3 * N + 2 ); FOR( i , 0 , 3 * N + 2 ){ G[i] *= PW( MNP::DeRP( i * 2 ) , N ); } G = MoeviusComposition( 3 * N + 2 , G , -one , zero , one , two ); assert( G.SZ() <= 3 * N + 2 ); Shift( G , -one ); assert( G.SZ() <= 3 * N + 2 ); G /= eR; FOREQ( i , 0 , N + 1 ){ cout << G[i] << " \n"[i==N+1]; } } REPEAT_MAIN(1); #else // INCLUDE_MAIN #ifdef INCLUDE_SUB inline void Experiment() {} inline void SmallTest() {} #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。 TE CL PW_CE{PU:T m_val[EX_lim];IN CE PW_CE(CO T& t);};TE CE PW_CE::PW_CE(CO T& t):m_val(){T PW{t};for(uint EX = EX_lim - 1;EX + 1 > 0;EX--){m_val[EX]= -PW;m_val[EX]*= PW *= PW;}} #define PS_FOR_FFT(MOD,LE,BORDER,PR,IPR)TE <> CE CO uint LimitOfPWForFFT > = LE - 1;TE <> CE CO uint LimitOfPWForFFT > = LimitOfPWForFFT >;TE <> CE CO uint BorderForFFT > = BORDER;TE <> CE CO uint BorderForFFT > = BorderForFFT >;TE <> IN CO Mod(&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT >]{ST CE PW_CE,LimitOfPWForFFT > > PRT{PR};static_assert(PRT.m_val[0] == Mod::DeRP(1));RE PRT.m_val;}TE <> IN CO Mod(&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT >]{ST CE PW_CE,LimitOfPWForFFT > > IPRT{IPR};static_assert(IPRT.m_val[0]== Mod::DeRP(1) && (Mod::DeRP(PR)*= Mod::DeRP(IPR))==Mod::DeRP(1));RE IPRT.m_val;}TE <> IN CO MN(&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT >]{ST CE PW_CE ,LimitOfPWForFFT > > PRT{PR};RE PRT.m_val;}TE <> IN CO MN(&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT >]{ST CE PW_CE,LimitOfPWForFFT > > IPRT{IPR};RE IPRT.m_val;} TE CE CO uint LimitOfPWForFFT{};TE CE CO uint BorderForFFT{};TE IN CO T(&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT];TE IN CO T(&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT]; PS_FOR_FFT(998244353,24,4,31,128805723);PS_FOR_FFT(167772161,26,4,17,29606852);PS_FOR_FFT(469762049,27,4,30,15658735);PS_FOR_FFT(754974721,25,4,362,415027540); TE VO CooleyTukey(VE& f,CRUI N_input_start,CRUI N_input_lim,CRUI N_output_start,CRUI N_output_lim,CRUI two_PW,CRUI EX,CO T(&PRT)[LimitOfPWForFFT]) { CO uint LE = two_PW + N_input_start + N_output_start;f.reserve(LE);WH(f.SZ()< LE){f.push_back(0);}ST VE bit_reverse[32]={VE(1)};ST uint e_next = 1;ST uint two_PW_next = 1;ST uint two_PW_next2 = 2;ST VE* p_bit_reverse_prev = bit_reverse;ST VE* p_bit_reverse_curr = p_bit_reverse_prev + 1;WH(e_next <= EX){*p_bit_reverse_curr = VE(two_PW_next2);uint* p_bit_reverse_curr_i = &((*p_bit_reverse_curr)[0]);uint* p_bit_reverse_curr_i_plus = p_bit_reverse_curr_i + two_PW_next;uint* p_bit_reverse_prev_i = &((*p_bit_reverse_prev)[0]);for(uint i = 0;i < two_PW_next;i++){(*(p_bit_reverse_curr_i_plus++)= *(p_bit_reverse_curr_i++)= *(p_bit_reverse_prev_i++)* 2)+= 1;}e_next++;swap(two_PW_next,two_PW_next2);two_PW_next2 *= 4;p_bit_reverse_prev++;p_bit_reverse_curr++;}CO VE& bit_reverse_EX = bit_reverse[EX];uint bit_num = 0;CO uint* p_bit_num_reverse = &(bit_reverse_EX[bit_num]);WH(bit_num < two_PW){if(*p_bit_num_reverse < bit_num){swap(f[*p_bit_num_reverse + N_input_start],f[bit_num + N_input_start]);}bit_num++;p_bit_num_reverse++;} CO T& one = PRT[0]; T zeta,diff; uint i,j,j_lim,two_PW_curr = 1,two_PW_curr_2 = 2; WH(two_PW_curr < two_PW){ const uint N_input_start_plus = N_input_start + two_PW_curr; bit_num = 0; i = 0; zeta = one; WH(i < two_PW){ j = i; j_lim = i + two_PW_curr; WH(j < j_lim){ diff = f[j + N_input_start] - f[j + N_input_start_plus]; f[j + N_input_start] += f[j + N_input_start_plus]; f[j + N_input_start_plus] = zeta * diff; j++; } bit_num++; i += two_PW_curr_2; zeta *= PRT[__builtin_popcount((bit_num&-bit_num)-1)+1]; } two_PW_curr <<= 1; two_PW_curr_2 <<= 1; } CO uint LE_fixed = N_output_lim + N_input_start; WH(f.SZ()> LE_fixed){ f.pop_back(); } for(uint i = 0;i < N_output_start;i++){ f[N_input_start + i]= 0; } RE; } TE IN VO FFT(VE& f,CRUI N_input_start,CRUI N_input_lim,CRUI two_PW,CRUI EX){CooleyTukey(f,N_input_start,N_input_lim,0,two_PW,two_PW,EX,PrimitiveRootOfTwoForFFT());}TE IN VO FFT(VE& f,CRUI N_input_start,CRUI N_input_lim,CRUI N_output_start,CRUI N_output_lim,CRUI two_PW,CRUI EX){CooleyTukey(f,N_input_start,N_input_lim,N_output_start,N_output_lim,two_PW,EX,PrimitiveRootOfTwoForFFT());}TE IN VO IFFT(VE& f,CRUI N_input_start,CRUI N_input_lim,CRUI two_PW,CO T& two_PW_inv,CRUI EX){CooleyTukey(f,N_input_start,N_input_lim,0,two_PW,two_PW,EX,InversePrimitiveRootOfTwoForFFT());CO uint SZ = two_PW + N_input_start;for(uint i = N_input_start;i < SZ;i++){f[i]*= two_PW_inv;}}TE IN VO IFFT(VE& f,CRUI N_input_start,CRUI N_input_lim,CRUI N_output_start,CRUI N_output_lim,CRUI two_PW,CO T& two_PW_inv,CRUI EX){CooleyTukey(f,N_input_start,N_input_lim,N_output_start,N_output_lim,two_PW,EX,InversePrimitiveRootOfTwoForFFT());CO uint SZ = N_output_lim + N_input_start;for(uint i = N_output_start + N_input_start;i < SZ;i++){f[i]*= two_PW_inv;}} #define SFINAE_FOR_PO(DEFAULT)TY Arg,enable_if_t >::value>* DEFAULT #define DF_BODY_OF_PS_OF_MU_OF_PO_PROTH_MOD(TYPE,ARG,RHS)TE <> PO& PO::OP*=(ARG f){if(m_SZ != 0){VE v{};v.swap(m_f);TRPO TH_copy{m_SZ + f.m_SZ - 1,MO(v)};TH_copy *= RHS;m_f = MO(TH_copy.PO::m_f);m_SZ = m_f.SZ();}RE *TH;} TE CL PO{PU:VE m_f;uint m_SZ;PU:IN PO();IN PO(CO T& t);IN PO(T&& t);TE IN PO(CO Arg& n);IN PO(CO PO& f);IN PO(PO&& f);IN PO(CRUI i,CO T& t);IN PO(CRUI i,T&& t);TE IN PO(CRUI i,CO Arg& n);IN PO(CO VE& f);IN PO(VE&& f);IN PO& OP=(CO T& t);IN PO& OP=(T&& t);TE IN PO& OP=(CO Arg& n);IN PO& OP=(CO PO& f);IN PO& OP=(PO&& f);IN PO& OP=(CO VE& f);IN PO& OP=(VE&& f);IN CO T& OP[](CRUI i)CO;IN T& OP[](CRUI i);IN T OP()(CO T& t)CO;PO& OP+=(CO PO& f);PO& OP-=(CO PO& f);PO& OP*=(CO PO& f);PO& OP*=(PO&& f);PO& OP/=(CO T& t);IN PO& OP/=(CO PO& f);PO& OP%=(CO T& t);PO& OP%=(CO PO& f);IN PO OP-()CO;IN CO VE& GetCoefficient()CO NE;IN CRUI SZ()CO NE;IN VO reSZ(CRUI deg_plus)NE;IN VO swap(PO& f);IN VO swap(VE& f);VO ReMORedundantZero();IN string Display()CO NE;ST PO Quotient(CO PO& f0,CO PO& f1);ST PO Transpose(CO PO& f,CRUI f_transpose_SZ);ST IN CO PO& zero();ST IN CO PO& one();ST IN CO T& CO_zero();ST IN CO T& CO_one();ST IN CO T& CO_minus_one();}; #define RE_ZERO_FOR_MU_FOR_TR_PO_IF(CONDITION)if(CONDITION){RE OP=(zero);} #define RE_ZERO_FOR_TR_MU_CO_FOR_TR_PO_IF(CONDITION)if(CONDITION){RE TRPO(m_N);} #define RE_ZERO_FOR__FOR_TR_PO_IF(MU,CONDITION)RE_ZERO_FOR_ ## MU ## _FOR_TR_PO_IF(CONDITION) #define SET_VE_FOR_AN_OF_MU_FOR_TR_PO(N_OUTPUT_LIM)if(PO::m_SZ < N_OUTPUT_LIM){for(uint i = PO::m_SZ;i < N_OUTPUT_LIM;i++){PO::m_f.push_back(0);}PO::m_SZ = N_OUTPUT_LIM;} #define SET_VE_FOR_AN_OF_TR_MU_CO_FOR_TR_PO(N_OUTPUT_LIM)VE AN(N_OUTPUT_LIM) #define SET_VE_FOR_AN_OF__FOR_TR_PO(MU,N_OUTPUT_LIM)SET_VE_FOR_AN_OF_ ## MU ## _FOR_TR_PO(N_OUTPUT_LIM) #define SET_SUM_OF_MU_FOR_TR_PO PO::m_f[i]= sum #define SET_SUM_OF_TR_MU_CO_FOR_TR_PO AN[i]= sum #define SET_SUM_OF__FOR_TR_PO(MU)SET_SUM_OF_ ## MU ## _FOR_TR_PO #define SET_N_INPUT_START_FOR_MU_FOR_TR_PO(F,SZ,N_INPUT_START_NUM)uint N_INPUT_START_NUM{};for(uint i = 0;i < SZ && searching;i++){if(F[i]!= zero){N_INPUT_START_NUM = i;searching = false;}} #define SET_N_INPUT_MAX_FOR_MU_FOR_TR_PO(F,SZ,N_INPUT_MAX_NUM)uint N_INPUT_MAX_NUM{};searching = true;for(uint i =(SZ)- 1;searching;i--){if(F[i]!= zero){N_INPUT_MAX_NUM = i;searching = false;}} #define CN_FOR_MU_FOR_TR_PO(J_MIN)CO uint j_max = i < N_input_max_0_start_1?i - N_input_start_1:N_input_max_0;T sum{zero};for(uint j = J_MIN;j <= j_max;j++){sum += PO::m_f[j]* f.PO::m_f[i - j];}PO::m_f[i]= sum; #define CN_FOR_TR_MU_CO_FOR_TR_PO(J_MIN)CO uint j_max = i < N_input_max_0_start_1?i - N_input_start_1:N_input_max_0;T& m_fi = AN[i];for(uint j = J_MIN;j <= j_max;j++){m_fi += PO::m_f[j]* f.PO::m_f[i - j];} #define CN_FOR__FOR_TR_PO(MU,J_MIN)CN_FOR_ ## MU ## _FOR_TR_PO(J_MIN) #define ZEROIFICATION_FOR_MU_FOR_TR_PO for(uint i = 0;i < N_input_start_0_start_1;i++){PO::m_f[i]= 0;} #define ZEROIFICATION_FOR_TR_MU_CO_FOR_TR_PO CRUI N_output_start_fixed = N_output_start < N_input_start_0_start_1?N_output_start:N_input_start_0_start_1;for(uint i = 0;i < N_output_start_fixed;i++){AN[i]= 0;} #define ZEROIFICATION_FOR__FOR_TR_PO(MU)ZEROIFICATION_FOR_ ## MU ## _FOR_TR_PO #define DF_0_OF__FOR_TR_PO(MU,ACCESS_ENTRY,N_OUTPUT_START)RE_ZERO_FOR__FOR_TR_PO_IF(MU,PO::m_SZ == 0);uint N_output_max = PO::m_SZ + f.PO::m_SZ - 2;if(N_output_max >= m_N){N_output_max = m_N - 1;}CO uint N_output_lim = N_output_max + 1;SET_VE_FOR_AN_OF__FOR_TR_PO(MU,N_output_lim);for(uint i = N_output_max;searching;i--){T sum{zero};for(uint j = 0;j <= i;j++){sum += ACCESS_ENTRY * f.PO::OP[](i - j);}SET_SUM_OF__FOR_TR_PO(MU);searching = i > N_OUTPUT_START;} #define DF_1_OF__FOR_TR_PO(MU)SET_N_INPUT_START_FOR_MU_FOR_TR_PO(PO::m_f,PO::m_SZ,N_input_start_0);RE_ZERO_FOR__FOR_TR_PO_IF(MU,searching);searching = true;SET_N_INPUT_START_FOR_MU_FOR_TR_PO(f,f.PO::m_SZ,N_input_start_1); #define SET_N_INPUT_RANGE SET_N_INPUT_MAX_FOR_MU_FOR_TR_PO(PO::m_f,PO::m_SZ,N_input_max_0);SET_N_INPUT_MAX_FOR_MU_FOR_TR_PO(f,f.PO::m_SZ < m_N?f.PO::m_SZ:m_N,N_input_max_1);CO uint N_input_max_0_max_1 = N_input_max_0 + N_input_max_1;CO uint N_input_start_0_start_1 = N_input_start_0 + N_input_start_1;uint N_output_lim_fixed = N_input_max_0_max_1 < m_N?N_input_max_0_max_1 + 1:m_N; #define DF_3_OF__FOR_TR_PO(MU)CO uint N_input_start_0_max_1 = N_input_start_0 + N_input_max_1;CO uint N_input_max_0_start_1 = N_input_max_0 + N_input_start_1;CO uint N_output_max_fixed = N_output_lim_fixed - 1;SET_VE_FOR_AN_OF__FOR_TR_PO(MU,N_output_lim_fixed);for(uint i = N_output_max_fixed;i > N_input_start_0_max_1;i--){CN_FOR__FOR_TR_PO(MU,i - N_input_max_1);}searching = true;for(uint i = N_input_start_0_max_1 < N_output_max_fixed?N_input_start_0_max_1:N_output_max_fixed;searching;i--){CN_FOR__FOR_TR_PO(MU,N_input_start_0);searching = i > N_input_start_0_start_1;}ZEROIFICATION_FOR__FOR_TR_PO(MU); #define SET_SHIFTED_VE_FOR_MU(V,F,I_START,I_MAX,I_SHIFT)VE V(product_LE);for(uint i = I_START;i <= I_MAX;i++){V[I_SHIFT + i]= F[i];} #define DF_OF_MU_FOR_TR_PO(RE_LINE_0,RE_LINE_1,RE_LINE_2,RE_LINE_3,RE_LINE_4,MU,ACCESS_ENTRY,N_OUTPUT_START,FIX_N_OUTPUT_LIM)CE CRUI border_0 = FFT_MU_border_0;CO T& zero = PO::CO_zero();bool searching = true;if(PO::m_SZ < border_0 && f.PO::m_SZ < border_0){RE_LINE_0;DF_0_OF__FOR_TR_PO(MU,ACCESS_ENTRY,N_OUTPUT_START);RE_LINE_1;}DF_1_OF__FOR_TR_PO(MU);RE_LINE_2;SET_N_INPUT_RANGE;FIX_N_OUTPUT_LIM;RE_LINE_3;DF_3_OF__FOR_TR_PO(MU);RE_LINE_4; #define DF_OF_FFT_MU_FOR_TR_PO(RE_LINE_0,RE_LINE_1,RE_LINE_2,RE_LINE_3,RE_LINE_4,RE_LINE_5,MU,ACCESS_ENTRY,N_OUTPUT_START,N_OUTPUT_START_SHIFTED,FIX_N_OUTPUT_LIM,DC_OF_F0,N_INPUT_START_0,N_INPUT_LIM_0,DC_OF_F1,N_INPUT_START_1,N_INPUT_LIM_1,VE_FOR_IFFT,RESZ_VE_FOR_IFFT,I_START,MU_FORMULA,SET_AN)CE CRUI border_0 = FFT_MU_border_0;CO T& zero = PO::CO_zero();bool searching = true;if(PO::m_SZ < border_0 && f.PO::m_SZ < border_0){RE_LINE_0;DF_0_OF__FOR_TR_PO(MU,ACCESS_ENTRY,N_OUTPUT_START);RE_LINE_1;}DF_1_OF__FOR_TR_PO(MU);RE_LINE_2;SET_N_INPUT_RANGE;FIX_N_OUTPUT_LIM;RE_LINE_3;CO uint N_input_TR_deg_0_deg_1 = N_input_max_0 - N_input_start_0 + N_input_max_1 - N_input_start_1;CE CRUI border_1 = FFT_MU_border_1;if(N_input_TR_deg_0_deg_1 < border_1){DF_3_OF__FOR_TR_PO(MU);RE_LINE_4;}uint two_PW = FFT_MU_border_1_2;uint EX = FFT_MU_border_1_2_EX;T two_PW_inv{FFT_MU_border_1_2_inv};WH(N_input_TR_deg_0_deg_1 >= two_PW){two_PW *= 2;two_PW_inv /= 2;EX++;}CO uint product_LE = N_input_start_0_start_1 + two_PW;DC_OF_F0;DC_OF_F1;FFT(f0,N_INPUT_START_0,N_INPUT_LIM_0,two_PW,EX);FFT(f1,N_INPUT_START_1,N_INPUT_LIM_1,two_PW,EX);RESZ_VE_FOR_IFFT;for(uint i = I_START + two_PW - 1;i + 1 > I_START;i--){MU_FORMULA;}CO uint N_output_lim_shifted = N_output_lim_fixed - N_input_start_0_start_1;uint N_output_start_shifted = N_OUTPUT_START_SHIFTED;if(N_output_start_shifted > N_output_lim_shifted){N_output_start_shifted = N_output_lim_shifted; }IFFT(VE_FOR_IFFT,N_input_start_0_start_1,product_LE,N_output_start_shifted,N_output_lim_shifted,two_PW,two_PW_inv,EX);SET_AN;RE_LINE_5; #define DF_OF_INVERSE_FOR_TR_PO(TYPE,RECURSION)CRUI N = f.GetTruncation();uint PW;uint PW_2 = 1;TRPO< TYPE > f_inv{PW_2,PO< TYPE >::CO_one()/ f[0]};WH(PW_2 < N){PW = PW_2;PW_2 *= 2;f_inv.SetTruncation(PW_2);RECURSION;}f_inv.SetTruncation(N);RE f_inv #define DF_OF_EXP_FOR_TR_PO(TYPE,RECURSION)assert(f[0]== PO< TYPE >::CO_zero());CRUI N = f.GetTruncation();uint PW;uint PW_2 = 1;TRPO< TYPE > f_exp{PW_2,PO< TYPE >::CO_one()};WH(PW_2 < N){PW = PW_2;PW_2 *= 2;f_exp.SetTruncation(PW_2);RECURSION;}f_exp.SetTruncation(N);RE f_exp #define DF_OF_PS_OF_MU_OF_TR_PO(TYPE,BORDER_0,BORDER_1,BORDER_1_2,BORDER_1_2_EX,BORDER_1_2_INV)TE <> CE CO uint FFT_MU_border_0< TYPE > = BORDER_0;TE <> CE CO uint FFT_MU_border_1< TYPE > = BORDER_1;static_assert(FFT_MU_border_0< TYPE > <= FFT_MU_border_1< TYPE >);TE <> CE CO uint FFT_MU_border_1_2< TYPE > = BORDER_1_2;static_assert(FFT_MU_border_1< TYPE > < FFT_MU_border_1_2< TYPE > && FFT_MU_border_1_2< TYPE > <= FFT_MU_border_1< TYPE > * 2 );TE <> CE CO uint FFT_MU_border_1_2_EX< TYPE > = BORDER_1_2_EX;static_assert(FFT_MU_border_1_2< TYPE > == 1 << FFT_MU_border_1_2_EX< TYPE > );TE <> CE CO uint FFT_MU_border_1_2_inv< TYPE > = BORDER_1_2_INV;static_assert((TYPE::DeRP(FFT_MU_border_1_2< TYPE >)*= TYPE::DeRP(FFT_MU_border_1_2_inv< TYPE >))== TYPE::DeRP(1));TE <> IN TRPO< TYPE >& TRPO< TYPE >::OP*=(CO PO< TYPE >& f){RE TRPO< TYPE >::FFT_MU(f);}TE <> IN TRPO< TYPE >& TRPO< TYPE >::OP*=(PO< TYPE >&& f){RE TRPO< TYPE >::FFT_MU(MO(f));}TE <> TRPO< TYPE > Inverse(CO TRPO< TYPE >& f){DF_OF_INVERSE_FOR_TR_PO(TYPE,f_inv.TRMinus(f_inv.FFT_TRMU_CO(f,PW,PW_2).FFT_TRMU(f_inv,PW,PW_2),PW,PW_2));}TE <> TRPO< TYPE > Exp(CO TRPO< TYPE >& f){DF_OF_EXP_FOR_TR_PO(TYPE,f_exp.TRMinus((TRIntegral(Differential(f_exp).FFT_TRMU_CO(Inverse(f_exp),PW - 1,PW_2),PW).TRMinus(f,PW,PW_2)).FFT_TRMU(f_exp,PW,PW_2),PW,PW_2));} #define DF_OF_PS_OF_MU_OF_PO_PROTH_MOD(MOD,BORDER_1_2_INV)DF_OF_PS_OF_MU_OF_TR_PO(Mod,17,512,1024,10,BORDER_1_2_INV);DF_OF_PS_OF_MU_OF_TR_PO(MN,17,512,1024,10,BORDER_1_2_INV);DF_BODY_OF_PS_OF_MU_OF_PO_PROTH_MOD(Mod,CO PO >&,TH == &f?TH_copy:f);DF_BODY_OF_PS_OF_MU_OF_PO_PROTH_MOD(Mod,PO >&&,MO(f));DF_BODY_OF_PS_OF_MU_OF_PO_PROTH_MOD(MN,CO PO >&,TH == &f?TH_copy:f);DF_BODY_OF_PS_OF_MU_OF_PO_PROTH_MOD(MN,PO >&&,MO(f)); TE CL TRPO :PU PO{PU:uint m_N;PU:IN TRPO(CRUI N = 0);IN TRPO(CO TRPO& f);IN TRPO(TRPO&& f);IN TRPO(CRUI N,CO T& t);IN TRPO(CRUI N,CO PO& f);IN TRPO(CRUI N,PO&& f);IN TRPO(CRUI N,CRUI i,CO T& t);IN TRPO(CRUI N,CRUI i,T&& t);TE IN TRPO(CRUI N,CRUI i,CO Arg& t);IN TRPO(CRUI N,VE&& f);IN TRPO& OP=(CO TRPO& f);IN TRPO& OP=(TRPO&& f);IN TRPO& OP=(CO T& t);IN TRPO& OP=(T&& t);TE IN TRPO& OP=(CO Arg& n);IN TRPO& OP=(CO PO& f);IN TRPO& OP=(PO&& f);IN TRPO& OP+=(CO T& t);IN TRPO& OP+=(CO PO& f);IN TRPO& OP+=(CO TRPO& f);TRPO& TRPlus(CO PO& f,CRUI N_input_start,CRUI N_input_limit);IN TRPO& OP-=(CO T& t);IN TRPO& OP-=(CO PO& f);IN TRPO& OP-=(CO TRPO& f);TRPO& TRMinus(CO PO& f,CRUI N_input_start,CRUI N_input_limit);IN TRPO& OP*=(CO T& t);TRPO& OP*=(CO PO& f);IN TRPO& OP*=(PO&& f);TRPO& FFT_MU(CO PO& f);TRPO& TRMU(CO PO& f,CRUI N_output_start,CRUI N_output_lim);TRPO& FFT_TRMU(CO PO& f,CRUI N_output_start,CRUI N_output_lim);TRPO& FFT_TRMU(PO&& f,CRUI N_output_start,CRUI N_output_lim);TRPO TRMU_CO(CO PO& f,CRUI N_output_start,CRUI N_output_lim)CO;TRPO FFT_TRMU_CO(CO PO& f,CRUI N_output_start,CRUI N_output_lim)CO;TRPO FFT_TRMU_CO(PO&& f,CRUI N_output_start,CRUI N_output_lim)CO;IN TRPO& OP/=(CO T& t);IN TRPO& OP/=(CO TRPO& t);IN TRPO& OP%=(CO T& t);IN TRPO OP-()CO;IN VO SetTruncation(CRUI N)NE;IN CRUI GetTruncation()CO NE;IN TRPO& TruncateInitial(CRUI N)NE;IN TRPO& TruncateFinal(CRUI N)NE;};TE CE CO uint FFT_MU_border_0 = 17;TE CE CO uint FFT_MU_border_1{};TE CE CO uint FFT_MU_border_1_2{};TE CE CO uint FFT_MU_border_1_2_EX{};TE CE CO uint FFT_MU_border_1_2_inv{}; TE IN TRPO::TRPO(CRUI N):PO(),m_N(N){}TE IN TRPO::TRPO(CO TRPO& f):PO(f),m_N(f.m_N){}TE IN TRPO::TRPO(TRPO&& f):PO(MO(f)),m_N(MO(f.m_N)){}TE IN TRPO::TRPO(CRUI N,CO T& t):PO(t),m_N(N){}TE IN TRPO::TRPO(CRUI N,CO PO& f):PO(),m_N(N){PO::m_SZ = f.PO::m_SZ < m_N?f.PO::m_SZ:m_N;PO::m_f = VE(PO::m_SZ);for(uint i = 0;i < PO::m_SZ;i++){PO::m_f[i]= f.PO::m_f[i];}}TE IN TRPO::TRPO(CRUI N,PO&& f):PO(),m_N(N){if(f.PO::m_SZ < m_N * 2){PO::OP=(MO(f));if(f.PO::m_SZ > m_N){TruncateFinal(m_N);}}else{PO::m_f = VE(m_N);for(uint i = 0;i < m_N;i++){PO::m_f[i]= MO(f.PO::m_f[i]);}PO::m_SZ = m_N;}}TE IN TRPO::TRPO(CRUI N,CRUI i,CO T& t):PO(),m_N(N){if(i < m_N?t != PO::CO_zero():false){PO::OP[](i)= t;}}TE IN TRPO::TRPO(CRUI N,CRUI i,T&& t):PO(),m_N(N){if(i < m_N?t != PO::CO_zero():false){PO::OP[](i)= MO(t);}}TE TE IN TRPO::TRPO(CRUI N,CRUI i,CO Arg& n):TRPO(N,i,T(n)){}TE IN TRPO::TRPO(CRUI N,VE&& f):PO(),m_N(N){CO uint f_SZ = f.SZ();if(f_SZ < m_N * 2){PO::OP=(MO(f));if(f_SZ > m_N){TruncateFinal(m_N);}}else{PO::m_f = VE(m_N);for(uint i = 0;i < m_N;i++){PO::m_f[i]= MO(f[i]);}}} TE IN TRPO& TRPO::OP=(CO TRPO& f){PO::OP=(f);m_N = f.m_N;RE *TH;} TE IN TRPO& TRPO::OP=(TRPO&& f){PO::OP=(MO(f));m_N = MO(f.m_N);RE *TH;} TE IN TRPO& TRPO::OP=(CO T& t){PO::OP=(t);RE *TH;} TE IN TRPO& TRPO::OP=(T&& t){PO::OP=(MO(t));RE *TH;} TE TE IN TRPO& TRPO::OP=(CO Arg& n){PO::OP=(T(n));RE *TH;} TE IN TRPO& TRPO::OP=(CO PO& f){RE OP=(TRPO(m_N,f));} TE IN TRPO& TRPO::OP=(PO&& f){RE OP=(TRPO(m_N,MO(f)));} TE IN TRPO& TRPO::OP+=(CO T& t){PO::OP+=(t);RE *TH;}TE IN TRPO& TRPO::OP+=(CO PO& f){RE TRPlus(f,0,f.m_SZ);}TE IN TRPO& TRPO::OP+=(CO TRPO& f){RE m_N == 0?OP=(f):TRPlus(f,0,f.PO::m_SZ);}TE TRPO& TRPO::TRPlus(CO PO& f,CRUI N_input_start,CRUI N_input_lim){CRUI SZ = N_input_lim < m_N?N_input_lim < f.PO::m_SZ?N_input_lim:f.PO::m_SZ:m_N < f.PO::m_SZ?m_N:f.PO::m_SZ;if(PO::m_SZ < SZ){PO::m_f.reserve(SZ);for(uint i = N_input_start;i < PO::m_SZ;i++){PO::m_f[i]+= f.PO::m_f[i];}for(uint i = PO::m_SZ;i < SZ;i++){PO::m_f.push_back(f.PO::m_f[i]);}PO::m_SZ = SZ;}else{for(uint i = N_input_start;i < SZ;i++){PO::m_f[i]+= f.PO::m_f[i];}}RE *TH;}TE IN TRPO& TRPO::OP-=(CO T& t){PO::OP-=(t);RE *TH;}TE IN TRPO& TRPO::OP-=(CO PO& f){RE TRMinus(f,0,f.m_SZ);}TE IN TRPO& TRPO::OP-=(CO TRPO& f){RE m_N == 0?OP=(-f):TRMinus(f,0,f.PO::m_SZ);}TE TRPO& TRPO::TRMinus(CO PO& f,CRUI N_input_start,CRUI N_input_lim){CRUI SZ = N_input_lim < m_N?N_input_lim < f.PO::m_SZ?N_input_lim:f.PO::m_SZ:m_N < f.PO::m_SZ?m_N:f.PO::m_SZ;if(PO::m_SZ < SZ){PO::m_f.reserve(SZ);for(uint i = N_input_start;i < PO::m_SZ;i++){PO::m_f[i]-= f.PO::m_f[i];}for(uint i = PO::m_SZ;i < SZ;i++){PO::m_f.push_back(- f.PO::m_f[i]);}PO::m_SZ = SZ;}else{for(uint i = N_input_start;i < SZ;i++){PO::m_f[i]-= f.PO::m_f[i];}}RE *TH;}TE IN TRPO& TRPO::OP*=(CO T& t){PO::OP*=(t);RE *TH;}TE TRPO& TRPO::OP*=(CO PO& f){DF_OF_MU_FOR_TR_PO(RE_ZERO_FOR_MU_FOR_TR_PO_IF(f.PO::m_SZ == 0),RE *TH,RE_ZERO_FOR_MU_FOR_TR_PO_IF(searching),RE_ZERO_FOR_MU_FOR_TR_PO_IF(N_input_start_0_start_1 >= m_N),RE *TH,MU,PO::m_f[j],0,);}TE IN TRPO& TRPO::OP*=(PO&& f){RE OP*=(f);}TE TRPO& TRPO::FFT_MU(CO PO& f){DF_OF_FFT_MU_FOR_TR_PO(RE_ZERO_FOR_MU_FOR_TR_PO_IF(f.PO::m_SZ == 0),RE *TH,RE_ZERO_FOR_MU_FOR_TR_PO_IF(searching),RE_ZERO_FOR_MU_FOR_TR_PO_IF(N_input_start_0_start_1 >= N_output_lim_fixed),RE *TH,RE *TH,MU,PO::m_f[j],0,0,,VE& f0 = PO::m_f,N_input_start_0,N_input_max_0 + 1,SET_SHIFTED_VE_FOR_MU(f1,f.PO::m_f,N_input_start_1,N_input_max_1,N_input_start_0),N_input_start_0_start_1,N_input_start_0 + N_input_max_1 + 1,f1,,N_input_start_0,f1[N_input_start_1 + i]*= f0[i],OP=(TRPO(m_N,MO(f1))));}TE TRPO& TRPO::TRMU(CO PO& f,CRUI N_output_start,CRUI N_output_lim){DF_OF_MU_FOR_TR_PO(,RE *TH,,RE_ZERO_FOR_MU_FOR_TR_PO_IF(N_input_start_0_start_1 >= N_output_lim_fixed),RE *TH,MU,PO::m_f[j],N_output_start,if(N_output_lim_fixed > N_output_lim){N_output_lim_fixed = N_output_lim;});}TE TRPO& TRPO::FFT_TRMU(CO PO& f,CRUI N_output_start,CRUI N_output_lim){DF_OF_FFT_MU_FOR_TR_PO(,RE *TH,,RE_ZERO_FOR_MU_FOR_TR_PO_IF(N_input_start_0_start_1 >= N_output_lim_fixed),RE *TH,RE *TH,MU,PO::m_f[j],N_output_start,N_output_start < N_input_start_0_start_1?0:N_output_start - N_input_start_0_start_1,if(N_output_lim_fixed > N_output_lim){N_output_lim_fixed = N_output_lim;},VE& f0 = PO::m_f,N_input_start_0,N_input_max_0 + 1,SET_SHIFTED_VE_FOR_MU(f1,f.PO::m_f,N_input_start_1,N_input_max_1,N_input_start_0),N_input_start_0_start_1,N_input_start_0 + N_input_max_1 + 1,f1,,N_input_start_0,f1[N_input_start_1 + i]*= f0[i],OP=(TRPO(m_N,MO(f1))));}TE TRPO& TRPO::FFT_TRMU(PO&& f,CRUI N_output_start,CRUI N_output_lim){DF_OF_FFT_MU_FOR_TR_PO(,RE *TH,,RE_ZERO_FOR_MU_FOR_TR_PO_IF(N_input_start_0_start_1 >= N_output_lim_fixed),RE *TH,RE *TH,MU,PO::m_f[j],N_output_start,N_output_start < N_input_start_0_start_1?0:N_output_start - N_input_start_0_start_1,if(N_output_lim_fixed > N_output_lim){N_output_lim_fixed = N_output_lim;},VE& f0 = PO::m_f,N_input_start_0,N_input_max_0 + 1,VE&& f1 = MO(f.PO::m_f),N_input_start_1,N_input_max_1 + 1,f0,f0.reserve(product_LE),0,f1[N_input_start_0_start_1 + i]= f0[N_input_start_0 + i]* f1[N_input_start_1 + i],for(uint i = N_input_start_0;i < N_input_start_0_start_1;i++){f0[i]= 0;}PO::m_SZ = f0.SZ();SetTruncation(m_N););}TE TRPO TRPO::TRMU_CO(CO PO& f,CRUI N_output_start,CRUI N_output_lim)CO{DF_OF_MU_FOR_TR_PO(,RE TRPO(m_N,MO(AN)),,RE_ZERO_FOR_TR_MU_CO_FOR_TR_PO_IF(N_input_start_0_start_1 >= N_output_lim_fixed),RE TRPO(m_N,MO(AN)),TR_MU_CO,PO::OP[](j),N_output_start,if(N_output_lim_fixed > N_output_lim){N_output_lim_fixed = N_output_lim;});}TE TRPO TRPO::FFT_TRMU_CO(CO PO& f,CRUI N_output_start,CRUI N_output_lim)CO{DF_OF_FFT_MU_FOR_TR_PO(,RE TRPO(m_N,MO(AN)),,RE_ZERO_FOR_TR_MU_CO_FOR_TR_PO_IF(N_input_start_0_start_1 >= N_output_lim_fixed),RE TRPO(m_N,MO(AN)),RE TRPO(m_N,MO(f0)),TR_MU_CO,PO::OP[](j),N_output_start,N_output_start < N_input_start_0_start_1?0:N_output_start - N_input_start_0_start_1,if(N_output_lim_fixed > N_output_lim){N_output_lim_fixed = N_output_lim;},SET_SHIFTED_VE_FOR_MU(f0,PO::m_f,N_input_start_0,N_input_max_0,N_input_start_1),N_input_start_0_start_1,N_input_start_1 + N_input_max_0 + 1,VE f1 = f.PO::m_f,N_input_start_1,N_input_max_1 + 1,f0,,N_input_start_1,f0[N_input_start_0 + i]*= f1[i],);}TE TRPO TRPO::FFT_TRMU_CO(PO&& f,CRUI N_output_start,CRUI N_output_lim)CO{DF_OF_FFT_MU_FOR_TR_PO(,RE TRPO(m_N,MO(AN)),,RE_ZERO_FOR_TR_MU_CO_FOR_TR_PO_IF(N_input_start_0_start_1 >= N_output_lim_fixed),RE TRPO(m_N,MO(AN)),RE TRPO(m_N,MO(f0)),TR_MU_CO,PO::OP[](j),N_output_start,N_output_start < N_input_start_0_start_1?0:N_output_start - N_input_start_0_start_1,if(N_output_lim_fixed > N_output_lim){N_output_lim_fixed = N_output_lim;},SET_SHIFTED_VE_FOR_MU(f0,PO::m_f,N_input_start_0,N_input_max_0,N_input_start_1),N_input_start_0_start_1,N_input_start_1 + N_input_max_0 + 1,VE&& f1 = MO(f.PO::m_f),N_input_start_1,N_input_max_1 + 1,f0,,N_input_start_1,f0[N_input_start_0 + i]*= f1[i],);}TE IN TRPO& TRPO::OP/=(CO T& t){PO::OP/=(t);RE *TH;}TE IN TRPO& TRPO::OP/=(CO TRPO& f){RE OP*=(Inverse(m_N <= f.m_N?f:TRPO(m_N,f)));}TE IN TRPO& TRPO::OP%=(CO T& t){PO::OP%=(t);RE *TH;}TE IN TRPO TRPO::OP-()CO{RE MO(TRPO(m_N)-= *TH);}TE IN VO TRPO::SetTruncation(CRUI N)NE{if(N < m_N){TruncateFinal(N);}else{PO::m_f.reserve(N);}m_N = N;}TE IN CRUI TRPO::GetTruncation()CO NE{RE m_N;}TE IN TRPO& TRPO::TruncateInitial(CRUI N)NE{CRUI SZ = N < PO::m_SZ?N:PO::m_SZ;for(uint i = 0;i < SZ;i++){PO::m_f[i]= 0;}RE *TH;}TE IN TRPO& TRPO::TruncateFinal(CRUI N)NE{WH(PO::m_SZ > N){PO::m_f.pop_back();PO::m_SZ--;}RE *TH;}TE IN TRPO OP+(CO TRPO& f0,CO P& f1){RE MO(TRPO(f0)+= f1);}TE IN TRPO OP-(CO TRPO& f){RE MO(TRPO(f.GetTurncation())-= f);}TE IN TRPO OP-(CO TRPO& f0,CO P& f1){RE MO(TRPO(f0)-= f1);}TE IN TRPO OP*(CO TRPO& f0,CO P& f1){RE MO(TRPO(f0)*= f1);}TE IN TRPO OP/(CO TRPO& f0,CO P& f1){RE MO(TRPO(f0)/= f1);}TE IN TRPO OP%(CO TRPO& f0,CO T& t1){RE MO(TRPO(f0)%= t1);}TE TRPO Differential(CRUI n,CO TRPO& f){if(f.PO::m_SZ < n){RE TRPO(f.m_N - n,PO::zero());}VE df(f.PO::m_SZ - n);T coef = T::Factorial(n);uint i = n;WH(i < f.PO::m_SZ){df[i - n]= f[i]* coef;i++;(coef *= i)/=(i - n);}RE TRPO(f.m_N - n,MO(df));}TE TRPO TRDifferential(CO TRPO& f,CRUI N_output_start_plus_one){assert(f.m_N > 0);TRPO f_dif{f.m_N - 1};if(N_output_start_plus_one < f.PO::m_SZ){CO uint SZ = f.PO::m_SZ - 1;f_dif.PO::m_f = VE(SZ);for(uint i = N_output_start_plus_one;i < f.PO::m_SZ;i++){f_dif.PO::m_f[i-1]= f.PO::m_f[i]* i;}f_dif.PO::m_SZ = SZ;}RE f_dif;}TE IN TRPO Differential(CO TRPO& f){RE TRDifferential(f,1);}TE TRPO TRIntegral(CO TRPO& f,CRUI N_output_start){TRPO f_int{f.m_N + 1};if(N_output_start <= f.PO::m_SZ){CO uint SZ = f.PO::m_SZ + 1;f_int.PO::m_f = VE(SZ);for(uint i = N_output_start;i <= f.PO::m_SZ;i++){f_int.PO::m_f[i]= f.PO::m_f[i - 1]/ T(i);}f_int.PO::m_SZ = SZ;}RE f_int;}TE IN TRPO Integral(CO TRPO& f){RE TRIntegral(f,1);}TE TRPO Inverse(CO TRPO& f){DF_OF_INVERSE_FOR_TR_PO(T,f_inv.TRMinus(f_inv.TRMU_CO(f,PW,PW_2).TRMU(f_inv,PW,PW_2),PW,PW_2));}TE TRPO Exp(CO TRPO& f){DF_OF_EXP_FOR_TR_PO(T,f_exp.TRMinus((TRIntegral(Differential(f_exp).TRMU_CO(Inverse(f_exp),PW - 1,PW_2),PW).TRMinus(f,PW,PW_2)).TRMU(f_exp,PW),PW,PW_2));}TE IN TRPO Log(CO TRPO& f){assert(f[0]== PO::CO_one());RE Integral(Differential(f)/= f);} DF_OF_PS_OF_MU_OF_PO_PROTH_MOD(P,997269505); TE IN PO::PO():m_f(),m_SZ(0){}TE IN PO::PO(CO T& t):PO(){if(t != CO_zero()){OP[](0)= t;}}TE IN PO::PO(T&& t):PO(){if(t != CO_zero()){OP[](0)= MO(t);}}TE TE IN PO::PO(CO Arg& n):PO(T(n)){}TE IN PO::PO(CO PO& f):m_f(f.m_f),m_SZ(f.m_SZ){}TE IN PO::PO(PO&& f):m_f(MO(f.m_f)),m_SZ(MO(f.m_SZ)){}TE IN PO::PO(CRUI i,CO T& t):PO(){if(t != CO_zero()){OP[](i)= t;}}TE IN PO::PO(CRUI i,T&& t):PO(){if(t != CO_zero()){OP[](i)= MO(t);}}TE TE IN PO::PO(CRUI i,CO Arg& n):PO(i,T(n)){}TE IN PO::PO(CO VE& f):m_f(f),m_SZ(m_f.SZ()){}TE IN PO::PO(VE&& f):m_f(MO(f)),m_SZ(m_f.SZ()){}TE IN PO& PO::OP=(CO T& t){m_f.clear();m_SZ = 0;OP[](0)= t;RE *TH;}TE IN PO& PO::OP=(T&& t){m_f.clear();m_SZ = 0;OP[](0)= MO(t);RE *TH;}TE TE IN PO& PO::OP=(CO Arg& n){RE OP=(T(n));}TE IN PO& PO::OP=(CO PO& f){m_f = f.m_f;m_SZ = f.m_SZ;RE *TH;}TE IN PO& PO::OP=(PO&& f){m_f = MO(f.m_f);m_SZ = MO(f.m_SZ);RE *TH;}TE IN PO& PO::OP=(CO VE& f){m_f = f;m_SZ = f.m_SZ;RE *TH;}TE IN PO& PO::OP=(VE&& f){m_f = MO(f);m_SZ = m_f.SZ();RE *TH;}TE CO T& PO::OP[](CRUI i)CO{if(m_SZ <= i){RE CO_zero();}RE m_f[i];}TE IN T& PO::OP[](CRUI i){if(m_SZ <= i){CO T& z = CO_zero();WH(m_SZ <= i){m_f.push_back(z);m_SZ++;}}RE m_f[i];}TE IN T PO::OP()(CO T& t)CO{RE MO((*TH %(PO(1,CO_one())- t))[0]);}TE PO& PO::OP+=(CO PO& f){for(uint i = 0;i < f.m_SZ;i++){OP[](i)+= f.m_f[i];}RE *TH;}TE PO& PO::OP-=(CO PO& f){for(uint i = 0;i < f.m_SZ;i++){OP[](i)-= f.m_f[i];}RE *TH;}TE PO& PO::OP*=(CO PO& f){if(m_SZ == 0){RE *TH;}if(f.m_SZ == 0){m_f.clear();m_SZ = 0;RE *TH;}CO uint SZ = m_SZ + f.m_SZ - 1;PO product{};for(uint i = 0;i < SZ;i++){T& product_i = product[i];CO uint j_min = m_SZ <= i?i - m_SZ + 1:0;CO uint j_lim = i < f.m_SZ?i + 1:f.m_SZ;for(uint j = j_min;j < j_lim;j++){product_i += m_f[i - j]* f.m_f[j];}}RE OP=(MO(product));}TE IN PO& PO::OP*=(PO&& f){RE OP*=(f);};TE PO& PO::OP/=(CO T& t){if(t == CO_one()){RE *TH;}CO T t_inv{CO_one()/ t};for(uint i = 0;i < m_SZ;i++){OP[](i)*= t_inv;}RE *TH;}TE IN PO& PO::OP/=(CO PO& f){RE m_SZ < f.m_SZ?*TH:OP=(Quotient(*TH,f));}TE PO PO::Quotient(CO PO& f0,CO PO& f1){if(f0.m_SZ < f1.m_SZ){RE PO::zero();}assert(f1.m_SZ > 0);CO uint f0_transpose_SZ = f0.m_SZ - f1.m_SZ + 1;CO uint f1_transpose_SZ = f0_transpose_SZ < f1.m_SZ?f0_transpose_SZ:f1.m_SZ;CO TRPO f1_transpose_inverse = Inverse(TRPO(f0_transpose_SZ,Transpose(f1,f1_transpose_SZ)));TRPO f0_transpose{f0_transpose_SZ,Transpose(f0,f0_transpose_SZ)};f0_transpose *= f1_transpose_inverse;for(uint d0 =(f0_transpose_SZ + 1)/ 2;d0 < f0_transpose_SZ;d0++){::swap(f0_transpose[d0],f0_transpose[f0_transpose_SZ - 1 - d0]);}RE f0_transpose;}TE PO PO::Transpose(CO PO& f,CRUI f_transpose_SZ){VE f_transpose(f_transpose_SZ);for(uint d = 0;d < f_transpose_SZ;d++){f_transpose[d]= f.m_f[f.m_SZ - 1 - d];}RE PO(MO(f_transpose));}TE PO& PO::OP%=(CO T& t){if(t == CO_one()){RE OP=(zero());}for(uint i = 0;i < m_SZ;i++){m_f[i]%= t;}RE *TH;}TE PO& PO::OP%=(CO PO& f){if(m_SZ >= f.m_SZ){OP-=((*TH / f)* f);ReMORedundantZero();}RE *TH;}TE IN PO PO::OP-()CO{RE MO(PO()-= *TH);}TE IN CO VE& PO::GetCoefficient()CO NE{RE m_f;}TE IN CRUI PO::SZ()CO NE{RE m_SZ;}TE IN VO PO::reSZ(CRUI deg_plus)NE{m_f.resize(m_SZ = deg_plus);}TE IN VO PO::swap(PO& f){m_f.swap(f.m_f);swap(m_SZ,f.m_SZ);}TE IN VO PO::swap(VE& f){m_f.swap(f);m_SZ = m_f.SZ();}TE VO PO::ReMORedundantZero(){CO T& z = CO_zero();WH(m_SZ > 0?m_f[m_SZ - 1]== z:false){m_f.pop_back();m_SZ--;}RE;}TE string PO::Display()CO NE{string s = "(";if(m_SZ > 0){s += to_string(m_f[0]);for(uint i = 1;i < m_SZ;i++){s += "," + to_string(m_f[i]);}}s += ")";RE s;}TE IN CO PO& PO::zero(){ST CO PO z{};RE z;}TE IN CO PO& PO::one(){ST CO PO o{CO_one()};RE o;}TE IN CO T& PO::CO_zero(){ST CO T z{0};RE z;}TE IN CO T& PO::CO_one(){ST CO T o{1};RE o;}TE IN CO T& PO::CO_minus_one(){ST CO T m{-1};RE m;}TE bool OP==(CO PO& f0,CO T& t1){CRUI SZ = f0.SZ();CO T& zero = PO::CO_zero();for(uint i = 1;i < SZ;i++){if(f0[i]!= zero){RE false;}}RE f0[0]== t1;}TE bool OP==(CO PO& f0,CO PO& f1){CRUI SZ0 = f0.SZ();CRUI SZ1 = f1.SZ();CRUI SZ = SZ0 < SZ1?SZ1:SZ0;for(uint i = 0;i < SZ;i++){if(f0[i]!= f1[i]){RE false;}}RE true;}TE IN bool OP!=(CO PO& f0,CO P& f1){RE !(f0 == f1);}TE IN PO OP+(CO PO& f0,CO P& f1){RE MO(PO(f0)+= f1);}TE IN PO OP-(CO PO& f){RE PO::zero()- f;}TE IN PO OP-(CO PO& f0,CO P& f1){RE MO(PO(f0)-= f1);}TE IN PO OP*(CO PO& f0,CO P& f1){RE MO(PO(f0)*= f1);}TE IN PO OP/(CO PO& f0,CO T& t1){RE MO(PO(f0)/= t1);}TE IN PO OP/(CO PO& f0,CO PO& f1){RE PO::Quotient(f0,f1);}TE IN PO OP%(CO PO& f0,CO P& f1){RE MO(PO(f0)%= f1);}TE PO Differential(CRUI n,CO PO& f){CRUI SZ = f.SZ();if(SZ < n){RE PO::zero();}VE df(SZ - n);T coef = T::Factorial(n);uint i = n;WH(i < SZ){df[i - n]= f[i]* coef;i++;(coef *= i)/=(i - n);}RE PO(MO(df));} #define DF_OF_PROD(RECURSION,UNIT,APPLY)if(f.empty()){f.push_back(UNIT);}if(f.SZ()== 1){RE f.front();}auto IT = f.BE(),EN = f.EN();WH(IT != EN){auto& t = *IT;IT++;if(IT != EN){APPLY;IT = f.erase(IT);}}RE RECURSION; #define EXPRESSION1_FOR_RATIONAL_SUM {PO::zero(),PO::one()} #define EXPRESSION2_FOR_RATIONAL_SUM {t.first * IT->second + t.second * IT->first,t.second * IT->second} #define EXPRESSION3_FOR_RATIONAL_SUM {TRPO(),TRPO(1,PO::one())} // Tに拡張された冪乗のN次打ち切り。 TE IN TRPO PW(CO TRPO& f,CO T& t){RE Exp(Log(f)*= t);} // 冪乗のN次打ち切り。 TE TRPO PW(CO TRPO& f,CRUI e){CO T& one = PO::CO_one();if(f[0] == one){RE PW(f,T(e));}CO T& zero = PO::CO_zero();CRUI SZ = f.SZ();uint v = 0;WH(v < SZ?f[v] == zero:false){v++;}CO uint ve = v * e;CRUI N = f.GetTruncation();if(v == SZ || ve >= N){RE TRPO(N);}TRPO g(N - ve);CO T fv_inv = one / f[v];for(uint d = v;d < SZ;d++){g[d - v] = f[d] * fv_inv;}g = Exp(Log(g) *= T(e)) * PW(f[v],e);g.SetTruncation(N);for(uint d = N - 1;d + 1 > ve;d--){g[d] = g[d - ve];}for(uint d = 0;d < ve;d++){g[d] = zero;}RE g;} // 指数関数の線形結合のN次打ち切り(有理式の総和のN次打ち切りを用いる) TE TY V> TRPO EXialSum(CRUI N,CO V>& coef){ V,TRPO>> f{};for(auto IT = coef.BE(),EN = coef.EN();IT != EN;IT++){f.push_back({TRPO(N,IT->first),TRPO(N,1,- IT->second)+ PO::one()});}auto&[g,h]= RationalSum(f);g /= h;CO uint& SZ = g.SZ();for(uint d = 0;d < SZ;d++){g[d]*= T::FactorialInverse(d);}RE MO(g);} // 反転のN次打ち切り TE VO Reverse(CRUI N,PO& f){f.reSZ(N);CO uint N_half = N / 2;for(uint d = 0;d < N_half;d++){swap(f[d],f[N - 1 - d]);}RE;} // 平行移動 TE VO Shift(PO& f,CO T& t,CO bool& EXial = false){f.ReMORedundantZero();CRUI SZ = f.SZ();if(SZ > 0 && t != PO::CO_zero()){TRPO exp_t_transpose{SZ * 2};T PW_t = PO::CO_one();for(uint d = 0;d < SZ;d++){exp_t_transpose[SZ - 1 - d]= PW_t * T::FactorialInverse(d);PW_t *= t;}if(EXial){exp_t_transpose *= f;for(uint d = 0;d < SZ;d++){f[d]= exp_t_transpose[d + SZ - 1];}}else{for(uint d = 0;d < SZ;d++){f[d]*= T::Factorial(d);}exp_t_transpose *= f;for(uint d = 0;d < SZ;d++){f[d]= exp_t_transpose[d + SZ - 1]* T::FactorialInverse(d);}}}RE;} // アフィン変換 TE VO AffineTransformation(PO& f,CO T& t,CO T& u = PO::CO_zero(),CO bool& EXial = false){Shift(f,u,EXial);CRUI SZ = f.SZ();T PW = PO::CO_one();for(uint d = 0;d < SZ;d++){f[d]*= PW;PW *= t;}RE;} // ../Sum/compress.txtを先に貼る。(PWを使用) // メビウス変換のN次打ち切り(反転のN次打ち切りを使用) TE TRPO MoeviusComposition(CRUI N,PO f,T a,T b,T c,T d){CO T& zero = PO::CO_zero();CO T& one = PO::CO_one();if(c == zero){d = one / d;AffineTransformation(f,a *= d,b *= d);}else{a /= c;b -= a * d;if(b == zero){f = f(a);}else{b = one / b;c *= b;d *= b;Shift(f,a);CRUI SZ = f.SZ();if(SZ>0){Reverse(SZ,f);AffineTransformation(f,c,d);TRPO g{N};g[0]= MO(d);g[1]= MO(c);g = Inverse(PW(g,SZ-1));g *= f;f = MO(g);}}}RE TRPO(N,f);} // 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 // #define REACTIVE // #define USE_GETLINE #ifdef 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 constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE ) #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX ) #define SOLVE_ONLY #define CERR( ... ) #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL #define CERR_A( A , N ) #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL #define CERR_ITR( A ) #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL #endif #ifdef REACTIVE #define ENDL endl #else #define ENDL "\n" #endif #ifdef USE_GETLINE #define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); } #define GETLINE_SEPARATE( SEPARATOR , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ ) #define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ ) #else #define SET_LL( A ) cin >> A #define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ ) #define SET_A( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; } #define CIN_A( LL , A , N ) vector A( N ); SET_A( A , N ); #endif #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; #define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) ) #define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define FINISH_MAIN REPEAT( test_case_num ){ if constexpr( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } } #define TYPE_OF( VAR ) decay_t #define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE #define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS #define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.begin() , END_FOR_OUTPUT_ITR = A.end(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; while( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS #define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); return // 入出力用 template inline basic_istream& VariadicCin( basic_istream& is ) { return is; } template inline basic_istream& VariadicCin( basic_istream& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); } template inline basic_istream& VariadicGetline( basic_istream& is , const char& separator ) { return is; } template inline basic_istream& VariadicGetline( basic_istream& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); } template inline basic_ostream& VariadicCout( basic_ostream& os , const Arg& arg ) { return os << arg; } template inline basic_ostream& VariadicCout( basic_ostream& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); } // 圧縮用 #define TE template #define TY typename #define US using #define ST static #define IN inline #define CL class #define PU public #define OP operator #define CE constexpr #define CO const #define NE noexcept #define RE return #define WH while #define VO void #define VE vector #define LI list #define BE begin #define EN end #define SZ size #define MO move #define TH this #define CRI CO int& #define CRUI CO uint& #define CRL CO ll& // VVV 常設ライブラリは以下に挿入する。 // ConstexprModulo // c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/ConstexprModulo/a.hpp CEXPR(uint,P,998244353);TE CE INT& RS(INT& n)NE{RE n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n %= M;}TE CE uint& RS(uint& n)NE{RE n %= M;}TE CE ull& RS(ull& n)NE{RE n %= M;}TE CE INT& RSP(INT& n)NE{CE CO uint trunc =(1 << 23)- 1;INT n_u = n >> 23;n &= trunc;INT n_uq =(n_u / 7)/ 17;n_u -= n_uq * 119;n += n_u << 23;RE n < n_uq?n += P - n_uq:n -= n_uq;}TE <> CE ull& RS(ull& n)NE{CE CO ull Pull = P;CE CO ull Pull2 =(Pull - 1)*(Pull - 1);RE RSP(n > Pull2?n -= Pull2:n);}TE CE INT RS(INT&& n)NE{RE MO(RS(n));}TE CE INT RS(CO INT& n)NE{RE RS(INT(n));} #define SFINAE_FOR_MOD(DEFAULT)TY T,enable_if_t >::value>* DEFAULT #define DC_OF_CM_FOR_MOD(FUNC)CE bool OP FUNC(CO Mod& n)CO NE #define DC_OF_AR_FOR_MOD(FUNC)CE Mod OP FUNC(CO Mod& n)CO NE;TE CE Mod OP FUNC(T&& n)CO NE; #define DF_OF_CM_FOR_MOD(FUNC)TE CE bool Mod::OP FUNC(CO Mod& n)CO NE{RE m_n FUNC n.m_n;} #define DF_OF_AR_FOR_MOD(FUNC,FORMULA)TE CE Mod Mod::OP FUNC(CO Mod& n)CO NE{RE MO(Mod(*TH)FUNC ## = n);}TE TE CE Mod Mod::OP FUNC(T&& n)CO NE{RE FORMULA;}TE CE Mod OP FUNC(T&& n0,CO Mod& n1)NE{RE MO(Mod(forward(n0))FUNC ## = n1);} TE CL Mod{PU:uint m_n;CE Mod()NE;CE Mod(CO Mod& n)NE;CE Mod(Mod& n)NE;CE Mod(Mod&& n)NE;TE CE Mod(CO T& n)NE;TE CE Mod(T& n)NE;TE CE Mod(T&& n)NE;CE Mod& OP=(CO Mod& 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/=(CO Mod& n);CE Mod& OP<<=(int n)NE;CE Mod& OP>>=(int n)NE;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(+);DC_OF_AR_FOR_MOD(-);DC_OF_AR_FOR_MOD(*);DC_OF_AR_FOR_MOD(/);CE Mod OP<<(int n)CO NE;CE Mod OP>>(int n)CO NE;CE Mod OP-()CO NE;CE Mod& SignInvert()NE;CE Mod& Double()NE;CE Mod& Halve()NE;IN Mod& Invert();TE CE Mod& PositivePW(T&& EX)NE;TE CE Mod& NonNegativePW(T&& EX)NE;TE CE Mod& PW(T&& EX);CE VO swap(Mod& n)NE;CE CRUI RP()CO NE;ST CE Mod DeRP(CRUI n)NE;ST CE uint& Normalise(uint& n)NE;ST IN CO Mod& Inverse(CRUI n)NE;ST IN CO Mod& Factorial(CRUI n)NE;ST IN CO Mod& FactorialInverse(CRUI n)NE;ST IN Mod Combination(CRUI n,CRUI i)NE;ST IN CO Mod& zero()NE;ST IN CO Mod& one()NE;TE CE Mod& Ref(T&& n)NE;}; #define SFINAE_FOR_MN(DEFAULT)TY T,enable_if_t,decay_t >::value>* DEFAULT #define DC_OF_AR_FOR_MN(FUNC)IN MN OP FUNC(CO MN& n)CO NE;TE IN MN OP FUNC(T&& n)CO NE; #define DF_OF_CM_FOR_MN(FUNC)TE IN bool MN::OP FUNC(CO MN& n)CO NE{RE m_n FUNC n.m_n;} #define DF_OF_AR_FOR_MN(FUNC,FORMULA)TE IN MN MN::OP FUNC(CO MN& n)CO NE{RE MO(MN(*TH)FUNC ## = n);}TE TE IN MN MN::OP FUNC(T&& n)CO NE{RE FORMULA;}TE IN MN OP FUNC(T&& n0,CO MN& n1)NE{RE MO(MN(forward(n0))FUNC ## = n1);} TE CL MN:PU Mod{PU:CE MN()NE;CE MN(CO MN& n)NE;CE MN(MN& n)NE;CE MN(MN&& n)NE;TE CE MN(CO T& n)NE;TE CE MN(T&& n)NE;CE MN& OP=(CO MN& n)NE;CE MN& OP=(MN&& n)NE;CE MN& OP+=(CO MN& n)NE;CE MN& OP-=(CO MN& n)NE;CE MN& OP*=(CO MN& n)NE;IN MN& OP/=(CO MN& n);CE MN& OP<<=(int n)NE;CE MN& OP>>=(int n)NE;CE MN& OP++()NE;CE MN OP++(int)NE;CE MN& OP--()NE;CE MN OP--(int)NE;DC_OF_AR_FOR_MN(+);DC_OF_AR_FOR_MN(-);DC_OF_AR_FOR_MN(*);DC_OF_AR_FOR_MN(/);CE MN OP<<(int n)CO NE;CE MN OP>>(int n)CO NE;CE MN OP-()CO NE;CE MN& SignInvert()NE;CE MN& Double()NE;CE MN& Halve()NE;CE MN& Invert();TE CE MN& PositivePW(T&& EX)NE;TE CE MN& NonNegativePW(T&& EX)NE;TE CE MN& PW(T&& EX);CE uint RP()CO NE;CE Mod Reduce()CO NE;ST CE MN DeRP(CRUI n)NE;ST IN CO MN& Formise(CRUI n)NE;ST IN CO MN& Inverse(CRUI n)NE;ST IN CO MN& Factorial(CRUI n)NE;ST IN CO MN& FactorialInverse(CRUI n)NE;ST IN MN Combination(CRUI n,CRUI i)NE;ST IN CO MN& zero()NE;ST IN CO MN& one()NE;ST CE uint Form(CRUI n)NE;ST CE ull& Reduction(ull& n)NE;ST CE ull& ReducedMU(ull& n,CRUI m)NE;ST CE uint MU(CRUI n0,CRUI n1)NE;ST CE uint BaseSquareTruncation(uint& n)NE;TE CE MN& Ref(T&& n)NE;};TE CE MN Twice(CO MN& n)NE;TE CE MN Half(CO MN& n)NE;TE CE MN Inverse(CO MN& n);TE CE MN PW(MN n,T EX);TE CE MN<2> PW(CO MN<2>& n,CO T& p);TE CE T Square(CO T& t);TE <> CE MN<2> Square >(CO MN<2>& t);TE CE VO swap(MN& n0,MN& n1)NE;TE IN string to_string(CO MN& n)NE;TE IN basic_istream& OP>>(basic_istream& is,MN& n);TE IN basic_ostream& OP<<(basic_ostream& os,CO MN& n); TE CL COantsForMod{PU:COantsForMod()= delete;ST CE CO bool g_even =((M & 1)== 0);ST CE CO uint g_memory_bound = 1000000;ST CE CO uint g_memory_LE = M < g_memory_bound?M:g_memory_bound;ST CE ull MNBasePW(ull&& EX)NE;ST CE uint g_M_minus = M - 1;ST CE uint g_M_minus_2 = M - 2;ST CE uint g_M_minus_2_neg = 2 - M;ST CE CO int g_MN_digit = 32;ST CE CO ull g_MN_base = ull(1)<< g_MN_digit;ST CE CO uint g_MN_base_minus = uint(g_MN_base - 1);ST CE CO uint g_MN_digit_half =(g_MN_digit + 1)>> 1;ST CE CO uint g_MN_base_sqrt_minus =(1 << g_MN_digit_half)- 1;ST CE CO uint g_MN_M_neg_inverse = uint((g_MN_base - MNBasePW((ull(1)<<(g_MN_digit - 1))- 1))& g_MN_base_minus);ST CE CO uint g_MN_base_mod = uint(g_MN_base % M);ST CE CO uint g_MN_base_square_mod = uint(((g_MN_base % M)*(g_MN_base % M))% M);};TE CE ull COantsForMod::MNBasePW(ull&& EX)NE{ull prod = 1;ull PW = M;WH(EX != 0){(EX & 1)== 1?(prod *= PW)&= g_MN_base_minus:prod;EX >>= 1;(PW *= PW)&= g_MN_base_minus;}RE prod;} US MP = Mod

;US MNP = MN

;TE CE uint MN::Form(CRUI n)NE{ull n_copy = n;RE uint(MO(Reduction(n_copy *= COantsForMod::g_MN_base_square_mod)));}TE CE ull& MN::Reduction(ull& n)NE{ull n_sub = n & COantsForMod::g_MN_base_minus;RE((n +=((n_sub *= COantsForMod::g_MN_M_neg_inverse)&= COantsForMod::g_MN_base_minus)*= M)>>= COantsForMod::g_MN_digit)< M?n:n -= M;}TE CE ull& MN::ReducedMU(ull& n,CRUI m)NE{RE Reduction(n *= m);}TE CE uint MN::MU(CRUI n0,CRUI n1)NE{ull n0_copy = n0;RE uint(MO(ReducedMU(ReducedMU(n0_copy,n1),COantsForMod::g_MN_base_square_mod)));}TE CE uint MN::BaseSquareTruncation(uint& n)NE{CO uint n_u = n >> COantsForMod::g_MN_digit_half;n &= COantsForMod::g_MN_base_sqrt_minus;RE n_u;}TE CE MN::MN()NE:Mod(){static_assert(! COantsForMod::g_even);}TE CE MN::MN(CO MN& n)NE:Mod(n){}TE CE MN::MN(MN& n)NE:Mod(n){}TE CE MN::MN(MN&& n)NE:Mod(MO(n)){}TE TE CE MN::MN(CO T& n)NE:Mod(n){static_assert(! COantsForMod::g_even);Mod::m_n = Form(Mod::m_n);}TE TE CE MN::MN(T&& n)NE:Mod(forward(n)){static_assert(! COantsForMod::g_even);Mod::m_n = Form(Mod::m_n);}TE CE MN& MN::OP=(CO MN& n)NE{RE Ref(Mod::OP=(n));}TE CE MN& MN::OP=(MN&& n)NE{RE Ref(Mod::OP=(MO(n)));}TE CE MN& MN::OP+=(CO MN& n)NE{RE Ref(Mod::OP+=(n));}TE CE MN& MN::OP-=(CO MN& n)NE{RE Ref(Mod::OP-=(n));}TE CE MN& MN::OP*=(CO MN& n)NE{ull m_n_copy = Mod::m_n;RE Ref(Mod::m_n = MO(ReducedMU(m_n_copy,n.m_n)));}TE IN MN& MN::OP/=(CO MN& n){RE OP*=(MN(n).Invert());}TE CE MN& MN::OP<<=(int n)NE{RE Ref(Mod::OP<<=(n));}TE CE MN& MN::OP>>=(int n)NE{RE Ref(Mod::OP>>=(n));}TE CE MN& MN::OP++()NE{RE Ref(Mod::Normalise(Mod::m_n += COantsForMod::g_MN_base_mod));}TE CE MN MN::OP++(int)NE{MN n{*TH};OP++();RE n;}TE CE MN& MN::OP--()NE{RE Ref(Mod::m_n < COantsForMod::g_MN_base_mod?((Mod::m_n += M)-= COantsForMod::g_MN_base_mod):Mod::m_n -= COantsForMod::g_MN_base_mod);}TE CE MN MN::OP--(int)NE{MN n{*TH};OP--();RE n;}DF_OF_AR_FOR_MN(+,MN(forward(n))+= *TH);DF_OF_AR_FOR_MN(-,MN(forward(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MN(*,MN(forward(n))*= *TH);DF_OF_AR_FOR_MN(/,MN(forward(n)).Invert()*= *TH);TE CE MN MN::OP<<(int n)CO NE{RE MO(MN(*TH)<<= n);}TE CE MN MN::OP>>(int n)CO NE{RE MO(MN(*TH)>>= n);}TE CE MN MN::OP-()CO NE{RE MO(MN(*TH).SignInvert());}TE CE MN& MN::SignInvert()NE{RE Ref(Mod::m_n > 0?Mod::m_n = M - Mod::m_n:Mod::m_n);}TE CE MN& MN::Double()NE{RE Ref(Mod::Double());}TE CE MN& MN::Halve()NE{RE Ref(Mod::Halve());}TE CE MN& MN::Invert(){assert(Mod::m_n > 0);RE PositivePW(uint(COantsForMod::g_M_minus_2));}TE TE CE MN& MN::PositivePW(T&& EX)NE{MN PW{*TH};(--EX)%= COantsForMod::g_M_minus_2;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE TE CE MN& MN::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(Mod::m_n = COantsForMod::g_MN_base_mod):PositivePW(forward(EX));}TE TE CE MN& MN::PW(T&& EX){bool neg = EX < 0;assert(!(neg && Mod::m_n == 0));RE neg?PositivePW(forward(EX *= COantsForMod::g_M_minus_2_neg)):NonNegativePW(forward(EX));}TE CE uint MN::RP()CO NE{ull m_n_copy = Mod::m_n;RE MO(Reduction(m_n_copy));}TE CE Mod MN::Reduce()CO NE{ull m_n_copy = Mod::m_n;RE Mod::DeRP(MO(Reduction(m_n_copy)));}TE CE MN MN::DeRP(CRUI n)NE{RE MN(Mod::DeRP(n));}TE IN CO MN& MN::Formise(CRUI n)NE{ST MN memory[COantsForMod::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = DeRP(LE_curr);LE_curr++;}RE memory[n];}TE IN CO MN& MN::Inverse(CRUI n)NE{ST MN memory[COantsForMod::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN(Mod::Inverse(LE_curr));LE_curr++;}RE memory[n];}TE IN CO MN& MN::Factorial(CRUI n)NE{ST MN memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN val_curr{one()};ST MN val_last{one()};WH(LE_curr <= n){memory[LE_curr++] = val_curr *= ++val_last;}RE memory[n];}TE IN CO MN& MN::FactorialInverse(CRUI n)NE{ST MN memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN val_curr{one()};ST MN val_last{one()};WH(LE_curr <= n){memory[LE_curr] = val_curr *= Inverse(LE_curr);LE_curr++;}RE memory[n];}TE IN MN MN::Combination(CRUI n,CRUI i)NE{RE i <= n?Factorial(n)*FactorialInverse(i)*FactorialInverse(n - i):zero();}TE IN CO MN& MN::zero()NE{ST CE CO MN z{};RE z;}TE IN CO MN& MN::one()NE{ST CE CO MN o{DeRP(1)};RE o;}TE TE CE MN& MN::Ref(T&& n)NE{RE *TH;}TE CE MN Twice(CO MN& n)NE{RE MO(MN(n).Double());}TE CE MN Half(CO MN& n)NE{RE MO(MN(n).Halve());}TE CE MN Inverse(CO MN& n){RE MO(MN(n).Invert());}TE CE MN PW(MN n,T EX){RE MO(n.PW(EX));}TE CE VO swap(MN& n0,MN& n1)NE{n0.swap(n1);}TE IN string to_string(CO MN& n)NE{RE to_string(n.RP())+ " + MZ";}TE IN basic_istream& OP>>(basic_istream& is,MN& n){ll m;is >> m;n = m;RE is;}TE IN basic_ostream& OP<<(basic_ostream& os,CO MN& n){RE os << n.RP();} 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(n.m_n){}TE CE Mod::Mod(Mod&& n)NE:m_n(MO(n.m_n)){}TE TE CE Mod::Mod(CO T& n)NE:m_n(RS(n)){}TE TE CE Mod::Mod(T& n)NE:m_n(RS(decay_t(n))){}TE TE CE Mod::Mod(T&& n)NE:m_n(RS(forward(n))){}TE CE Mod& Mod::OP=(CO Mod& n)NE{RE Ref(m_n = n.m_n);}TE CE Mod& Mod::OP=(Mod&& n)NE{RE Ref(m_n = MO(n.m_n));}TE CE Mod& Mod::OP+=(CO Mod& n)NE{RE Ref(Normalise(m_n += n.m_n));}TE CE Mod& Mod::OP-=(CO Mod& n)NE{RE Ref(m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n);}TE CE Mod& Mod::OP*=(CO Mod& n)NE{RE Ref(m_n = COantsForMod::g_even?RS(ull(m_n)* n.m_n):MN::MU(m_n,n.m_n));}TE <> CE MP& MP::OP*=(CO MP& n)NE{ull m_n_copy = m_n;RE Ref(m_n = MO((m_n_copy *= n.m_n)< P?m_n_copy:RSP(m_n_copy)));}TE IN Mod& Mod::OP/=(CO Mod& n){RE OP*=(Mod(n).Invert());}TE CE Mod& Mod::OP<<=(int n)NE{WH(n-- > 0){Normalise(m_n <<= 1);}RE *TH;}TE CE Mod& Mod::OP>>=(int n)NE{WH(n-- > 0){((m_n & 1)== 0?m_n:m_n += M)>>= 1;}RE *TH;}TE CE Mod& Mod::OP++()NE{RE Ref(m_n < COantsForMod::g_M_minus?++m_n:m_n = 0);}TE CE Mod Mod::OP++(int)NE{Mod n{*TH};OP++();RE n;}TE CE Mod& Mod::OP--()NE{RE Ref(m_n == 0?m_n = COantsForMod::g_M_minus:--m_n);}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(+,Mod(forward(n))+= *TH);DF_OF_AR_FOR_MOD(-,Mod(forward(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MOD(*,Mod(forward(n))*= *TH);DF_OF_AR_FOR_MOD(/,Mod(forward(n)).Invert()*= *TH);TE CE Mod Mod::OP<<(int n)CO NE{RE MO(Mod(*TH)<<= n);}TE CE Mod Mod::OP>>(int n)CO NE{RE MO(Mod(*TH)>>= n);}TE CE Mod Mod::OP-()CO NE{RE MO(Mod(*TH).SignInvert());}TE CE Mod& Mod::SignInvert()NE{RE Ref(m_n > 0?m_n = M - m_n:m_n);}TE CE Mod& Mod::Double()NE{RE Ref(Normalise(m_n <<= 1));}TE CE Mod& Mod::Halve()NE{RE Ref(((m_n & 1)== 0?m_n:m_n += M)>>= 1);}TE IN Mod& Mod::Invert(){assert(m_n > 0);uint m_n_neg;RE m_n < COantsForMod::g_memory_LE?Ref(m_n = Inverse(m_n).m_n):((m_n_neg = M - m_n)< COantsForMod::g_memory_LE)?Ref(m_n = M - Inverse(m_n_neg).m_n):PositivePW(uint(COantsForMod::g_M_minus_2));}TE <> IN Mod<2>& Mod<2>::Invert(){assert(m_n > 0);RE *TH;}TE TE CE Mod& Mod::PositivePW(T&& EX)NE{Mod PW{*TH};EX--;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <> TE CE Mod<2>& Mod<2>::PositivePW(T&& EX)NE{RE *TH;}TE TE CE Mod& Mod::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(m_n = 1):Ref(PositivePW(forward(EX)));}TE TE CE Mod& Mod::PW(T&& EX){bool neg = EX < 0;assert(!(neg && m_n == 0));neg?EX *= COantsForMod::g_M_minus_2_neg:EX;RE m_n == 0?*TH:(EX %= COantsForMod::g_M_minus)== 0?Ref(m_n = 1):PositivePW(forward(EX));}TE IN CO Mod& Mod::Inverse(CRUI n)NE{ST Mod memory[COantsForMod::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr].m_n = M - MN::MU(memory[M % LE_curr].m_n,M / LE_curr);LE_curr++;}RE memory[n];}TE IN CO Mod& Mod::Factorial(CRUI n)NE{ST Mod memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN::Factorial(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE IN CO Mod& Mod::FactorialInverse(CRUI n)NE{ST Mod memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN::FactorialInverse(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE IN Mod Mod::Combination(CRUI n,CRUI i)NE{RE MN::Combination(n,i).Reduce();}TE CE VO Mod::swap(Mod& n)NE{std::swap(m_n,n.m_n);}TE CE CRUI Mod::RP()CO NE{RE m_n;}TE CE Mod Mod::DeRP(CRUI n)NE{Mod n_copy{};n_copy.m_n = n;RE n_copy;}TE CE uint& Mod::Normalise(uint& n)NE{RE n < M?n:n -= M;}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{DeRP(1)};RE o;}TE TE CE Mod& Mod::Ref(T&& n)NE{RE *TH;}TE CE Mod Twice(CO Mod& n)NE{RE MO(Mod(n).Double());}TE CE Mod Half(CO Mod& n)NE{RE MO(Mod(n).Halve());}TE IN Mod Inverse(CO Mod& n){RE MO(Mod(n).Invert());}TE CE Mod Inverse_COrexpr(CRUI n)NE{RE MO(Mod::DeRP(RS(n)).NonNegativePW(M - 2));}TE CE Mod PW(Mod n,T EX){RE MO(n.PW(EX));}TE CE Mod<2> PW(Mod<2> n,const T& p){RE p == 0?Mod<2>::one():move(n);}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())+ " + MZ";}TE IN basic_istream& OP>>(basic_istream& is,Mod& n){ll m;is >> m;n = m;RE is;}TE IN basic_ostream& OP<<(basic_ostream& os,CO Mod& n){RE os << n.RP();} // 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