#pragma GCC optimize ( "O3" ) #pragma GCC optimize( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE ) #define CERR( MESSAGE ) #define COUT( ANSWER ) cout << ANSWER << "\n" #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #define LIBRARY_SEARCH #define START_WATCH( PROCESS_NAME ) #define STOP_WATCH( HOW_MANY_TIMES ) #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 TYPE_OF( VAR ) decay_t #define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE #define CIN( LL , A ) LL A; cin >> A #define CIN_ASSERT( A , MIN , MAX ) CIN( TYPE_OF( MAX ) , A ); ASSERT( A , MIN , MAX ) #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX ) #define GETLINE( A ) string A; getline( cin , A ) #define GETLINE_SEPARATE( A , SEPARATOR ) string A; getline( cin , A , SEPARATOR ) #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 FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR >= FINAL ; VAR -- ) #define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end() #define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define QUIT return 0 #define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS_ ) #define RETURN( ANSWER ) COUT( ( ANSWER ) ); QUIT // 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& US ull = unsigned long long;IN CEXPR(uint,P,998244353);TE IN CE INT& RS(INT& n)NE{RE n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n %= M;}TE IN CE uint& RS(uint& n)NE{RE n %= M;}TE IN CE ull& RS(ull& n)NE{RE n %= M;}TE IN 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 <> IN 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 IN CE INT RS(INT&& n)NE{RE MO(RS(n));}TE IN 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)IN bool OP FUNC(CO Mod& n)CO NE #define DC_OF_AR_FOR_MOD(FUNC)IN Mod OP FUNC(CO Mod& n)CO NE;TE IN Mod OP FUNC(T&& n)CO NE; #define DF_OF_CM_FOR_MOD(FUNC)TE IN 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 IN Mod Mod::OP FUNC(CO Mod& n)CO NE{RE MO(Mod(*TH)FUNC ## = n);}TE TE IN Mod Mod::OP FUNC(T&& n)CO NE{RE FORMULA;}TE IN Mod OP FUNC(T&& n0,CO Mod& n1)NE{RE MO(Mod(forward(n0))FUNC ## = n1);} TE CL Mod{PU:uint m_n;IN CE Mod()NE;IN CE Mod(CO Mod& n)NE;IN CE Mod(Mod& n)NE;IN CE Mod(Mod&& n)NE;TE IN CE Mod(CO T& n)NE;TE IN CE Mod(T& n)NE;TE IN CE Mod(T&& n)NE;IN CE Mod& OP=(CO Mod& n)NE;IN CE Mod& OP=(Mod&& n)NE;IN CE Mod& OP+=(CO Mod& n)NE;IN CE Mod& OP-=(CO Mod& n)NE;IN CE Mod& OP*=(CO Mod& n)NE;IN Mod& OP/=(CO Mod& n);IN CE Mod& OP<<=(int n)NE;IN CE Mod& OP>>=(int n)NE;IN CE Mod& OP++()NE;IN CE Mod OP++(int)NE;IN CE Mod& OP--()NE;IN 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(/);IN CE Mod OP<<(int n)CO NE;IN CE Mod OP>>(int n)CO NE;IN CE Mod OP-()CO NE;IN CE Mod& SignInvert()NE;IN CE Mod& Double()NE;IN CE Mod& Halve()NE;IN Mod& Invert();TE IN CE Mod& PositivePW(T&& EX)NE;TE IN CE Mod& NonNegativePW(T&& EX)NE;TE IN CE Mod& PW(T&& EX);IN CE VO swap(Mod& n)NE;IN CE CO uint& RP()CO NE;ST IN CE Mod DeRP(CO uint& n)NE;ST IN CE uint& Normalise(uint& n)NE;ST IN CO Mod& Inverse(CO uint& n)NE;ST IN CO Mod& Factorial(CO uint& n)NE;ST IN CO Mod& FactorialInverse(CO uint& n)NE;ST IN CO Mod& zero()NE;ST IN CO Mod& one()NE;TE IN 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:IN CE MN()NE;IN CE MN(CO MN& n)NE;IN CE MN(MN& n)NE;IN CE MN(MN&& n)NE;TE IN CE MN(CO T& n)NE;TE IN CE MN(T&& n)NE;IN CE MN& OP=(CO MN& n)NE;IN CE MN& OP=(MN&& n)NE;IN CE MN& OP+=(CO MN& n)NE;IN CE MN& OP-=(CO MN& n)NE;IN CE MN& OP*=(CO MN& n)NE;IN MN& OP/=(CO MN& n);IN CE MN& OP<<=(int n)NE;IN CE MN& OP>>=(int n)NE;IN CE MN& OP++()NE;IN CE MN OP++(int)NE;IN CE MN& OP--()NE;IN 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(/);IN CE MN OP<<(int n)CO NE;IN CE MN OP>>(int n)CO NE;IN CE MN OP-()CO NE;IN CE MN& SignInvert()NE;IN CE MN& Double()NE;IN CE MN& Halve()NE;IN CE MN& Invert();TE IN CE MN& PositivePW(T&& EX)NE;TE IN CE MN& NonNegativePW(T&& EX)NE;TE IN CE MN& PW(T&& EX);IN CE uint RP()CO NE;IN CE Mod Reduce()CO NE;ST IN CE MN DeRP(CO uint& n)NE;ST IN CO MN& Formise(CO uint& n)NE;ST IN CO MN& Inverse(CO uint& n)NE;ST IN CO MN& Factorial(CO uint& n)NE;ST IN CO MN& FactorialInverse(CO uint& n)NE;ST IN CO MN& zero()NE;ST IN CO MN& one()NE;ST IN CE uint Form(CO uint& n)NE;ST IN CE ull& Reduction(ull& n)NE;ST IN CE ull& ReducedMU(ull& n,CO uint& m)NE;ST IN CE uint MU(CO uint& n0,CO uint& n1)NE;ST IN CE uint BaseSquareTruncation(uint& n)NE;TE IN CE MN& Ref(T&& n)NE;};TE IN CE MN Twice(CO MN& n)NE;TE IN CE MN Half(CO MN& n)NE;TE IN CE MN Inverse(CO MN& n);TE IN CE MN PW(CO MN& n,CO T& EX);TE IN CE MN<2> PW(CO MN<2>& n,CO T& p);TE IN CE T Square(CO T& t);TE <> IN CE MN<2> Square >(CO MN<2>& t);TE IN CE VO swap(MN& n0,MN& n1)NE;TE IN string to_string(CO MN& n)NE;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 IN 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 IN 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;} #include #define SET_VE_32_128_FOR_SIMD(UINT,VE_NAME,SCALAR0,SCALAR1,SCALAR2,SCALAR3)CE CO UINT VE_NAME ## _copy[4] ={SCALAR0,SCALAR1,SCALAR2,SCALAR3};ST CO __m128i v_ ## VE_NAME = _mm_load_si128((__m128i*)VE_NAME ##_copy) #define SET_VE_64_128_FOR_SIMD(UINT,VE_NAME,SCALAR0,SCALAR1)CE CO UINT VE_NAME ## _copy[2] ={SCALAR0,SCALAR1};ST CO __m128i v_ ## VE_NAME = _mm_load_si128((__m128i*)VE_NAME ##_copy) #define SET_VE_64_256_FOR_SIMD(ULL,VE_NAME,SCALAR0,SCALAR1,SCALAR2,SCALAR3)CE CO ULL VE_NAME ## _copy[4] ={SCALAR0,SCALAR1,SCALAR2,SCALAR3};ST CO __m256i v_ ## VE_NAME = _mm256_load_si256((__m256i*)VE_NAME ##_copy) #define SET_CO_VE_32_128_FOR_SIMD(UINT,VE_NAME,SCALAR)SET_VE_32_128_FOR_SIMD(UINT,VE_NAME,SCALAR,SCALAR,SCALAR,SCALAR) #define SET_CO_VE_64_128_FOR_SIMD(ULL,VE_NAME,SCALAR)SET_VE_64_128_FOR_SIMD(ULL,VE_NAME,SCALAR,SCALAR) #define SET_CO_VE_64_256_FOR_SIMD(ULL,VE_NAME,SCALAR)SET_VE_64_256_FOR_SIMD(ULL,VE_NAME,SCALAR,SCALAR,SCALAR,SCALAR) TE CL COantsForSIMDForMod{PU:COantsForSIMDForMod()= delete;ST IN CO __m128i& v_M()NE;ST IN CO __m128i& v_Mull()NE;ST IN CO __m128i& v_M_minus()NE;ST IN CO __m128i& v_M_neg_inverse()NE;ST IN CO __m128i& v_digitull()NE;};TE IN CO __m128i& COantsForSIMDForMod::v_M()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M,M);RE v_M;}TE IN CO __m128i& COantsForSIMDForMod::v_Mull()NE{SET_CO_VE_64_128_FOR_SIMD(ull,Mull,M);RE v_Mull;}TE IN CO __m128i& COantsForSIMDForMod::v_M_minus()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M_minus,M - 1);RE v_M_minus;}TE IN CO __m128i& COantsForSIMDForMod::v_M_neg_inverse()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M_neg_inverse,COantsForMod::g_MN_M_neg_inverse);RE v_M_neg_inverse;}TE IN CO __m128i& COantsForSIMDForMod::v_digitull()NE{SET_CO_VE_64_128_FOR_SIMD(ull,digitull,COantsForMod::g_MN_digit);RE v_digitull;}TE IN __m128i& SIMD_RS_32_128(__m128i& v)NE{CO __m128i& v_M = COantsForSIMDForMod::v_M();RE v -= v_M * _mm_cmpgt_epi32(v,v_M);}TE IN __m128i& SIMD_RS_64_128(__m128i& v)NE{ull v_copy[2];_mm_store_si128((__m128i*)v_copy,v);for(uint i = 0;i < 2;i++){ull& v_copy_i = v_copy[i];v_copy_i = (v_copy_i < M?0:M);}RE v -= _mm_load_si128((__m128i*)v_copy);}TE IN __m256i& SIMD_RS_64_256(__m256i& v)NE{ull v_copy[4];_mm256_store_si256((__m256i*)v_copy,v);for(uint i = 0;i < 4;i++){ull& v_copy_i = v_copy[i];v_copy_i = (v_copy_i < M?0:M);}RE v -= _mm256_load_si256((__m256i*)v_copy);}IN CE int SIMD_Shuffle(CRI a0,CRI a1,CRI a2,CRI a3)NE{RE (a0 << (0 << 1))+ (a1 << (1 << 1))+ (a2 << (2 << 1))+ (a3 << (3 << 1));}TE IN VO SIMD_Addition_32_64(CO Mod& a0,CO Mod& a1,CO Mod& b0,CO Mod& b1,Mod& c0,Mod& c1)NE{uint a_copy[4] ={a0.m_n,a1.m_n,0,0};uint b_copy[4] ={b0.m_n,b1.m_n,0,0};__m128i v_a = _mm_load_si128((__m128i*)a_copy);v_a += _mm_load_si128((__m128i*)b_copy);ST CO __m128i& v_M_minus = COantsForSIMDForMod::v_M_minus();ST CO __m128i& v_M = COantsForSIMDForMod::v_M();v_a += _mm_cmpgt_epi32(v_a,v_M_minus)& v_M;_mm_store_si128((__m128i*)a_copy,v_a);c0.m_n = MO(a_copy[0]);c1.m_n = MO(a_copy[1]);RE;}TE IN VO SIMD_Addition_32_128(CO Mod& a0,CO Mod& a1,CO Mod& a2,CO Mod& a3,CO Mod& b0,CO Mod& b1,CO Mod& b2,CO Mod& b3,Mod& c0,Mod& c1,Mod& c2,Mod& c3)NE{uint a_copy[4] ={a0.m_n,a1.m_n,a2.m_n,a3.m_n};uint b_copy[4] ={b0.m_n,b1.m_n,b2.m_n,b3.m_n};__m128i v_a = _mm_load_si128((__m128i*)a_copy)+ _mm_load_si128((__m128i*)b_copy);_mm_store_si128((__m128i*)a_copy,v_a);for(uint i = 0;i < 4;i++){b_copy[i] = a_copy[i] < M?0:M;}v_a -= _mm_load_si128((__m128i*)b_copy);_mm_store_si128((__m128i*)a_copy,v_a);c0.m_n = MO(a_copy[0]);c1.m_n = MO(a_copy[1]);c2.m_n = MO(a_copy[2]);c3.m_n = MO(a_copy[3]);RE;}TE IN VO SIMD_Substracition_32_64(CO Mod& a0,CO Mod& a1,CO Mod& b0,CO Mod& b1,Mod& c0,Mod& c1)NE{uint a_copy[4] ={a0.m_n,a1.m_n,0,0};uint b_copy[4] ={b0.m_n,b1.m_n,0,0};__m128i v_a = _mm_load_si128((__m128i*)a_copy);__m128i v_b = _mm_load_si128((__m128i*)b_copy);_mm_store_si128((__m128i*)a_copy,v_a);for(uint i = 0;i < 2;i++){b_copy[i] = a_copy[i] < b_copy[i]?M:0;}(v_a += _mm_load_si128((__m128i*)b_copy))-= v_b;_mm_store_si128((__m128i*)a_copy,v_a);c0.m_n = MO(a_copy[0]);c1.m_n = MO(a_copy[1]);RE;}TE IN VO SIMD_Subtraction_32_128(CO Mod& a0,CO Mod& a1,CO Mod& a2,CO Mod& a3,CO Mod& b0,CO Mod& b1,CO Mod& b2,CO Mod& b3,Mod& c0,Mod& c1,Mod& c2,Mod& c3)NE{uint a_copy[4] ={a0.m_n,a1.m_n,a2.m_n,a3.m_n};uint b_copy[4] ={b0.m_n,b1.m_n,b2.m_n,b3.m_n};__m128i v_a = _mm_load_si128((__m128i*)a_copy);__m128i v_b = _mm_load_si128((__m128i*)b_copy);_mm_store_si128((__m128i*)a_copy,v_a);for(uint i = 0;i < 4;i++){b_copy[i] = a_copy[i] < b_copy[i]?M:0;}(v_a += _mm_load_si128((__m128i*)b_copy))-= v_b;_mm_store_si128((__m128i*)a_copy,v_a);c0.m_n = MO(a_copy[0]);c1.m_n = MO(a_copy[1]);c2.m_n = MO(a_copy[2]);c3.m_n = MO(a_copy[3]);RE;} US MP = Mod

;US MNP = MN

;TE IN CE uint MN::Form(CO uint& n)NE{ull n_copy = n;RE uint(MO(Reduction(n_copy *= COantsForMod::g_MN_base_square_mod)));}TE IN 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 IN CE ull& MN::ReducedMU(ull& n,CO uint& m)NE{RE Reduction(n *= m);}TE IN CE uint MN::MU(CO uint& n0,CO uint& n1)NE{ull n0_copy = n0;RE uint(MO(ReducedMU(ReducedMU(n0_copy,n1),COantsForMod::g_MN_base_square_mod)));}TE IN 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 IN CE MN::MN()NE:Mod(){static_assert(! COantsForMod::g_even);}TE IN CE MN::MN(CO MN& n)NE:Mod(n){}TE IN CE MN::MN(MN& n)NE:Mod(n){}TE IN CE MN::MN(MN&& n)NE:Mod(MO(n)){}TE TE IN CE MN::MN(CO T& n)NE:Mod(n){static_assert(! COantsForMod::g_even);Mod::m_n = Form(Mod::m_n);}TE TE IN CE MN::MN(T&& n)NE:Mod(forward(n)){static_assert(! COantsForMod::g_even);Mod::m_n = Form(Mod::m_n);}TE IN CE MN& MN::OP=(CO MN& n)NE{RE Ref(Mod::OP=(n));}TE IN CE MN& MN::OP=(MN&& n)NE{RE Ref(Mod::OP=(MO(n)));}TE IN CE MN& MN::OP+=(CO MN& n)NE{RE Ref(Mod::OP+=(n));}TE IN CE MN& MN::OP-=(CO MN& n)NE{RE Ref(Mod::OP-=(n));}TE IN 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 IN CE MN& MN::OP<<=(int n)NE{RE Ref(Mod::OP<<=(n));}TE IN CE MN& MN::OP>>=(int n)NE{RE Ref(Mod::OP>>=(n));}TE IN CE MN& MN::OP++()NE{RE Ref(Mod::Normalise(Mod::m_n += COantsForMod::g_MN_base_mod));}TE IN CE MN MN::OP++(int)NE{MN n{*TH};OP++();RE n;}TE IN 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 IN 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 IN CE MN MN::OP<<(int n)CO NE{RE MO(MN(*TH)<<= n);}TE IN CE MN MN::OP>>(int n)CO NE{RE MO(MN(*TH)>>= n);}TE IN CE MN MN::OP-()CO NE{RE MO(MN(*TH).SignInvert());}TE IN CE MN& MN::SignInvert()NE{RE Ref(Mod::m_n > 0?Mod::m_n = M - Mod::m_n:Mod::m_n);}TE IN CE MN& MN::Double()NE{RE Ref(Mod::Double());}TE IN CE MN& MN::Halve()NE{RE Ref(Mod::Halve());}TE IN CE MN& MN::Invert(){assert(Mod::m_n > 0);RE PositivePW(uint(COantsForMod::g_M_minus_2));}TE TE IN 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 IN CE MN& MN::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(Mod::m_n = 1):PositivePW(forward(EX));}TE TE IN 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 IN CE uint MN::RP()CO NE{ull m_n_copy = Mod::m_n;RE MO(Reduction(m_n_copy));}TE IN CE Mod MN::Reduce()CO NE{ull m_n_copy = Mod::m_n;RE Mod::DeRP(MO(Reduction(m_n_copy)));}TE IN CE MN MN::DeRP(CO uint& n)NE{RE MN(Mod::DeRP(n));}TE IN CO MN& MN::Formise(CO uint& 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(CO uint& 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(CO uint& n)NE{ST MN memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN val_curr{one()};MN val_last{one()};WH(LE_curr <= n){memory[LE_curr++] = val_curr *= ++val_last;}RE memory[n];}TE IN CO MN& MN::FactorialInverse(CO uint& n)NE{ST MN memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN val_curr{one()};MN val_last{one()};WH(LE_curr <= n){memory[LE_curr] = val_curr *= Inverse(LE_curr);LE_curr++;}RE memory[n];}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 IN CE MN& MN::Ref(T&& n)NE{RE *TH;}TE IN CE MN Twice(CO MN& n)NE{RE MO(MN(n).Double());}TE IN CE MN Half(CO MN& n)NE{RE MO(MN(n).Halve());}TE IN CE MN Inverse(CO MN& n){RE MO(MN(n).Invert());}TE IN CE MN PW(CO MN& n,CO T& EX){RE MO(MN(n).PW(T(EX)));}TE IN 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_ostream& OP<<(basic_ostream& os,CO MN& n){RE os << n.RP();} TE IN CE Mod::Mod()NE:m_n(){}TE IN CE Mod::Mod(CO Mod& n)NE:m_n(n.m_n){}TE IN CE Mod::Mod(Mod& n)NE:m_n(n.m_n){}TE IN CE Mod::Mod(Mod&& n)NE:m_n(MO(n.m_n)){}TE TE IN CE Mod::Mod(CO T& n)NE:m_n(RS(n)){}TE TE IN CE Mod::Mod(T& n)NE:m_n(RS(decay_t(n))){}TE TE IN CE Mod::Mod(T&& n)NE:m_n(RS(forward(n))){}TE IN CE Mod& Mod::OP=(CO Mod& n)NE{RE Ref(m_n = n.m_n);}TE IN CE Mod& Mod::OP=(Mod&& n)NE{RE Ref(m_n = MO(n.m_n));}TE IN CE Mod& Mod::OP+=(CO Mod& n)NE{RE Ref(Normalise(m_n += n.m_n));}TE IN 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 IN 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 <> IN 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 IN CE Mod& Mod::OP<<=(int n)NE{WH(n-- > 0){Normalise(m_n <<= 1);}RE *TH;}TE IN CE Mod& Mod::OP>>=(int n)NE{WH(n-- > 0){((m_n & 1)== 0?m_n:m_n += M)>>= 1;}RE *TH;}TE IN CE Mod& Mod::OP++()NE{RE Ref(m_n < COantsForMod::g_M_minus?++m_n:m_n = 0);}TE IN CE Mod Mod::OP++(int)NE{Mod n{*TH};OP++();RE n;}TE IN CE Mod& Mod::OP--()NE{RE Ref(m_n == 0?m_n = COantsForMod::g_M_minus:--m_n);}TE IN 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 IN CE Mod Mod::OP<<(int n)CO NE{RE MO(Mod(*TH)<<= n);}TE IN CE Mod Mod::OP>>(int n)CO NE{RE MO(Mod(*TH)>>= n);}TE IN CE Mod Mod::OP-()CO NE{RE MO(Mod(*TH).SignInvert());}TE IN CE Mod& Mod::SignInvert()NE{RE Ref(m_n > 0?m_n = M - m_n:m_n);}TE IN CE Mod& Mod::Double()NE{RE Ref(Normalise(m_n <<= 1));}TE IN 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 IN 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 IN CE Mod<2>& Mod<2>::PositivePW(T&& EX)NE{RE *TH;}TE TE IN CE Mod& Mod::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(m_n = 1):Ref(PositivePW(forward(EX)));}TE TE IN 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(CO uint& 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(CO uint& 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(CO uint& 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 CE VO Mod::swap(Mod& n)NE{std::swap(m_n,n.m_n);}TE IN CE CO uint& Mod::RP()CO NE{RE m_n;}TE IN CE Mod Mod::DeRP(CO uint& n)NE{Mod n_copy{};n_copy.m_n = n;RE n_copy;}TE IN 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 IN CE Mod& Mod::Ref(T&& n)NE{RE *TH;}TE IN CE Mod Twice(CO Mod& n)NE{RE MO(Mod(n).Double());}TE IN 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 IN CE Mod Inverse_COrexpr(CO uint& n)NE{RE MO(Mod::DeRP(RS(n)).NonNegativePW(M - 2));}TE IN CE Mod PW(CO Mod& n,CO T& EX){RE MO(Mod(n).PW(T(EX)));}TE IN 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_ostream& OP<<(basic_ostream& os,CO Mod& n){RE os << n.RP();} #define SFINAE_FOR_PO(DEFAULT) TY Arg,enable_if_t >::value>* DEFAULT TE CL PO{PU:VE m_f;uint m_SZ;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;PO& OP<<=(CO T& t);IN CO VE& GetCoefficient() CO NE;IN CRUI SZ() CO 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 TPQuotient(CO PO& f0,CRUI f0_TP_SZ,CO PO& f1_TP_inverse,CRUI f1_SZ);ST PO TP(CO PO& f,CRUI f_TP_SZ);ST IN CO PO& zero();ST IN CO T& CO_zero();ST IN CO T& CO_one();ST IN CO T& CO_minus_one();}; 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){if(m_SZ < f.m_SZ){m_f.reserve(f.m_SZ);for(uint i = 0;i < m_SZ;i++){m_f[i] += f.m_f[i];}for(uint i = m_SZ;i < f.m_SZ;i++){m_f.push_back(f.m_f[i]);}m_SZ = f.m_SZ;}else{for(uint i = 0;i < f.m_SZ;i++){m_f[i] += f.m_f[i];}}RE *TH;}TE PO& PO::OP-=(CO PO& f){if(m_SZ < f.m_SZ){m_f.reserve(f.m_SZ);for(uint i = 0;i < m_SZ;i++){m_f[i] -= f.m_f[i];}for(uint i = m_SZ;i < f.m_SZ;i++){m_f.push_back(- f.m_f[i]);}m_SZ = f.m_SZ;}else{for(uint i = 0;i < f.m_SZ;i++){m_f[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?0:i - m_SZ + 1;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 PO PO::TP(CO PO& f,CRUI f_TP_SZ){VE f_TP(f_TP_SZ);for(uint d = 0;d < f_TP_SZ;d++){f_TP[d] = f.m_f[f.m_SZ - 1 - d];}RE PO(MO(f_TP));}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 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::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 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 TY V>T& Prod(V& f){if(f.empty()){f.push_back(T(1));}if(f.SZ() == 1){RE f.front();}auto IT = f.BE(),EN = f.EN();WH(IT != EN){T& t = *IT;IT++;if(IT != EN){t *= *IT;IT = f.erase(IT);}}RE Prod(f);} TE CL PW_CE{PU:T m_val[EX_lim];IN CE PW_CE(CO T& t,CO T& init = T(1));};TE IN CE PW_CE::PW_CE(CO T& t,CO T& init):m_val() {T PW{init};for( uint EX = 0;EX < EX_lim;EX++){m_val[EX] = PW;PW *= t;}} TE IN CE CO uint LimitOfPWForFFT{};TE IN CE CO uint BorderForFFT{};TE IN CO T (&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT];TE IN CO T (&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT];TE <> IN CE CO uint LimitOfPWForFFT = 24;TE <> IN CE CO uint LimitOfPWForFFT = LimitOfPWForFFT;TE <> IN CE CO uint BorderForFFT = 4;TE <> IN CE CO uint BorderForFFT = BorderForFFT;TE <> IN CO MP (&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT]{ST CO PW_CE > PRT{31};RE PRT.m_val;}TE <> IN CO MP (&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT]{ST CO PW_CE > IPRT{128805723};RE IPRT.m_val;}TE <> IN CO MNP (&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT]{ST CO PW_CE > PRT{31};RE PRT.m_val;}TE <> IN CO MNP (&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT]{ST CO PW_CE > IPRT{128805723};RE IPRT.m_val;}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;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++;}uint two_PW_curr = 1;uint two_PW_curr_2 = 2;CO T& zeta_0 = PRT[0];T zeta,diff;CO T* p_zeta_i;uint bit_num_copy,i,j,j_butterfly,j_lim;WH(two_PW_curr < two_PW){bit_num = 0;i = 0;WH(i < two_PW){zeta = zeta_0;p_zeta_i = &zeta_0 + 2;bit_num_copy = bit_num;WH(bit_num_copy != 0){if(bit_num_copy % 2 == 1){zeta *= *p_zeta_i;}bit_num_copy /= 2;p_zeta_i++;}j = i;j_lim = i + two_PW_curr;WH(j < j_lim){j_butterfly = j + two_PW_curr;T& f_j = f[j + N_input_start];T& f_j_butterfly = f[j_butterfly + N_input_start];diff = f_j - f_j_butterfly;f_j += f_j_butterfly;f_j_butterfly = zeta * diff;j++;}bit_num++;i += two_PW_curr_2;}swap(two_PW_curr,two_PW_curr_2);two_PW_curr_2 *= 4;}CO uint LE_fixed = N_output_lim + N_input_start;WH(f.SZ() > LE_fixed){f.pop_back();}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 DF_BODY_OF_PARTIAL_SPECIALISATION_OF_PO(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;} #define DF_OF_PARTIAL_SPECIALISATION_OF_PO(TYPE) DF_BODY_OF_PARTIAL_SPECIALISATION_OF_PO(TYPE,CO PO&,TH == &f?TH_copy:f);DF_BODY_OF_PARTIAL_SPECIALISATION_OF_PO(TYPE,PO&&,MO(f)); #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;FFT(f0,N_INPUT_START_0,N_INPUT_LIM_0,two_PW,EX);DC_OF_F1;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;true;i--){MU_FORMULA;if(i == I_START){break;}}CO uint N_output_start_shifted = N_OUTPUT_START_SHIFTED;CO uint N_output_lim_shifted = N_output_lim_fixed - N_input_start_0_start_1;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) 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_PARTIAL_SPECIALISATION_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;TE <> CE CO uint FFT_MU_border_1_2< TYPE > = BORDER_1_2;TE <> CE CO uint FFT_MU_border_1_2_EX< TYPE > = BORDER_1_2_EX;TE <> CE CO uint FFT_MU_border_1_2_inv< TYPE > = BORDER_1_2_INV;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));} TE CL TRPO :PU PO{PU:uint m_N;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& FFT_MU(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 IN CE CO uint FFT_MU_border_0{};TE IN CE CO uint FFT_MU_border_1{};TE IN CE CO uint FFT_MU_border_1_2{};TE IN CE CO uint FFT_MU_border_1_2_EX{};TE IN CE CO uint FFT_MU_border_1_2_inv{}; TE IN TRPO::TRPO(CRUI N):PO(),m_N(N){PO::m_f.reserve(m_N);}TE IN TRPO::TRPO(CO TRPO& f):PO(f),m_N(f.m_N){PO::m_f.reserve(m_N);}TE IN TRPO::TRPO(TRPO&& f):PO(MO(f)),m_N(MO(f.m_N)){PO::m_f.reserve(m_N);}TE IN TRPO::TRPO(CRUI N,CO T& t):PO(t),m_N(N){PO::m_f.reserve(m_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];}PO::m_f.reserve(m_N);}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){PO::m_f.reserve(m_N);}else{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;}PO::m_f.reserve(m_N);}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);}PO::m_f.reserve(m_N);}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){PO::m_f.reserve(m_N);}else{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]);}PO::m_f.reserve(m_N);}}TE IN TRPO& TRPO::OP=(CO TRPO& f){PO::OP=(f);m_N = f.m_N;PO::m_f.reserve(m_N);RE *TH;}TE IN TRPO& TRPO::OP=(TRPO&& f){PO::OP=(MO(f));m_N = MO(f.m_N);PO::m_f.reserve(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 TRPO::TRPlus(f,0,f.m_SZ);}TE IN TRPO& TRPO::OP+=(CO TRPO& f){RE m_N == 0?OP=(f):TRPO::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 TRPO::TRMinus(f,0,f.m_SZ);}TE IN TRPO& TRPO::OP-=(CO TRPO& f){RE m_N == 0?OP=(-f):TRPO::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_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,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::FFT_MU(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,VE&& f1 = MO(f.PO::m_f),N_input_start_1,N_input_max_1 + 1,f0,f0.resize(product_LE),0,f0[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 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_0,N_input_max_1,N_input_start_1),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,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(m_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] = i * f.PO::m_f[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){RE Integral(Differential(f) /= f);}TE IN TRPO PW(CO TRPO& f,CO T& t){RE Exp(Log(f) *= t);} TE IN PO& PO::OP/=(CO PO& f){RE m_SZ < f.m_SZ?*TH:OP=(Quotient(*TH,f));}TE PO& PO::OP%=(CO PO& f){if(m_SZ >= f.m_SZ){OP-=((*TH / f) * f);ReMORedundantZero();}RE *TH;}TE PO PO::Quotient(CO PO& f0,CO PO& f1){if(f0.m_SZ < f1.m_SZ){RE f0;}assert(f1.m_SZ > 0);CO uint f0_TP_SZ = f0.m_SZ - f1.m_SZ + 1;CO uint f1_TP_SZ = f0_TP_SZ < f1.m_SZ?f0_TP_SZ:f1.m_SZ;RE TPQuotient(f0,f0_TP_SZ,Inverse(TRPO(f0_TP_SZ,TP(f1,f1_TP_SZ))),f1.m_SZ);}TE PO PO::TPQuotient(CO PO& f0,CRUI f0_TP_SZ,CO PO& f1_TP_inverse,CRUI f1_SZ){TRPO f0_TP{f0_TP_SZ,TP(f0,f0_TP_SZ)};f0_TP *= f1_TP_inverse;for(uint d0 = (f0_TP_SZ + 1) / 2;d0 < f0_TP_SZ;d0++){::swap(f0_TP.PO::m_f[d0],f0_TP.PO::m_f[ f0_TP_SZ - 1 - d0 ]);}RE f0_TP;}TE PO& PO::OP<<=(CO T& t){if(m_SZ > 0){for(uint d = 0;d < m_SZ;d++){m_f[d] *= T::Factorial(d);}TRPO exp_t_TP{m_SZ * 2};T PW_t = CO_one();for(uint d = 0;d < m_SZ;d++){exp_t_TP[m_SZ - 1 - d] = PW_t * T::FactorialInverse(d);PW_t *= t;}exp_t_TP *= *TH;for(uint d = 0;d < m_SZ;d++){m_f[d] = exp_t_TP.PO::m_f[d + m_SZ - 1] * T::FactorialInverse(d);}}RE *TH;}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 OP<<(CO PO& f,CO T& t){RE MO(PO(f) <<= t);}DF_OF_PARTIAL_SPECIALISATION_OF_MU_OF_TR_PO(MP,17,512,1024,10,997269505);DF_OF_PARTIAL_SPECIALISATION_OF_MU_OF_TR_PO(MNP,17,512,1024,10,997269505);DF_OF_PARTIAL_SPECIALISATION_OF_PO(MP); int main() { UNTIE; LIBRARY_SEARCH; // DEXPR( int , bound_T , 100000 , 100 ); // CIN_ASSERT( T , 1 , bound_T ); // REPEAT( T ){ // } // CEXPR( int , bound_N , 10 ); DEXPR( int , bound_N , 200000 , 100 ); // 0が5個 // CEXPR( int , bound_N , 1000000000 ); // 0が9個 // CEXPR( ll , bound_N , 1000000000000000000 ); // 0が18個 CIN_ASSERT( N , 0 , bound_N ); // CEXPR( int , bound_M , 10 ); DEXPR( int , bound_M , 200000 , 100 ); // 0が5個 // CEXPR( int , bound_M , 1000000000 ); // 0が9個 // CEXPR( ll , bound_M , 1000000000000000000 ); // 0が18個 CIN_ASSERT( M , 0 , bound_M ); // CEXPR( ll , P , 998244353 ); // CEXPR( ll , P , 1000000007 ); // DEXPR( int , bound_Q , 100000 , 100 ); // CIN_ASSERT( Q , 1 , bound_Q ); // REPEAT( Q ){ // COUT( N ); // } CEXPR( int , bound_XY , 100 ); CIN_ASSERT( X , 0 , bound_XY ); CEXPR( int , bound_C , 5 ); vector C_prep[bound_C] = {}; FOR( i , 0 , bound_C ){ C_prep[i].resize( N + 1 ); } FOR( i , 0 , N ){ CIN_ASSERT( Ci , 1 , bound_C ); C_prep[--Ci][N-i] = 1; } PO C[bound_C]; FOR( i , 0 , bound_C ){ C[i] = move( C_prep[i] ); } vector A_prep[bound_C] = {}; FOR( i , 0 , bound_C ){ A_prep[i].resize( N ); } FOR( i , 0 , M ){ CIN_ASSERT( Ai , 1 , N ); CIN_ASSERT( Bi , 1 , bound_C ); CIN_ASSERT( Yi , 1 , bound_XY ); A_prep[--Bi][--Ai] += Yi; } PO A[bound_C]; FOR( i , 0 , bound_C ){ A[i] = move( A_prep[i] ); A[i] *= C[i]; } ll answer = 0; FOREQ( i , 0 , N ){ ll temp = X * i; FOR( c , 0 , bound_C ){ temp += A[c][N - i].RP(); } answer < temp ? answer = temp : answer; } RETURN( answer ); // QUIT; }