#838974 (C++17(clang)) No.2215 Slide Subset Sum

提出ソース

結果

問題	No.2215 Slide Subset Sum
ユーザー	👑 p-adic
提出日時	2023-02-10 22:18:47
言語	C++17(clang) (17.0.6 + boost 1.83.0)
結果	WA
実行時間	-
コード長	63,176 bytes
コンパイル時間	11,251 ms
コンパイル使用メモリ	240,252 KB
実行使用メモリ	62,096 KB
最終ジャッジ日時	2023-09-21 23:34:50
合計ジャッジ時間	23,522 ms
ジャッジサーバーID （参考情報）	judge13 / judge15

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	WA	-
testcase_01	TLE	-
testcase_02	--	-
testcase_03	--	-
testcase_04	--	-
testcase_05	--	-
testcase_06	--	-
testcase_07	--	-
testcase_08	--	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-
testcase_26	--	-
testcase_27	--	-
testcase_28	--	-
testcase_29	--	-
testcase_30	--	-
testcase_31	--	-
testcase_32	--	-
testcase_33	--	-
testcase_34	--	-
testcase_35	--	-
testcase_36	--	-
testcase_37	--	-
testcase_38	--	-
testcase_39	--	-
testcase_40	--	-
testcase_41	--	-
testcase_42	--	-
testcase_43	--	-
testcase_44	--	-
testcase_45	--	-
testcase_46	--	-

権限があれば一括ダウンロードができます

コンパイルメッセージ

main.cpp:183:2101: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call]
TE <uint M>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 <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M,M);RE v_M;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_Mull()NE{SET_CO_VE_64_128_FOR_SIMD(ull,Mull,M);RE v_Mull;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M_minus()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M_minus,M - 1);RE v_M_minus;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M_neg_inverse()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M_neg_inverse,COantsForMod<M>::g_MN_M_neg_inverse);RE v_M_neg_inverse;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_digitull()NE{SET_CO_VE_64_128_FOR_SIMD(ull,digitull,COantsForMod<M>::g_MN_digit);RE v_digitull;}TE <uint M> IN __m128i& SIMD_RS_32_128(__m128i& v)NE{CO __m128i& v_M = COantsForSIMDForMod<M>::v_M();RE v -= v_M * _mm_cmpgt_epi32(v,v_M);}TE <uint M> 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 <uint M> 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 <uint M> IN VO SIMD_Addition_32_64(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& b0,CO Mod<M>& b1,Mod<M>& c0,Mod<M>& 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&

ソースコード

raw source code

#pragma GCC optimize ( "O3" )
#pragma GCC optimize( "unroll-loops" )
#pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
#include <bits/stdc++.h>
using namespace std;

using uint = unsigned int;
using ll = long long;

#define TYPE_OF( VAR ) remove_const<remove_reference<decltype( VAR )>::type >::type
#define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN( LL , A ) LL A; cin >> A
#define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
#define CIN_ASSERT( A , MIN , MAX ) CIN( TYPE_OF( MAX ) , 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 FOR_ITR( ARRAY , ITR , END ) for( auto ITR = ARRAY .begin() , END = ARRAY .end() ; ITR != END ; ITR ++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT , 0 , HOW_MANY_TIMES )
#define QUIT return 0
#define COUT( ANSWER ) cout << ( ANSWER ) << "\n";
#define RETURN( ANSWER ) COUT( ANSWER ); QUIT
#define DOUBLE( PRECISION , ANSWER ) cout << fixed << setprecision( PRECISION ) << ( ANSWER ) << "\n"; QUIT

#define POWER( ANSWER , ARGUMENT , EXPONENT )				\
  TYPE_OF( ARGUMENT ) ANSWER{ 1 };					\
  {									\
    TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT );	\
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;			\
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;	\
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO )		\
  TYPE_OF( ARGUMENT ) ANSWER{ 1 };					\
  {									\
    TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( MODULO + ( ( ARGUMENT ) % MODULO ) ) % MODULO; \
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % MODULO;	\
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % MODULO; \
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_I , LENGTH , MODULO ) \
  static ll ANSWER[LENGTH];						\
  static ll ANSWER_INV[LENGTH];						\
  static ll INVERSE[LENGTH];						\
  {									\
    ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1;				\
    ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL;			\
    FOREQ( i , 1 , MAX_I ){						\
      ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= MODULO; \
    }									\
    ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \
    FOREQ( i , 2 , MAX_I ){						\
      ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = MODULO - ( ( ( MODULO / i ) * INVERSE[MODULO % i] ) % MODULO ) ) %= MODULO; \
    }									\
  }									\

// 通常の二分探索（単調関数-目的値が一意実数解を持つ場合にそれを超えない最大の整数を返す）
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  ll ANSWER = MAXIMUM;							\
  {									\
    ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM;				\
    ll VARIABLE_FOR_BINARY_SEARCH_U = ANSWER;				\
    ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( TARGET ) - ( EXPRESSION ); \
    if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){		\
      VARIABLE_FOR_BINARY_SEARCH_L = ANSWER;				\
    } else {								\
      ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
    }									\
    while( VARIABLE_FOR_BINARY_SEARCH_L != ANSWER ){			\
      VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( TARGET ) - ( EXPRESSION ); \
      if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){		\
	break;								\
      } else {								\
	if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH > 0 ){		\
	  VARIABLE_FOR_BINARY_SEARCH_L = ANSWER;			\
	} else {							\
	  VARIABLE_FOR_BINARY_SEARCH_U = ANSWER;			\
	}								\
	ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
      }									\
    }									\
  }									\
									\


// 二進法の二分探索（単調関数-目的値が一意実数解を持つ場合にそれを超えない最大の整数を返す）
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  ll ANSWER = MINIMUM;							\
  {									\
    ll VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 = 1;			\
    ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( MAXIMUM ) - ANSWER; \
    while( VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 <= VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ){ \
      VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 *= 2;			\
    }									\
    VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 /= 2;			\
    ll VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2 = ANSWER;		\
    while( VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 != 0 ){		\
      ANSWER = VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2 + VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2; \
      VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( TARGET ) - ( EXPRESSION ); \
      if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){		\
	VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2 = ANSWER;		\
	break;								\
      } else if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH > 0 ){	\
	VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2 = ANSWER;		\
      }									\
      VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 /= 2;			\
    }									\
    ANSWER = VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2;			\
  }									\
									\


template <typename T> inline T Absolute( const T& a ){ return a > 0 ? a : -a; }
template <typename T> inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }

#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 <uint M,TY INT> IN CE INT& RS(INT& n)NE{RE n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n %= M;}TE <uint M> IN CE uint& RS(uint& n)NE{RE n %= M;}TE <uint M> IN CE ull& RS(ull& n)NE{RE n %= M;}TE <TY INT> 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<P,ull>(ull& n)NE{CE CO ull Pull = P;CE CO ull Pull2 = (Pull - 1)* (Pull - 1);RE RSP(n > Pull2?n -= Pull2:n);}TE <uint M,TY INT> IN CE INT RS(INT&& n)NE{RE MO(RS<M>(n));}TE <uint M,TY INT> IN CE INT RS(CO INT& n)NE{RE RS<M>(INT(n));}

#define SFINAE_FOR_MOD(DEFAULT)TY T,enable_if_t<is_constructible<uint,decay_t<T> >::value>* DEFAULT
#define DC_OF_CM_FOR_MOD(FUNC)IN bool OP FUNC(CO Mod<M>& n)CO NE
#define DC_OF_AR_FOR_MOD(FUNC)IN Mod<M> OP FUNC(CO Mod<M>& n)CO NE;TE <SFINAE_FOR_MOD(= nullptr)> IN Mod<M> OP FUNC(T&& n)CO NE;
#define DF_OF_CM_FOR_MOD(FUNC)TE <uint M> IN bool Mod<M>::OP FUNC(CO Mod<M>& n)CO NE{RE m_n FUNC n.m_n;}
#define DF_OF_AR_FOR_MOD(FUNC,FORMULA)TE <uint M> IN Mod<M> Mod<M>::OP FUNC(CO Mod<M>& n)CO NE{RE MO(Mod<M>(*TH)FUNC ## = n);}TE <uint M> TE <SFINAE_FOR_MOD()> IN Mod<M> Mod<M>::OP FUNC(T&& n)CO NE{RE FORMULA;}TE <uint M,SFINAE_FOR_MOD(= nullptr)> IN Mod<M> OP FUNC(T&& n0,CO Mod<M>& n1)NE{RE MO(Mod<M>(forward<T>(n0))FUNC ## = n1);}

TE <uint M>CL Mod{PU:uint m_n;IN CE Mod()NE;IN CE Mod(CO Mod<M>& n)NE;IN CE Mod(Mod<M>& n)NE;IN CE Mod(Mod<M>&& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> IN CE Mod(CO T& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> IN CE Mod(T& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> IN CE Mod(T&& n)NE;IN CE Mod<M>& OP=(CO Mod<M>& n)NE;IN CE Mod<M>& OP=(Mod<M>&& n)NE;IN CE Mod<M>& OP+=(CO Mod<M>& n)NE;IN CE Mod<M>& OP-=(CO Mod<M>& n)NE;IN CE Mod<M>& OP*=(CO Mod<M>& n)NE;IN Mod<M>& OP/=(CO Mod<M>& n);IN CE Mod<M>& OP<<=(int n)NE;IN CE Mod<M>& OP>>=(int n)NE;IN CE Mod<M>& OP++()NE;IN CE Mod<M> OP++(int)NE;IN CE Mod<M>& OP--()NE;IN CE Mod<M> 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<M> OP<<(int n)CO NE;IN CE Mod<M> OP>>(int n)CO NE;IN CE Mod<M> OP-()CO NE;IN CE Mod<M>& SignInvert()NE;IN CE Mod<M>& Double()NE;IN CE Mod<M>& Halve()NE;IN Mod<M>& Invert();TE <TY T> IN CE Mod<M>& PositivePW(T&& EX)NE;TE <TY T> IN CE Mod<M>& NonNegativePW(T&& EX)NE;TE <TY T> IN CE Mod<M>& PW(T&& EX);IN CE VO swap(Mod<M>& n)NE;IN CE CO uint& RP()CO NE;ST IN CE Mod<M> DeRP(CO uint& n)NE;ST IN CE uint& Normalise(uint& n)NE;ST IN CO Mod<M>& Inverse(CO uint& n)NE;ST IN CO Mod<M>& Factorial(CO uint& n)NE;ST IN CO Mod<M>& FactorialInverse(CO uint& n)NE;ST IN CO Mod<M>& zero()NE;ST IN CO Mod<M>& one()NE;TE <TY T> IN CE Mod<M>& Ref(T&& n)NE;};

#define SFINAE_FOR_MN(DEFAULT)TY T,enable_if_t<is_constructible<Mod<M>,decay_t<T> >::value>* DEFAULT
#define DC_OF_AR_FOR_MN(FUNC)IN MN<M> OP FUNC(CO MN<M>& n)CO NE;TE <SFINAE_FOR_MOD(= nullptr)> IN MN<M> OP FUNC(T&& n)CO NE;
#define DF_OF_CM_FOR_MN(FUNC)TE <uint M> IN bool MN<M>::OP FUNC(CO MN<M>& n)CO NE{RE m_n FUNC n.m_n;}
#define DF_OF_AR_FOR_MN(FUNC,FORMULA)TE <uint M> IN MN<M> MN<M>::OP FUNC(CO MN<M>& n)CO NE{RE MO(MN<M>(*TH)FUNC ## = n);}TE <uint M> TE <SFINAE_FOR_MOD()> IN MN<M> MN<M>::OP FUNC(T&& n)CO NE{RE FORMULA;}TE <uint M,SFINAE_FOR_MOD(= nullptr)> IN MN<M> OP FUNC(T&& n0,CO MN<M>& n1)NE{RE MO(MN<M>(forward<T>(n0))FUNC ## = n1);}

TE <uint M>CL MN :PU Mod<M>{PU:IN CE MN()NE;IN CE MN(CO MN<M>& n)NE;IN CE MN(MN<M>& n)NE;IN CE MN(MN<M>&& n)NE;TE <SFINAE_FOR_MN(= nullptr)> IN CE MN(CO T& n)NE;TE <SFINAE_FOR_MN(= nullptr)> IN CE MN(T&& n)NE;IN CE MN<M>& OP=(CO MN<M>& n)NE;IN CE MN<M>& OP=(MN<M>&& n)NE;IN CE MN<M>& OP+=(CO MN<M>& n)NE;IN CE MN<M>& OP-=(CO MN<M>& n)NE;IN CE MN<M>& OP*=(CO MN<M>& n)NE;IN MN<M>& OP/=(CO MN<M>& n);IN CE MN<M>& OP<<=(int n)NE;IN CE MN<M>& OP>>=(int n)NE;IN CE MN<M>& OP++()NE;IN CE MN<M> OP++(int)NE;IN CE MN<M>& OP--()NE;IN CE MN<M> 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<M> OP<<(int n)CO NE;IN CE MN<M> OP>>(int n)CO NE;IN CE MN<M> OP-()CO NE;IN CE MN<M>& SignInvert()NE;IN CE MN<M>& Double()NE;IN CE MN<M>& Halve()NE;IN CE MN<M>& Invert();TE <TY T> IN CE MN<M>& PositivePW(T&& EX)NE;TE <TY T> IN CE MN<M>& NonNegativePW(T&& EX)NE;TE <TY T> IN CE MN<M>& PW(T&& EX);IN CE uint RP()CO NE;IN CE Mod<M> Reduce()CO NE;ST IN CE MN<M> DeRP(CO uint& n)NE;ST IN CO MN<M>& Formise(CO uint& n)NE;ST IN CO MN<M>& Inverse(CO uint& n)NE;ST IN CO MN<M>& Factorial(CO uint& n)NE;ST IN CO MN<M>& FactorialInverse(CO uint& n)NE;ST IN CO MN<M>& zero()NE;ST IN CO MN<M>& 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 <TY T> IN CE MN<M>& Ref(T&& n)NE;};TE <uint M> IN CE MN<M> Twice(CO MN<M>& n)NE;TE <uint M> IN CE MN<M> Half(CO MN<M>& n)NE;TE <uint M> IN CE MN<M> Inverse(CO MN<M>& n);TE <uint M,TY T> IN CE MN<M> PW(CO MN<M>& n,CO T& EX);TE <TY T> IN CE MN<2> PW(CO MN<2>& n,CO T& p);TE <TY T> IN CE T Square(CO T& t);TE <> IN CE MN<2> Square<MN<2> >(CO MN<2>& t);TE <uint M> IN CE VO swap(MN<M>& n0,MN<M>& n1)NE;TE <uint M> IN string to_string(CO MN<M>& n)NE;TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO MN<M>& n);

TE <uint M>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 <uint M> IN CE ull COantsForMod<M>::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 <immintrin.h>
#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 <uint M>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 <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M,M);RE v_M;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_Mull()NE{SET_CO_VE_64_128_FOR_SIMD(ull,Mull,M);RE v_Mull;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M_minus()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M_minus,M - 1);RE v_M_minus;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_M_neg_inverse()NE{SET_CO_VE_32_128_FOR_SIMD(uint,M_neg_inverse,COantsForMod<M>::g_MN_M_neg_inverse);RE v_M_neg_inverse;}TE <uint M> IN CO __m128i& COantsForSIMDForMod<M>::v_digitull()NE{SET_CO_VE_64_128_FOR_SIMD(ull,digitull,COantsForMod<M>::g_MN_digit);RE v_digitull;}TE <uint M> IN __m128i& SIMD_RS_32_128(__m128i& v)NE{CO __m128i& v_M = COantsForSIMDForMod<M>::v_M();RE v -= v_M * _mm_cmpgt_epi32(v,v_M);}TE <uint M> 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 <uint M> 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 <uint M> IN VO SIMD_Addition_32_64(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& b0,CO Mod<M>& b1,Mod<M>& c0,Mod<M>& 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<M>::v_M_minus();ST CO __m128i& v_M = COantsForSIMDForMod<M>::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 <uint M> IN VO SIMD_Addition_32_128(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& a2,CO Mod<M>& a3,CO Mod<M>& b0,CO Mod<M>& b1,CO Mod<M>& b2,CO Mod<M>& b3,Mod<M>& c0,Mod<M>& c1,Mod<M>& c2,Mod<M>& 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 <uint M> IN VO SIMD_Substracition_32_64(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& b0,CO Mod<M>& b1,Mod<M>& c0,Mod<M>& 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 <uint M> IN VO SIMD_Subtraction_32_128(CO Mod<M>& a0,CO Mod<M>& a1,CO Mod<M>& a2,CO Mod<M>& a3,CO Mod<M>& b0,CO Mod<M>& b1,CO Mod<M>& b2,CO Mod<M>& b3,Mod<M>& c0,Mod<M>& c1,Mod<M>& c2,Mod<M>& 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<P>;US MNP = MN<P>;TE <uint M> IN CE uint MN<M>::Form(CO uint& n)NE{ull n_copy = n;RE uint(MO(Reduction(n_copy *= COantsForMod<M>::g_MN_base_square_mod)));}TE <uint M> IN CE ull& MN<M>::Reduction(ull& n)NE{ull n_sub = n & COantsForMod<M>::g_MN_base_minus;RE ((n += ((n_sub *= COantsForMod<M>::g_MN_M_neg_inverse)&= COantsForMod<M>::g_MN_base_minus)*= M)>>= COantsForMod<M>::g_MN_digit)< M?n:n -= M;}TE <uint M> IN CE ull& MN<M>::ReducedMU(ull& n,CO uint& m)NE{RE Reduction(n *= m);}TE <uint M> IN CE uint MN<M>::MU(CO uint& n0,CO uint& n1)NE{ull n0_copy = n0;RE uint(MO(ReducedMU(ReducedMU(n0_copy,n1),COantsForMod<M>::g_MN_base_square_mod)));}TE <uint M> IN CE uint MN<M>::BaseSquareTruncation(uint& n)NE{CO uint n_u = n >> COantsForMod<M>::g_MN_digit_half;n &= COantsForMod<M>::g_MN_base_sqrt_minus;RE n_u;}TE <uint M> IN CE MN<M>::MN()NE:Mod<M>(){static_assert(! COantsForMod<M>::g_even);}TE <uint M> IN CE MN<M>::MN(CO MN<M>& n)NE:Mod<M>(n){}TE <uint M> IN CE MN<M>::MN(MN<M>& n)NE:Mod<M>(n){}TE <uint M> IN CE MN<M>::MN(MN<M>&& n)NE:Mod<M>(MO(n)){}TE <uint M> TE <SFINAE_FOR_MN()> IN CE MN<M>::MN(CO T& n)NE:Mod<M>(n){static_assert(! COantsForMod<M>::g_even);Mod<M>::m_n = Form(Mod<M>::m_n);}TE <uint M> TE <SFINAE_FOR_MN()> IN CE MN<M>::MN(T&& n)NE:Mod<M>(forward<T>(n)){static_assert(! COantsForMod<M>::g_even);Mod<M>::m_n = Form(Mod<M>::m_n);}TE <uint M> IN CE MN<M>& MN<M>::OP=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP=(MN<M>&& n)NE{RE Ref(Mod<M>::OP=(MO(n)));}TE <uint M> IN CE MN<M>& MN<M>::OP+=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP+=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP-=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP-=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP*=(CO MN<M>& n)NE{ull m_n_copy = Mod<M>::m_n;RE Ref(Mod<M>::m_n = MO(ReducedMU(m_n_copy,n.m_n)));}TE <uint M> IN MN<M>& MN<M>::OP/=(CO MN<M>& n){RE OP*=(MN<M>(n).Invert());}TE <uint M> IN CE MN<M>& MN<M>::OP<<=(int n)NE{RE Ref(Mod<M>::OP<<=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP>>=(int n)NE{RE Ref(Mod<M>::OP>>=(n));}TE <uint M> IN CE MN<M>& MN<M>::OP++()NE{RE Ref(Mod<M>::Normalise(Mod<M>::m_n += COantsForMod<M>::g_MN_base_mod));}TE <uint M> IN CE MN<M> MN<M>::OP++(int)NE{MN<M> n{*TH};OP++();RE n;}TE <uint M> IN CE MN<M>& MN<M>::OP--()NE{RE Ref(Mod<M>::m_n < COantsForMod<M>::g_MN_base_mod?((Mod<M>::m_n += M)-= COantsForMod<M>::g_MN_base_mod):Mod<M>::m_n -= COantsForMod<M>::g_MN_base_mod);}TE <uint M> IN CE MN<M> MN<M>::OP--(int)NE{MN<M> n{*TH};OP--();RE n;}DF_OF_AR_FOR_MN(+,MN<M>(forward<T>(n))+= *TH);DF_OF_AR_FOR_MN(-,MN<M>(forward<T>(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MN(*,MN<M>(forward<T>(n))*= *TH);DF_OF_AR_FOR_MN(/,MN<M>(forward<T>(n)).Invert()*= *TH);TE <uint M> IN CE MN<M> MN<M>::OP<<(int n)CO NE{RE MO(MN<M>(*TH)<<= n);}TE <uint M> IN CE MN<M> MN<M>::OP>>(int n)CO NE{RE MO(MN<M>(*TH)>>= n);}TE <uint M> IN CE MN<M> MN<M>::OP-()CO NE{RE MO(MN<M>(*TH).SignInvert());}TE <uint M> IN CE MN<M>& MN<M>::SignInvert()NE{RE Ref(Mod<M>::m_n > 0?Mod<M>::m_n = M - Mod<M>::m_n:Mod<M>::m_n);}TE <uint M> IN CE MN<M>& MN<M>::Double()NE{RE Ref(Mod<M>::Double());}TE <uint M> IN CE MN<M>& MN<M>::Halve()NE{RE Ref(Mod<M>::Halve());}TE <uint M> IN CE MN<M>& MN<M>::Invert(){assert(Mod<M>::m_n > 0);RE PositivePW(uint(COantsForMod<M>::g_M_minus_2));}TE <uint M> TE <TY T> IN CE MN<M>& MN<M>::PositivePW(T&& EX)NE{MN<M> PW{*TH};(--EX)%= COantsForMod<M>::g_M_minus_2;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <uint M> TE <TY T> IN CE MN<M>& MN<M>::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(Mod<M>::m_n = 1):PositivePW(forward<T>(EX));}TE <uint M> TE <TY T> IN CE MN<M>& MN<M>::PW(T&& EX){bool neg = EX < 0;assert(!(neg && Mod<M>::m_n == 0));RE neg?PositivePW(forward<T>(EX *= COantsForMod<M>::g_M_minus_2_neg)):NonNegativePW(forward<T>(EX));}TE <uint M> IN CE uint MN<M>::RP()CO NE{ull m_n_copy = Mod<M>::m_n;RE MO(Reduction(m_n_copy));}TE <uint M> IN CE Mod<M> MN<M>::Reduce()CO NE{ull m_n_copy = Mod<M>::m_n;RE Mod<M>::DeRP(MO(Reduction(m_n_copy)));}TE <uint M> IN CE MN<M> MN<M>::DeRP(CO uint& n)NE{RE MN<M>(Mod<M>::DeRP(n));}TE <uint M> IN CO MN<M>& MN<M>::Formise(CO uint& n)NE{ST MN<M> memory[COantsForMod<M>::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 <uint M> IN CO MN<M>& MN<M>::Inverse(CO uint& n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>(Mod<M>::Inverse(LE_curr));LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::Factorial(CO uint& n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN<M> val_curr{one()};MN<M> val_last{one()};WH(LE_curr <= n){memory[LE_curr++] = val_curr *= ++val_last;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::FactorialInverse(CO uint& n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN<M> val_curr{one()};MN<M> val_last{one()};WH(LE_curr <= n){memory[LE_curr] = val_curr *= Inverse(LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::zero()NE{ST CE CO MN<M> z{};RE z;}TE <uint M> IN CO MN<M>& MN<M>::one()NE{ST CE CO MN<M> o{DeRP(1)};RE o;}TE <uint M> TE <TY T> IN CE MN<M>& MN<M>::Ref(T&& n)NE{RE *TH;}TE <uint M> IN CE MN<M> Twice(CO MN<M>& n)NE{RE MO(MN<M>(n).Double());}TE <uint M> IN CE MN<M> Half(CO MN<M>& n)NE{RE MO(MN<M>(n).Halve());}TE <uint M> IN CE MN<M> Inverse(CO MN<M>& n){RE MO(MN<M>(n).Invert());}TE <uint M,TY T> IN CE MN<M> PW(CO MN<M>& n,CO T& EX){RE MO(MN<M>(n).PW(T(EX)));}TE <uint M> IN CE VO swap(MN<M>& n0,MN<M>& n1)NE{n0.swap(n1);}TE <uint M> IN string to_string(CO MN<M>& n)NE{RE to_string(n.RP())+ " + MZ";}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO MN<M>& n){RE os << n.RP();}

TE <uint M> IN CE Mod<M>::Mod()NE:m_n(){}TE <uint M> IN CE Mod<M>::Mod(CO Mod<M>& n)NE:m_n(n.m_n){}TE <uint M> IN CE Mod<M>::Mod(Mod<M>& n)NE:m_n(n.m_n){}TE <uint M> IN CE Mod<M>::Mod(Mod<M>&& n)NE:m_n(MO(n.m_n)){}TE <uint M> TE <SFINAE_FOR_MOD()> IN CE Mod<M>::Mod(CO T& n)NE:m_n(RS<M>(n)){}TE <uint M> TE <SFINAE_FOR_MOD()> IN CE Mod<M>::Mod(T& n)NE:m_n(RS<M>(decay_t<T>(n))){}TE <uint M> TE <SFINAE_FOR_MOD()> IN CE Mod<M>::Mod(T&& n)NE:m_n(RS<M>(forward<T>(n))){}TE <uint M> IN CE Mod<M>& Mod<M>::OP=(CO Mod<M>& n)NE{RE Ref(m_n = n.m_n);}TE <uint M> IN CE Mod<M>& Mod<M>::OP=(Mod<M>&& n)NE{RE Ref(m_n = MO(n.m_n));}TE <uint M> IN CE Mod<M>& Mod<M>::OP+=(CO Mod<M>& n)NE{RE Ref(Normalise(m_n += n.m_n));}TE <uint M> IN CE Mod<M>& Mod<M>::OP-=(CO Mod<M>& n)NE{RE Ref(m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n);}TE <uint M> IN CE Mod<M>& Mod<M>::OP*=(CO Mod<M>& n)NE{RE Ref(m_n = COantsForMod<M>::g_even?RS<M>(ull(m_n)* n.m_n):MN<M>::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 <uint M> IN Mod<M>& Mod<M>::OP/=(CO Mod<M>& n){RE OP*=(Mod<M>(n).Invert());}TE <uint M> IN CE Mod<M>& Mod<M>::OP<<=(int n)NE{WH(n-- > 0){Normalise(m_n <<= 1);}RE *TH;}TE <uint M> IN CE Mod<M>& Mod<M>::OP>>=(int n)NE{WH(n-- > 0){((m_n & 1)== 0?m_n:m_n += M)>>= 1;}RE *TH;}TE <uint M> IN CE Mod<M>& Mod<M>::OP++()NE{RE Ref(m_n < COantsForMod<M>::g_M_minus?++m_n:m_n = 0);}TE <uint M> IN CE Mod<M> Mod<M>::OP++(int)NE{Mod<M> n{*TH};OP++();RE n;}TE <uint M> IN CE Mod<M>& Mod<M>::OP--()NE{RE Ref(m_n == 0?m_n = COantsForMod<M>::g_M_minus:--m_n);}TE <uint M> IN CE Mod<M> Mod<M>::OP--(int)NE{Mod<M> 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<M>(forward<T>(n))+= *TH);DF_OF_AR_FOR_MOD(-,Mod<M>(forward<T>(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MOD(*,Mod<M>(forward<T>(n))*= *TH);DF_OF_AR_FOR_MOD(/,Mod<M>(forward<T>(n)).Invert()*= *TH);TE <uint M> IN CE Mod<M> Mod<M>::OP<<(int n)CO NE{RE MO(Mod<M>(*TH)<<= n);}TE <uint M> IN CE Mod<M> Mod<M>::OP>>(int n)CO NE{RE MO(Mod<M>(*TH)>>= n);}TE <uint M> IN CE Mod<M> Mod<M>::OP-()CO NE{RE MO(Mod<M>(*TH).SignInvert());}TE <uint M> IN CE Mod<M>& Mod<M>::SignInvert()NE{RE Ref(m_n > 0?m_n = M - m_n:m_n);}TE <uint M> IN CE Mod<M>& Mod<M>::Double()NE{RE Ref(Normalise(m_n <<= 1));}TE <uint M> IN CE Mod<M>& Mod<M>::Halve()NE{RE Ref(((m_n & 1)== 0?m_n:m_n += M)>>= 1);}TE <uint M> IN Mod<M>& Mod<M>::Invert(){assert(m_n > 0);uint m_n_neg;RE m_n < COantsForMod<M>::g_memory_LE?Ref(m_n = Inverse(m_n).m_n):(m_n_neg = M - m_n < COantsForMod<M>::g_memory_LE)?Ref(m_n = M - Inverse(m_n_neg).m_n):PositivePW(uint(COantsForMod<M>::g_M_minus_2));}TE <> IN Mod<2>& Mod<2>::Invert(){assert(m_n > 0);RE *TH;}TE <uint M> TE <TY T> IN CE Mod<M>& Mod<M>::PositivePW(T&& EX)NE{Mod<M> PW{*TH};EX--;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <> TE <TY T> IN CE Mod<2>& Mod<2>::PositivePW(T&& EX)NE{RE *TH;}TE <uint M> TE <TY T> IN CE Mod<M>& Mod<M>::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(m_n = 1):Ref(PositivePW(forward<T>(EX)));}TE <uint M> TE <TY T> IN CE Mod<M>& Mod<M>::PW(T&& EX){bool neg = EX < 0;assert(!(neg && m_n == 0));neg?EX *= COantsForMod<M>::g_M_minus_2_neg:EX;RE m_n == 0?*TH:(EX %= COantsForMod<M>::g_M_minus)== 0?Ref(m_n = 1):PositivePW(forward<T>(EX));}TE <uint M> IN CO Mod<M>& Mod<M>::Inverse(CO uint& n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr].m_n = M - MN<M>::MU(memory[M % LE_curr].m_n,M / LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::Factorial(CO uint& n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>::Factorial(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::FactorialInverse(CO uint& n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>::FactorialInverse(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE <uint M> IN CE VO Mod<M>::swap(Mod<M>& n)NE{std::swap(m_n,n.m_n);}TE <uint M> IN CE CO uint& Mod<M>::RP()CO NE{RE m_n;}TE <uint M> IN CE Mod<M> Mod<M>::DeRP(CO uint& n)NE{Mod<M> n_copy{};n_copy.m_n = n;RE n_copy;}TE <uint M> IN CE uint& Mod<M>::Normalise(uint& n)NE{RE n < M?n:n -= M;}TE <uint M> IN CO Mod<M>& Mod<M>::zero()NE{ST CE CO Mod<M> z{};RE z;}TE <uint M> IN CO Mod<M>& Mod<M>::one()NE{ST CE CO Mod<M> o{DeRP(1)};RE o;}TE <uint M> TE <TY T> IN CE Mod<M>& Mod<M>::Ref(T&& n)NE{RE *TH;}TE <uint M> IN CE Mod<M> Twice(CO Mod<M>& n)NE{RE MO(Mod<M>(n).Double());}TE <uint M> IN CE Mod<M> Half(CO Mod<M>& n)NE{RE MO(Mod<M>(n).Halve());}TE <uint M> IN Mod<M> Inverse(CO Mod<M>& n){RE MO(Mod<M>(n).Invert());}TE <uint M> IN CE Mod<M> Inverse_COrexpr(CO uint& n)NE{RE MO(Mod<M>::DeRP(RS<M>(n)).NonNegativePW(M - 2));}TE <uint M,TY T> IN CE Mod<M> PW(CO Mod<M>& n,CO T& EX){RE MO(Mod<M>(n).PW(T(EX)));}TE <uint M> IN CE VO swap(Mod<M>& n0,Mod<M>& n1)NE{n0.swap(n1);}TE <uint M> IN string to_string(CO Mod<M>& n)NE{RE to_string(n.RP())+ " + MZ";}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO Mod<M>& n){RE os << n.RP();}

#define SFINAE_FOR_PO(DEFAULT) TY Arg,enable_if_t<is_constructible<T,decay_t<Arg> >::value>* DEFAULT

TE <TY T>CL PO{PU:VE<T> m_f;uint m_SZ;IN PO();IN PO(CO T& t);IN PO(T&& t);TE <SFINAE_FOR_PO(= nullptr)> IN PO(CO Arg& n);IN PO(CO PO<T>& f);IN PO(PO<T>&& f);IN PO(CRUI i,CO T& t);IN PO(CRUI i,T&& t);TE <SFINAE_FOR_PO(= nullptr)> IN PO(CRUI i,CO Arg& n);IN PO(CO VE<T>& f);IN PO(VE<T>&& f);IN PO<T>& OP=(CO T& t);IN PO<T>& OP=(T&& t);TE <SFINAE_FOR_PO(= nullptr)> IN PO<T>& OP=(CO Arg& n);IN PO<T>& OP=(CO PO<T>& f);IN PO<T>& OP=(PO<T>&& f);IN PO<T>& OP=(CO VE<T>& f);IN PO<T>& OP=(VE<T>&& f);IN CO T& OP[](CRUI i) CO;IN T& OP[](CRUI i);IN T OP()(CO T& t) CO;PO<T>& OP+=(CO PO<T>& f);PO<T>& OP-=(CO PO<T>& f);PO<T>& OP*=(CO PO<T>& f);PO<T>& OP*=(PO<T>&& f);PO<T>& OP/=(CO T& t);IN PO<T>& OP/=(CO PO<T>& f);PO<T>& OP%=(CO T& t);PO<T>& OP%=(CO PO<T>& f);IN PO<T> OP-() CO;PO<T>& OP<<=(CO T& t);IN CO VE<T>& GetCoefficient() CO NE;IN CRUI SZ() CO NE;IN VO swap(PO<T>& f);IN VO swap(VE<T>& f);VO ReMORedundantZero();IN string Display() CO NE;ST PO<T> Quotient(CO PO<T>& f0,CO PO<T>& f1);ST PO<T> TPQuotient(CO PO<T>& f0,CRUI f0_TP_SZ,CO PO<T>& f1_TP_inverse,CRUI f1_SZ);ST PO<T> TP(CO PO<T>& f,CRUI f_TP_SZ);ST IN CO PO<T>& zero();ST IN CO T& CO_zero();ST IN CO T& CO_one();ST IN CO T& CO_minus_one();};

TE <TY T> IN PO<T>::PO():m_f(),m_SZ(0){}TE <TY T> IN PO<T>::PO(CO T& t):PO(){if(t != CO_zero()){OP[](0) = t;}}TE <TY T> IN PO<T>::PO(T&& t):PO(){if(t != CO_zero()){OP[](0) = MO(t);}}TE <TY T> TE <SFINAE_FOR_PO()> IN PO<T>::PO(CO Arg& n):PO(T(n)){}TE <TY T> IN PO<T>::PO(CO PO<T>& f):m_f(f.m_f),m_SZ(f.m_SZ){}TE <TY T> IN PO<T>::PO(PO<T>&& f):m_f(MO(f.m_f)),m_SZ(MO(f.m_SZ)){}TE <TY T> IN PO<T>::PO(CRUI i,CO T& t):PO(){if(t != CO_zero()){OP[](i) = t;}}TE <TY T> IN PO<T>::PO(CRUI i,T&& t):PO(){if(t != CO_zero()){OP[](i) = MO(t);}}TE <TY T> TE <SFINAE_FOR_PO()> IN PO<T>::PO(CRUI i,CO Arg& n):PO(i,T(n)){}TE <TY T> IN PO<T>::PO(CO VE<T>& f):m_f(f),m_SZ(m_f.SZ()){}TE <TY T> IN PO<T>::PO(VE<T>&& f):m_f(MO(f)),m_SZ(m_f.SZ()){}TE <TY T> IN PO<T>& PO<T>::OP=(CO T& t){m_f.clear();m_SZ = 0;OP[](0) = t;RE *TH;}TE <TY T> IN PO<T>& PO<T>::OP=(T&& t){m_f.clear();m_SZ = 0;OP[](0) = MO(t);RE *TH;}TE <TY T> TE <SFINAE_FOR_PO()> IN PO<T>& PO<T>::OP=(CO Arg& n){RE OP=(T(n));}TE <TY T> IN PO<T>& PO<T>::OP=(CO PO<T>& f){m_f = f.m_f;m_SZ = f.m_SZ;RE *TH;}TE <TY T> IN PO<T>& PO<T>::OP=(PO<T>&& f){m_f = MO(f.m_f);m_SZ = MO(f.m_SZ);RE *TH;}TE <TY T> IN PO<T>& PO<T>::OP=(CO VE<T>& f){m_f = f;m_SZ = f.m_SZ;RE *TH;}TE <TY T> IN PO<T>& PO<T>::OP=(VE<T>&& f){m_f = MO(f);m_SZ = m_f.SZ();RE *TH;}TE <TY T>CO T& PO<T>::OP[](CRUI i) CO{if(m_SZ <= i){RE CO_zero();}RE m_f[i];}TE <TY T> IN T& PO<T>::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 <TY T> IN T PO<T>::OP()(CO T& t) CO{RE MO((*TH % (PO<T>(1,CO_one()) - t))[0]);}TE <TY T>PO<T>& PO<T>::OP+=(CO PO<T>& 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 <TY T>PO<T>& PO<T>::OP-=(CO PO<T>& 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 <TY T>PO<T>& PO<T>::OP*=(CO PO<T>& 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<T> 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 <TY T> IN PO<T>& PO<T>::OP*=(PO<T>&& f){RE OP*=(f);};TE <TY T>PO<T>& PO<T>::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 <TY T>PO<T> PO<T>::TP(CO PO<T>& f,CRUI f_TP_SZ){VE<T> 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<T>(MO(f_TP));}TE <TY T>PO<T>& PO<T>::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 <TY T> IN PO<T> PO<T>::OP-() CO{RE MO(PO<T>() -= *TH);}TE <TY T> IN CO VE<T>& PO<T>::GetCoefficient() CO NE{RE m_f;}TE <TY T> IN CRUI PO<T>::SZ() CO NE{RE m_SZ;}TE <TY T> IN VO PO<T>::swap(PO<T>& f){m_f.swap(f.m_f);swap(m_SZ,f.m_SZ);}TE <TY T> IN VO PO<T>::swap(VE<T>& f){m_f.swap(f);m_SZ = m_f.SZ();}TE <TY T>VO PO<T>::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 <TY T>string PO<T>::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 <TY T> IN CO PO<T>& PO<T>::zero(){ST CO PO<T> z{};RE z;}TE <TY T> IN CO T& PO<T>::CO_zero(){ST CO T z{0};RE z;}TE <TY T> IN CO T& PO<T>::CO_one(){ST CO T o{1};RE o;}TE <TY T> IN CO T& PO<T>::CO_minus_one(){ST CO T m{-1};RE m;}TE <TY T>bool OP==(CO PO<T>& f0,CO T& t1){CRUI SZ = f0.SZ();CO T& zero = PO<T>::CO_zero();for(uint i = 1;i < SZ;i++){if(f0[i] != zero){RE false;}}RE f0[0] == t1;}TE <TY T>bool OP==(CO PO<T>& f0,CO PO<T>& 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 <TY T,TY P> IN bool OP!=(CO PO<T>& f0,CO P& f1){RE !(f0 == f1);}TE <TY T,TY P> IN PO<T> OP+(CO PO<T>& f0,CO P& f1){RE MO(PO<T>(f0) += f1);}TE <TY T,TY P> IN PO<T> OP-(CO PO<T>& f){RE PO<T>::zero() - f;}TE <TY T,TY P> IN PO<T> OP-(CO PO<T>& f0,CO P& f1){RE MO(PO<T>(f0) -= f1);}TE <TY T,TY P> IN PO<T> OP*(CO PO<T>& f0,CO P& f1){RE MO(PO<T>(f0) *= f1);}TE <TY T> IN PO<T> OP/(CO PO<T>& f0,CO T& t1){RE MO(PO<T>(f0) /= t1);}TE <TY T,TE <TY...> TY V>T& Prod(V<T>& 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 <TY T,uint EX_lim>CL PW_CE{PU:T m_val[EX_lim];IN CE PW_CE(CO T& t,CO T& init = T(1));};TE <TY T,uint EX_lim> IN CE PW_CE<T,EX_lim>::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 <TY T> IN CE CO uint LimitOfPWForFFT{};TE <TY T> IN CE CO uint BorderForFFT{};TE <TY T> IN CO T (&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT<T>];TE <TY T> IN CO T (&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT<T>];TE <> IN CE CO uint LimitOfPWForFFT<MP> = 24;TE <> IN CE CO uint LimitOfPWForFFT<MNP> = LimitOfPWForFFT<MP>;TE <> IN CE CO uint BorderForFFT<MP> = 4;TE <> IN CE CO uint BorderForFFT<MNP> = BorderForFFT<MP>;TE <> IN CO MP (&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT<MP>]{ST CO PW_CE<MP,LimitOfPWForFFT<MP> > PRT{31};RE PRT.m_val;}TE <> IN CO MP (&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT<MP>]{ST CO PW_CE<MP,LimitOfPWForFFT<MP> > IPRT{128805723};RE IPRT.m_val;}TE <> IN CO MNP (&PrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT<MNP>]{ST CO PW_CE<MNP,LimitOfPWForFFT<MNP> > PRT{31};RE PRT.m_val;}TE <> IN CO MNP (&InversePrimitiveRootOfTwoForFFT()NE)[LimitOfPWForFFT<MNP>]{ST CO PW_CE<MNP,LimitOfPWForFFT<MNP> > IPRT{128805723};RE IPRT.m_val;}TE <TY T>VO CooleyTukey(VE<T>& 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<T>]){CO uint LE = two_PW + N_input_start;f.reserve(LE);WH(f.SZ() < LE){f.push_back(0);}ST VE<uint> bit_reverse[32] ={VE<uint>(1)};ST uint e_next = 1;ST uint two_PW_next = 1;ST uint two_PW_next2 = 2;ST VE<uint>* p_bit_reverse_prev = bit_reverse;ST VE<uint>* p_bit_reverse_curr = p_bit_reverse_prev + 1;WH(e_next <= EX){*p_bit_reverse_curr = VE<uint>(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<uint>& 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 <TY T> IN VO FFT(VE<T>& f,CRUI N_input_start,CRUI N_input_lim,CRUI two_PW,CRUI EX){CooleyTukey<T>(f,N_input_start,N_input_lim,0,two_PW,two_PW,EX,PrimitiveRootOfTwoForFFT<T>());}TE <TY T> IN VO FFT(VE<T>& f,CRUI N_input_start,CRUI N_input_lim,CRUI N_output_start,CRUI N_output_lim,CRUI two_PW,CRUI EX){CooleyTukey<T>(f,N_input_start,N_input_lim,N_output_start,N_output_lim,two_PW,EX,PrimitiveRootOfTwoForFFT<T>());}TE <TY T> IN VO IFFT(VE<T>& f,CRUI N_input_start,CRUI N_input_lim,CRUI two_PW,CO T& two_PW_inv,CRUI EX){CooleyTukey<T>(f,N_input_start,N_input_lim,0,two_PW,two_PW,EX,InversePrimitiveRootOfTwoForFFT<T>());CO uint SZ = two_PW + N_input_start;for(uint i = N_input_start;i < SZ;i++){f[i] *= two_PW_inv;}}TE <TY T> IN VO IFFT(VE<T>& 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<T>(f,N_input_start,N_input_lim,N_output_start,N_output_lim,two_PW,EX,InversePrimitiveRootOfTwoForFFT<T>());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<TYPE>& PO<TYPE>::OP*=(ARG f){if(m_SZ != 0){VE<TYPE> v{};v.swap(m_f);TRPO<TYPE> TH_copy{m_SZ + f.m_SZ - 1,MO(v)};TH_copy *= RHS;m_f = MO(TH_copy.PO<TYPE>::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<TYPE>&,TH == &f?TH_copy:f);DF_BODY_OF_PARTIAL_SPECIALISATION_OF_PO(TYPE,PO<TYPE>&&,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<T>(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<T>::m_SZ < N_OUTPUT_LIM){for(uint i = PO<T>::m_SZ;i < N_OUTPUT_LIM;i++){PO<T>::m_f.push_back(0);}PO<T>::m_SZ = N_OUTPUT_LIM;}
#define SET_VE_FOR_AN_OF_TR_MU_CO_FOR_TR_PO(N_OUTPUT_LIM) VE<T> 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<T>::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<T>::m_f[j] * f.PO<T>::m_f[i - j];}PO<T>::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<T>::m_f[j] * f.PO<T>::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<T>::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<T>::m_SZ == 0);uint N_output_max = PO<T>::m_SZ + f.PO<T>::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<T>::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<T>::m_f,PO<T>::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<T>::m_SZ,N_input_start_1);
#define SET_N_INPUT_RANGE SET_N_INPUT_MAX_FOR_MU_FOR_TR_PO(PO<T>::m_f,PO<T>::m_SZ,N_input_max_0);SET_N_INPUT_MAX_FOR_MU_FOR_TR_PO(f,f.PO<T>::m_SZ < m_N?f.PO<T>::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<T> 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<T>;CO T& zero = PO<T>::CO_zero();bool searching = true;if(PO<T>::m_SZ < border_0 && f.PO<T>::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<T>;CO T& zero = PO<T>::CO_zero();bool searching = true;if(PO<T>::m_SZ < border_0 && f.PO<T>::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<T>;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<T>;uint EX = FFT_MU_border_1_2_EX<T>;T two_PW_inv{FFT_MU_border_1_2_inv<T>};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<T>(f0,N_INPUT_START_0,N_INPUT_LIM_0,two_PW,EX);DC_OF_F1;FFT<T>(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<T>(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 <TY T>CL TRPO :PU PO<T>{PU:uint m_N;IN TRPO(CRUI N = 0);IN TRPO(CO TRPO<T>& f);IN TRPO(TRPO<T>&& f);IN TRPO(CRUI N,CO T& t);IN TRPO(CRUI N,CO PO<T>& f);IN TRPO(CRUI N,PO<T>&& f);IN TRPO(CRUI N,CRUI i,CO T& t);IN TRPO(CRUI N,CRUI i,T&& t);TE <SFINAE_FOR_PO(= nullptr)> IN TRPO(CRUI N,CRUI i,CO Arg& t);IN TRPO(CRUI N,VE<T>&& f);IN TRPO<T>& OP=(CO TRPO<T>& f);IN TRPO<T>& OP=(TRPO<T>&& f);IN TRPO<T>& OP=(CO T& t);IN TRPO<T>& OP=(T&& t);TE <SFINAE_FOR_PO(= nullptr)> IN TRPO<T>& OP=(CO Arg& n);IN TRPO<T>& OP=(CO PO<T>& f);IN TRPO<T>& OP=(PO<T>&& f);IN TRPO<T>& OP+=(CO T& t);IN TRPO<T>& OP+=(CO PO<T>& f);IN TRPO<T>& OP+=(CO TRPO<T>& f);TRPO<T>& TRPlus(CO PO<T>& f,CRUI N_input_start,CRUI N_input_limit);IN TRPO<T>& OP-=(CO T& t);IN TRPO<T>& OP-=(CO PO<T>& f);IN TRPO<T>& OP-=(CO TRPO<T>& f);TRPO<T>& TRMinus(CO PO<T>& f,CRUI N_input_start,CRUI N_input_limit);IN TRPO<T>& OP*=(CO T& t);TRPO<T>& OP*=(CO PO<T>& f);IN TRPO<T>& OP*=(PO<T>&& f);TRPO<T>& FFT_MU(CO PO<T>& f);TRPO<T>& FFT_MU(PO<T>&& f);TRPO<T>& TRMU(CO PO<T>& f,CRUI N_output_start,CRUI N_output_lim);TRPO<T>& FFT_TRMU(CO PO<T>& f,CRUI N_output_start,CRUI N_output_lim);TRPO<T>& FFT_TRMU(PO<T>&& f,CRUI N_output_start,CRUI N_output_lim);TRPO<T> TRMU_CO(CO PO<T>& f,CRUI N_output_start,CRUI N_output_lim) CO;TRPO<T> FFT_TRMU_CO(CO PO<T>& f,CRUI N_output_start,CRUI N_output_lim) CO;TRPO<T> FFT_TRMU_CO(PO<T>&& f,CRUI N_output_start,CRUI N_output_lim) CO;IN TRPO<T>& OP/=(CO T& t);IN TRPO<T>& OP/=(CO TRPO<T>& t);IN TRPO<T>& OP%=(CO T& t);IN TRPO<T> OP-() CO;IN VO SetTruncation(CRUI N)NE;IN CRUI GetTruncation() CO NE;IN TRPO<T>& TruncateInitial(CRUI N)NE;IN TRPO<T>& TruncateFinal(CRUI N)NE;};TE <TY T> IN CE CO uint FFT_MU_border_0{};TE <TY T> IN CE CO uint FFT_MU_border_1{};TE <TY T> IN CE CO uint FFT_MU_border_1_2{};TE <TY T> IN CE CO uint FFT_MU_border_1_2_EX{};TE <TY T> IN CE CO uint FFT_MU_border_1_2_inv{};

TE <TY T> IN TRPO<T>::TRPO(CRUI N):PO<T>(),m_N(N){PO<T>::m_f.reserve(m_N);}TE <TY T> IN TRPO<T>::TRPO(CO TRPO<T>& f):PO<T>(f),m_N(f.m_N){PO<T>::m_f.reserve(m_N);}TE <TY T> IN TRPO<T>::TRPO(TRPO<T>&& f):PO<T>(MO(f)),m_N(MO(f.m_N)){PO<T>::m_f.reserve(m_N);}TE <TY T> IN TRPO<T>::TRPO(CRUI N,CO T& t):PO<T>(t),m_N(N){PO<T>::m_f.reserve(m_N);}TE <TY T> IN TRPO<T>::TRPO(CRUI N,CO PO<T>& f):PO<T>(),m_N(N){PO<T>::m_SZ = f.PO<T>::m_SZ < m_N?f.PO<T>::m_SZ:m_N;PO<T>::m_f = VE<T>(PO<T>::m_SZ);for(uint i = 0;i < PO<T>::m_SZ;i++){PO<T>::m_f[i] = f.PO<T>::m_f[i];}PO<T>::m_f.reserve(m_N);}TE <TY T> IN TRPO<T>::TRPO(CRUI N,PO<T>&& f):PO<T>(),m_N(N){if(f.PO<T>::m_SZ < m_N * 2){PO<T>::OP=(MO(f));if(f.PO<T>::m_SZ < m_N){PO<T>::m_f.reserve(m_N);}else{TruncateFinal(m_N);}}else{PO<T>::m_f = VE<T>(m_N);for(uint i = 0;i < m_N;i++){PO<T>::m_f[i] = MO(f.PO<T>::m_f[i]);}PO<T>::m_SZ = m_N;}}TE <TY T> IN TRPO<T>::TRPO(CRUI N,CRUI i,CO T& t):PO<T>(),m_N(N){if(i < m_N?t != PO<T>::CO_zero():false){PO<T>::OP[](i) = t;}PO<T>::m_f.reserve(m_N);}TE <TY T> IN TRPO<T>::TRPO(CRUI N,CRUI i,T&& t):PO<T>(),m_N(N){if(i < m_N?t != PO<T>::CO_zero():false){PO<T>::OP[](i) = MO(t);}PO<T>::m_f.reserve(m_N);}TE <TY T> TE <SFINAE_FOR_PO()> IN TRPO<T>::TRPO(CRUI N,CRUI i,CO Arg& n):TRPO(N,i,T(n)){}TE <TY T> IN TRPO<T>::TRPO(CRUI N,VE<T>&& f):PO<T>(),m_N(N){CO uint f_SZ = f.SZ();if(f_SZ < m_N * 2){PO<T>::OP=(MO(f));if(f_SZ < m_N){PO<T>::m_f.reserve(m_N);}else{TruncateFinal(m_N);}}else{PO<T>::m_f = VE<T>(m_N);for(uint i = 0;i < m_N;i++){PO<T>::m_f[i] = MO(f[i]);}PO<T>::m_f.reserve(m_N);}}TE <TY T> IN TRPO<T>& TRPO<T>::OP=(CO TRPO<T>& f){PO<T>::OP=(f);m_N = f.m_N;PO<T>::m_f.reserve(m_N);RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP=(TRPO<T>&& f){PO<T>::OP=(MO(f));m_N = MO(f.m_N);PO<T>::m_f.reserve(m_N);RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP=(CO T& t){PO<T>::OP=(t);RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP=(T&& t){PO<T>::OP=(MO(t));RE *TH;}TE <TY T> TE <SFINAE_FOR_PO()> IN TRPO<T>& TRPO<T>::OP=(CO Arg& n){PO<T>::OP=(T(n));RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP=(CO PO<T>& f){RE OP=(TRPO<T>(m_N,f));}TE <TY T> IN TRPO<T>& TRPO<T>::OP=(PO<T>&& f){RE OP=(TRPO<T>(m_N,MO(f)));}TE <TY T> IN TRPO<T>& TRPO<T>::OP+=(CO T& t){PO<T>::OP+=(t);RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP+=(CO PO<T>& f){RE TRPO<T>::TRPlus(f,0,f.m_SZ);}TE <TY T> IN TRPO<T>& TRPO<T>::OP+=(CO TRPO<T>& f){RE m_N == 0?OP=(f):TRPO<T>::TRPlus(f,0,f.PO<T>::m_SZ);}TE <TY T>TRPO<T>& TRPO<T>::TRPlus(CO PO<T>& f,CRUI N_input_start,CRUI N_input_lim){CRUI SZ = N_input_lim < m_N?N_input_lim < f.PO<T>::m_SZ?N_input_lim:f.PO<T>::m_SZ:m_N < f.PO<T>::m_SZ?m_N:f.PO<T>::m_SZ;if(PO<T>::m_SZ < SZ){PO<T>::m_f.reserve(SZ);for(uint i = N_input_start;i < PO<T>::m_SZ;i++){PO<T>::m_f[i] += f.PO<T>::m_f[i];}for(uint i = PO<T>::m_SZ;i < SZ;i++){PO<T>::m_f.push_back(f.PO<T>::m_f[i]);}PO<T>::m_SZ = SZ;}else{for(uint i = N_input_start;i < SZ;i++){PO<T>::m_f[i] += f.PO<T>::m_f[i];}}RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP-=(CO T& t){PO<T>::OP-=(t);RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP-=(CO PO<T>& f){RE TRPO<T>::TRMinus(f,0,f.m_SZ);}TE <TY T> IN TRPO<T>& TRPO<T>::OP-=(CO TRPO<T>& f){RE m_N == 0?OP=(-f):TRPO<T>::TRMinus(f,0,f.PO<T>::m_SZ);}TE <TY T>TRPO<T>& TRPO<T>::TRMinus(CO PO<T>& f,CRUI N_input_start,CRUI N_input_lim){CRUI SZ = N_input_lim < m_N?N_input_lim < f.PO<T>::m_SZ?N_input_lim:f.PO<T>::m_SZ:m_N < f.PO<T>::m_SZ?m_N:f.PO<T>::m_SZ;if(PO<T>::m_SZ < SZ){PO<T>::m_f.reserve(SZ);for(uint i = N_input_start;i < PO<T>::m_SZ;i++){PO<T>::m_f[i] -= f.PO<T>::m_f[i];}for(uint i = PO<T>::m_SZ;i < SZ;i++){PO<T>::m_f.push_back(- f.PO<T>::m_f[i]);}PO<T>::m_SZ = SZ;}else{for(uint i = N_input_start;i < SZ;i++){PO<T>::m_f[i] -= f.PO<T>::m_f[i];}}RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP*=(CO T& t){PO<T>::OP*=(t);RE *TH;}TE <TY T>TRPO<T>& TRPO<T>::OP*=(CO PO<T>& f){DF_OF_MU_FOR_TR_PO(RE_ZERO_FOR_MU_FOR_TR_PO_IF(f.PO<T>::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<T>::m_f,0,);}TE <TY T> IN TRPO<T>& TRPO<T>::OP*=(PO<T>&& f){RE OP*=(f);}TE <TY T>TRPO<T>& TRPO<T>::FFT_MU(CO PO<T>& f){DF_OF_FFT_MU_FOR_TR_PO(RE_ZERO_FOR_MU_FOR_TR_PO_IF(f.PO<T>::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<T>::m_f[j],0,0,,VE<T>& f0 = PO<T>::m_f,N_input_start_0,N_input_max_0 + 1,SET_SHIFTED_VE_FOR_MU(f1,f.PO<T>::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<T>(m_N,MO(f1))));}TE <TY T>TRPO<T>& TRPO<T>::FFT_MU(PO<T>&& f){DF_OF_FFT_MU_FOR_TR_PO(RE_ZERO_FOR_MU_FOR_TR_PO_IF(f.PO<T>::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<T>::m_f[j],0,0,,VE<T>& f0 = PO<T>::m_f,N_input_start_0,N_input_max_0 + 1,VE<T>&& f1 = MO(f.PO<T>::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<T>::m_SZ = f0.SZ();SetTruncation(m_N););}TE <TY T>TRPO<T>& TRPO<T>::TRMU(CO PO<T>& 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<T>::m_f[j],N_output_start,if(N_output_lim_fixed > N_output_lim){N_output_lim_fixed = N_output_lim;});}TE <TY T>TRPO<T>& TRPO<T>::FFT_TRMU(CO PO<T>& 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<T>::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<T>& f0 = PO<T>::m_f,N_input_start_0,N_input_max_0 + 1,SET_SHIFTED_VE_FOR_MU(f1,f.PO<T>::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<T>(m_N,MO(f1))));}TE <TY T>TRPO<T>& TRPO<T>::FFT_TRMU(PO<T>&& 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<T>::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<T>& f0 = PO<T>::m_f,N_input_start_0,N_input_max_0 + 1,VE<T>&& f1 = MO(f.PO<T>::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<T>::m_SZ = f0.SZ();SetTruncation(m_N););}TE <TY T>TRPO<T> TRPO<T>::TRMU_CO(CO PO<T>& f,CRUI N_output_start,CRUI N_output_lim) CO{DF_OF_MU_FOR_TR_PO(,RE TRPO<T>(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<T>(m_N,MO(AN)),TR_MU_CO,PO<T>::OP[](j),N_output_start,if(N_output_lim_fixed > N_output_lim){N_output_lim_fixed = N_output_lim;});}TE <TY T>TRPO<T> TRPO<T>::FFT_TRMU_CO(CO PO<T>& f,CRUI N_output_start,CRUI N_output_lim) CO{DF_OF_FFT_MU_FOR_TR_PO(,RE TRPO<T>(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<T>(m_N,MO(AN)),RE TRPO<T>(m_N,MO(f0)),TR_MU_CO,PO<T>::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<T>::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<T> f1 = f.PO<T>::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 <TY T>TRPO<T> TRPO<T>::FFT_TRMU_CO(PO<T>&& f,CRUI N_output_start,CRUI N_output_lim) CO{DF_OF_FFT_MU_FOR_TR_PO(,RE TRPO<T>(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<T>(m_N,MO(AN)),RE TRPO<T>(m_N,MO(f0)),TR_MU_CO,PO<T>::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<T>::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<T>&& f1 = MO(f.PO<T>::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 <TY T> IN TRPO<T>& TRPO<T>::OP/=(CO T& t){PO<T>::OP/=(t);RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::OP/=(CO TRPO<T>& f){RE OP*=(Inverse(m_N > f.m_N?f:TRPO<T>(m_N,f)));}TE <TY T> IN TRPO<T>& TRPO<T>::OP%=(CO T& t){PO<T>::OP%=(t);RE *TH;}TE <TY T> IN TRPO<T> TRPO<T>::OP-() CO{RE MO(TRPO<T>(m_N) -= *TH);}TE <TY T> IN VO TRPO<T>::SetTruncation(CRUI N)NE{if(N < m_N){TruncateFinal(m_N);}else{PO<T>::m_f.reserve(N);}m_N = N;}TE <TY T> IN CRUI TRPO<T>::GetTruncation() CO NE{RE m_N;}TE <TY T> IN TRPO<T>& TRPO<T>::TruncateInitial(CRUI N)NE{CRUI SZ = N < PO<T>::m_SZ?N:PO<T>::m_SZ;for(uint i = 0;i < SZ;i++){PO<T>::m_f[i] = 0;}RE *TH;}TE <TY T> IN TRPO<T>& TRPO<T>::TruncateFinal(CRUI N)NE{WH(PO<T>::m_SZ > N){PO<T>::m_f.pop_back();PO<T>::m_SZ--;}RE *TH;}TE <TY T,TY P> IN TRPO<T> OP+(CO TRPO<T>& f0,CO P& f1){RE MO(TRPO<T>(f0) += f1);}TE <TY T,TY P> IN TRPO<T> OP-(CO TRPO<T>& f){RE MO(TRPO<T>(f.GetTurncation()) -= f);}TE <TY T,TY P> IN TRPO<T> OP-(CO TRPO<T>& f0,CO P& f1){RE MO(TRPO<T>(f0) -= f1);}TE <TY T,TY P> IN TRPO<T> OP*(CO TRPO<T>& f0,CO P& f1){RE MO(TRPO<T>(f0) *= f1);}TE <TY T,TY P> IN TRPO<T> OP/(CO TRPO<T>& f0,CO P& f1){RE MO(TRPO<T>(f0) /= f1);}TE <TY T> IN TRPO<T> OP%(CO TRPO<T>& f0,CO T& t1){RE MO(TRPO<T>(f0) %= t1);}TE <TY T>TRPO<T> Differential(CRUI n,CO TRPO<T>& f){if(f.PO<T>::m_SZ < n){RE TRPO<T>(f.m_N - n,PO<T>::zero());}VE<T> df(f.PO<T>::m_SZ - n);T coef = T::Factorial(n);uint i = n;WH(i < f.PO<T>::m_SZ){df[i - n] = f[i] * coef;i++;(coef *= i) /= (i - n);}RE TRPO<T>(f.m_N - n,MO(df));}TE <TY T>TRPO<T> TRDifferential(CO TRPO<T>& f,CRUI N_output_start_plus_one){assert(f.m_N > 0);TRPO<T> f_dif{f.m_N - 1};if(N_output_start_plus_one < f.PO<T>::m_SZ){CO uint SZ = f.PO<T>::m_SZ - 1;f_dif.PO<T>::m_f = VE<T>(SZ);for(uint i = N_output_start_plus_one;i < f.PO<T>::m_SZ;i++){f_dif.PO<T>::m_f[i-1] = i * f.PO<T>::m_f[i];}f_dif.PO<T>::m_SZ = SZ;}RE f_dif;}TE <TY T> IN TRPO<T> Differential(CO TRPO<T>& f){RE TRDifferential<T>(f,1);}TE <TY T>TRPO<T> TRIntegral(CO TRPO<T>& f,CRUI N_output_start){TRPO<T> f_int{f.m_N + 1};if(N_output_start <= f.PO<T>::m_SZ){CO uint SZ = f.PO<T>::m_SZ + 1;f_int.PO<T>::m_f = VE<T>(SZ);for(uint i = N_output_start;i <= f.PO<T>::m_SZ;i++){f_int.PO<T>::m_f[i] = f.PO<T>::m_f[i - 1] / T(i);}f_int.PO<T>::m_SZ = SZ;}RE f_int;}TE <TY T> IN TRPO<T> Integral(CO TRPO<T>& f){RE TRIntegral<T>(f,1);}TE <TY T>TRPO<T> Inverse(CO TRPO<T>& 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 <TY T>TRPO<T> Exp(CO TRPO<T>& 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 <TY T> IN TRPO<T> Log(CO TRPO<T>& f){RE Integral<T>(Differential<T>(f) /= f);}TE <TY T> IN TRPO<T> PW(CO TRPO<T>& f,CO T& t){RE Exp(Log(f) *= t);}
TE <TY T> IN PO<T>& PO<T>::OP/=(CO PO<T>& f){RE m_SZ < f.m_SZ?*TH:OP=(Quotient(*TH,f));}TE <TY T>PO<T>& PO<T>::OP%=(CO PO<T>& f){if(m_SZ >= f.m_SZ){OP-=((*TH / f) * f);ReMORedundantZero();}RE *TH;}TE <TY T>PO<T> PO<T>::Quotient(CO PO<T>& f0,CO PO<T>& 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<T>(f0_TP_SZ,TP(f1,f1_TP_SZ))),f1.m_SZ);}TE <TY T>PO<T> PO<T>::TPQuotient(CO PO<T>& f0,CRUI f0_TP_SZ,CO PO<T>& f1_TP_inverse,CRUI f1_SZ){TRPO<T> 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<T>::m_f[d0],f0_TP.PO<T>::m_f[ f0_TP_SZ - 1 - d0 ]);}RE f0_TP;}TE <TY T >PO<T>& PO<T>::OP<<=(CO T& t){if(m_SZ > 0){for(uint d = 0;d < m_SZ;d++){m_f[d] *= T::Factorial(d);}TRPO<T> 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<T>::m_f[d + m_SZ - 1] * T::FactorialInverse(d);}}RE *TH;}TE <TY T> IN PO<T> OP/(CO PO<T>& f0,CO PO<T>& f1){RE PO<T>::Quotient(f0,f1);}TE <TY T,TY P> IN PO<T> OP%(CO PO<T>& f0,CO P& f1){RE MO(PO<T>(f0) %= f1);}TE <TY T> PO<T> OP<<(CO PO<T>& f,CO T& t){RE MO(PO<T>(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);


ll K = 1;
ll K2 = 2;
PO<MNP> mul( PO<MNP> f0 , PO<MNP> f1 )
{
  PO<MNP> ans = f0 * f1;
  while( ans.m_SZ > K ){
    ans.m_SZ--;
    ans.m_f[ans.m_SZ - K] += ans.m_f[ans.m_SZ];
    ans.m_f.pop_back();
  }
  return ans;
}
inline constexpr MNP one{ 1 };
inline PO<MNP> e(){ return PO<MNP>( 0 , one ); }

#include <atcoder/all>
using namespace atcoder;

int main()
{
  UNTIE;
  CIN( int , N );
  CIN( int , M );
  cin >> K;
  K2 = ( K << 1 );
  segtree<PO<MNP>,mul,e> a{ N };
  FOR( i , 0 , N ){
    CIN( uint , Ai );
    a.set( i , e() + PO<MNP>( Ai % K , 1 ) );
  }
  int k_lim = N - M + 1;
  FOR( k , 0 , k_lim ){
    COUT( a.prod( k , k + M ).m_f[0] - 1 );
  }
  RETURN( min( left , right ) );
}

yukicoder

結果

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