#ifdef DEBUG #define _GLIBCXX_DEBUG #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ); signal( SIGABRT , &AlertAbort ) #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE ) #define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl #define COUT( ... ) VariadicCout( cout << "出力: " , __VA_ARGS__ ) << endl #define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl #define COUT_A( A , N ) cout << "出力: "; OUTPUT_ARRAY( cout , A , N ) << endl #define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl #define COUT_ITR( A ) cout << "出力: "; OUTPUT_ITR( cout , A ) << endl #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック: " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) ) #define AUTO_CHECK bool auto_checked = true; AutoCheck( auto_checked ); if( auto_checked ){ return 0; }; #else #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( ... ) #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << "\n" #define CERR_A( A , N ) #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << "\n" #define CERR_ITR( A ) #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << "\n" #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #define AUTO_CHECK #endif #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using ld = long double; using lld = __float128; // #define RANDOM_TEST #if defined( DEBUG ) && defined( RANDOM_TEST ) ll GetRand( const ll& Rand_min , const ll& Rand_max ); #define SET_ASSERT( A , MIN , MAX ) CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ) #define RETURN( ANSWER ) if( ( ANSWER ) == guchoku ){ CERR( ANSWER , "==" , guchoku ); goto END_MAIN; } else { CERR( ANSWER , "!=" , guchoku ); QUIT; } #else #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX ) #define RETURN( ANSWER ) COUT( ANSWER ); QUIT #endif #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 , ... ) LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ ) #define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define CIN_A( LL , A , N ) LL A[N]; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; } #define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ ) #define GETLINE( ... ) GETLINE_SEPARATE( " " , ... ) #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 SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS ) #define OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS #define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.begin() , END_FOR_OUTPUT_ITR = A.end(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; while( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS #define QUIT goto END_MAIN #define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = 1; if constexpr( bound_T > 1 ){ SET_ASSERT( T , 1 , bound_T ); } #define START_MAIN REPEAT( T ){ { if constexpr( bound_T > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_T , ":" ); } #define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now() #define CURRENT_TIME static_cast( chrono::duration_cast( chrono::system_clock::now() - watch ).count() / 1000.0 ) #define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 ) #define FINISH_MAIN QUIT; } END_MAIN: CERR( "" ); } // 入出力用関数 template inline basic_istream& VariadicCin( basic_istream& is ) { return is; } template inline basic_istream& VariadicCin( basic_istream& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); } template inline basic_istream& VariadicGetline( basic_istream& is , const char& separator ) { return is; } template inline basic_istream& VariadicGetline( basic_istream& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); } template inline basic_ostream& VariadicCout( basic_ostream& os , const Arg& arg ) { return os << arg; } template inline basic_ostream& VariadicCout( basic_ostream& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); } // 算術用関数 template inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); } inline ll MIN( const ll& a , const ll& b ){ return min( a , b ); } inline ull MIN( const ull& a , const ull& b ){ return min( a , b ); } inline ll MAX( const ll& a , const ll& b ){ return max( a , b ); } inline ull MAX( const ull& a , const ull& b ){ return max( a , b ); } #define POWER( ANSWER , ARGUMENT , EXPONENT ) \ static_assert( ! is_same::value && ! is_same::value ); \ 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 ) \ ll ANSWER{ 1 }; \ { \ ll 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_INDEX , CONSTEXPR_LENGTH , MODULO ) \ static ll ANSWER[CONSTEXPR_LENGTH]; \ static ll ANSWER_INV[CONSTEXPR_LENGTH]; \ static ll INVERSE[CONSTEXPR_LENGTH]; \ { \ ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL; \ FOREQ( i , 1 , MAX_INDEX ){ \ 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_INDEX ){ \ ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \ } \ } \ // 二分探索テンプレート // EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= TARGETの整数解を格納。 #define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \ static_assert( ! is_same::value && ! is_same::value ); \ ll ANSWER = MINIMUM; \ if( MINIMUM <= MAXIMUM ){ \ ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM; \ ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM; \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH; \ while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \ VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \ CERR( "二分探索中: " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << "=" << VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ); \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH INEQUALITY_FOR_CHECK 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_U = UPDATE_U; \ } else { \ VARIABLE_FOR_BINARY_SEARCH_L = UPDATE_L; \ } \ ANSWER = UPDATE_ANSWER; \ } \ CERR( "二分探索終了: " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << ( EXPRESSION > TARGET ? ">" : EXPRESSION < TARGET ? "<" : "=" ) << TARGET ); \ if( EXPRESSION DESIRED_INEQUALITY TARGET ){ \ CERR( "二分探索成功" ); \ } else { \ CERR( "二分探索失敗" ); \ ANSWER = MAXIMUM + 1; \ } \ } else { \ CERR( "二分探索失敗: " << MINIMUM << ">" << MAXIMUM ); \ ANSWER = MAXIMUM + 1; \ } \ // 単調増加の時にEXPRESSION >= TARGETの最小解を格納。 #define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , >= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調増加の時にEXPRESSION <= TARGETの最大解を格納。 #define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , > , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調減少の時にEXPRESSION >= TARGETの最大解を格納。 #define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , < , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調減少の時にEXPRESSION <= TARGETの最小解を格納。 #define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , <= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。 template inline typename set::iterator MaximumLeq( set& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.upper_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; } // t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。 template inline typename set::iterator MaximumLt( set& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.lower_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; } // t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。 template inline typename set::iterator MinimumGeq( set& S , const T& t ) { return S.lower_bound( t ); } // tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。 template inline typename set::iterator MinimumGt( set& S , const T& t ) { return S.upper_bound( t ); } // データ構造用関数 template inline T add( const T& t0 , const T& t1 ) { return t0 + t1; } template inline T xor_add( const T& t0 , const T& t1 ){ return t0 ^ t1; } template inline T multiply( const T& t0 , const T& t1 ) { return t0 * t1; } template inline const T& zero() { static const T z = 0; return z; } template inline const T& one() { static const T o = 1; return o; }\ template inline T add_inv( const T& t ) { return -t; } template inline T id( const T& v ) { return v; } // グリッド問題用関数 int H , W , H_minus , W_minus , HW; inline pair EnumHW( const int& v ) { return { v / W , v % W }; } inline int EnumHW_inv( const int& h , const int& w ) { return h * W + w; } const string direction[4] = {"U","R","D","L"}; // (i,j)->(k,h)の方向番号を取得 inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return ik?0:jh?3:(assert(false),-1);} // v->wの方向番号を取得 inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);return DirectionNumberOnGrid(i,j,k,h);} // 方向番号の反転U<->D、R<->L inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;} // デバッグ用関数 #ifdef DEBUG inline void AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); } void AutoCheck( bool& auto_checked ); #endif // 圧縮用 #define TE template #define TY typename #define US using #define ST static #define IN inline #define CL class #define PU public #define OP operator #define CE constexpr #define CO const #define NE noexcept #define RE return #define WH while #define VO void #define VE vector #define LI list #define BE begin #define EN end #define SZ size #define MO move #define TH this #define CRI CO int& #define CRUI CO uint& #define CRL CO ll& // VVV ライブラリは以下に挿入する。 CEXPR(uint,P,998244353);TE CE INT& RS(INT& n)NE{RE n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n %= M;}TE CE uint& RS(uint& n)NE{RE n %= M;}TE CE ull& RS(ull& n)NE{RE n %= M;}TE CE INT& RSP(INT& n)NE{CE CO uint trunc = (1 << 23)- 1;INT n_u = n >> 23;n &= trunc;INT n_uq = (n_u / 7)/ 17;n_u -= n_uq * 119;n += n_u << 23;RE n < n_uq?n += P - n_uq:n -= n_uq;}TE <> CE ull& RS(ull& n)NE{CE CO ull Pull = P;CE CO ull Pull2 = (Pull - 1)* (Pull - 1);RE RSP(n > Pull2?n -= Pull2:n);}TE CE INT RS(INT&& n)NE{RE MO(RS(n));}TE CE INT RS(CO INT& n)NE{RE RS(INT(n));} #define SFINAE_FOR_MOD(DEFAULT)TY T,enable_if_t >::value>* DEFAULT #define DC_OF_CM_FOR_MOD(FUNC)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;CE Mod()NE;CE Mod(CO Mod& n)NE;CE Mod(Mod& n)NE;CE Mod(Mod&& n)NE;TE CE Mod(CO T& n)NE;TE CE Mod(T& n)NE;TE CE Mod(T&& n)NE;CE Mod& OP=(CO Mod& n)NE;CE Mod& OP=(Mod&& n)NE;CE Mod& OP+=(CO Mod& n)NE;CE Mod& OP-=(CO Mod& n)NE;CE Mod& OP*=(CO Mod& n)NE;IN Mod& OP/=(CO Mod& n);CE Mod& OP<<=(int n)NE;CE Mod& OP>>=(int n)NE;CE Mod& OP++()NE;CE Mod OP++(int)NE;CE Mod& OP--()NE;CE Mod OP--(int)NE;DC_OF_CM_FOR_MOD(==);DC_OF_CM_FOR_MOD(!=);DC_OF_CM_FOR_MOD(<);DC_OF_CM_FOR_MOD(<=);DC_OF_CM_FOR_MOD(>);DC_OF_CM_FOR_MOD(>=);DC_OF_AR_FOR_MOD(+);DC_OF_AR_FOR_MOD(-);DC_OF_AR_FOR_MOD(*);DC_OF_AR_FOR_MOD(/);CE Mod OP<<(int n)CO NE;CE Mod OP>>(int n)CO NE;CE Mod OP-()CO NE;CE Mod& SignInvert()NE;CE Mod& Double()NE;CE Mod& Halve()NE;IN Mod& Invert();TE CE Mod& PositivePW(T&& EX)NE;TE CE Mod& NonNegativePW(T&& EX)NE;TE CE Mod& PW(T&& EX);CE VO swap(Mod& n)NE;CE CRUI RP()CO NE;ST CE Mod DeRP(CRUI n)NE;ST CE uint& Normalise(uint& n)NE;ST IN CO Mod& Inverse(CRUI n)NE;ST IN CO Mod& Factorial(CRUI n)NE;ST IN CO Mod& FactorialInverse(CRUI n)NE;ST IN Mod Combination(CRUI n,CRUI i)NE;ST IN CO Mod& zero()NE;ST IN CO Mod& one()NE;TE CE Mod& Ref(T&& n)NE;}; #define SFINAE_FOR_MN(DEFAULT)TY T,enable_if_t,decay_t >::value>* DEFAULT #define DC_OF_AR_FOR_MN(FUNC)IN MN OP FUNC(CO MN& n)CO NE;TE IN MN OP FUNC(T&& n)CO NE; #define DF_OF_CM_FOR_MN(FUNC)TE IN bool MN::OP FUNC(CO MN& n)CO NE{RE m_n FUNC n.m_n;} #define DF_OF_AR_FOR_MN(FUNC,FORMULA)TE IN MN MN::OP FUNC(CO MN& n)CO NE{RE MO(MN(*TH)FUNC ## = n);}TE TE IN MN MN::OP FUNC(T&& n)CO NE{RE FORMULA;}TE IN MN OP FUNC(T&& n0,CO MN& n1)NE{RE MO(MN(forward(n0))FUNC ## = n1);} TE CL MN:PU Mod{PU:CE MN()NE;CE MN(CO MN& n)NE;CE MN(MN& n)NE;CE MN(MN&& n)NE;TE CE MN(CO T& n)NE;TE CE MN(T&& n)NE;CE MN& OP=(CO MN& n)NE;CE MN& OP=(MN&& n)NE;CE MN& OP+=(CO MN& n)NE;CE MN& OP-=(CO MN& n)NE;CE MN& OP*=(CO MN& n)NE;IN MN& OP/=(CO MN& n);CE MN& OP<<=(int n)NE;CE MN& OP>>=(int n)NE;CE MN& OP++()NE;CE MN OP++(int)NE;CE MN& OP--()NE;CE MN OP--(int)NE;DC_OF_AR_FOR_MN(+);DC_OF_AR_FOR_MN(-);DC_OF_AR_FOR_MN(*);DC_OF_AR_FOR_MN(/);CE MN OP<<(int n)CO NE;CE MN OP>>(int n)CO NE;CE MN OP-()CO NE;CE MN& SignInvert()NE;CE MN& Double()NE;CE MN& Halve()NE;CE MN& Invert();TE CE MN& PositivePW(T&& EX)NE;TE CE MN& NonNegativePW(T&& EX)NE;TE CE MN& PW(T&& EX);CE uint RP()CO NE;CE Mod Reduce()CO NE;ST CE MN DeRP(CRUI n)NE;ST IN CO MN& Formise(CRUI n)NE;ST IN CO MN& Inverse(CRUI n)NE;ST IN CO MN& Factorial(CRUI n)NE;ST IN CO MN& FactorialInverse(CRUI n)NE;ST IN MN Combination(CRUI n,CRUI i)NE;ST IN CO MN& zero()NE;ST IN CO MN& one()NE;ST CE uint Form(CRUI n)NE;ST CE ull& Reduction(ull& n)NE;ST CE ull& ReducedMU(ull& n,CRUI m)NE;ST CE uint MU(CRUI n0,CRUI n1)NE;ST CE uint BaseSquareTruncation(uint& n)NE;TE CE MN& Ref(T&& n)NE;};TE CE MN Twice(CO MN& n)NE;TE CE MN Half(CO MN& n)NE;TE CE MN Inverse(CO MN& n);TE CE MN PW(MN n,T EX);TE CE MN<2> PW(CO MN<2>& n,CO T& p);TE CE T Square(CO T& t);TE <> CE MN<2> Square >(CO MN<2>& t);TE CE VO swap(MN& n0,MN& n1)NE;TE IN string to_string(CO MN& n)NE;TE IN basic_ostream& OP<<(basic_ostream& os,CO MN& n); TE CL COantsForMod{PU:COantsForMod()= delete;ST CE CO bool g_even = ((M & 1)== 0);ST CE CO uint g_memory_bound = 1000000;ST CE CO uint g_memory_LE = M < g_memory_bound?M:g_memory_bound;ST CE ull MNBasePW(ull&& EX)NE;ST CE uint g_M_minus = M - 1;ST CE uint g_M_minus_2 = M - 2;ST CE uint g_M_minus_2_neg = 2 - M;ST CE CO int g_MN_digit = 32;ST CE CO ull g_MN_base = ull(1)<< g_MN_digit;ST CE CO uint g_MN_base_minus = uint(g_MN_base - 1);ST CE CO uint g_MN_digit_half = (g_MN_digit + 1)>> 1;ST CE CO uint g_MN_base_sqrt_minus = (1 << g_MN_digit_half)- 1;ST CE CO uint g_MN_M_neg_inverse = uint((g_MN_base - MNBasePW((ull(1)<< (g_MN_digit - 1))- 1))& g_MN_base_minus);ST CE CO uint g_MN_base_mod = uint(g_MN_base % M);ST CE CO uint g_MN_base_square_mod = uint(((g_MN_base % M)* (g_MN_base % M))% M);};TE CE ull COantsForMod::MNBasePW(ull&& EX)NE{ull prod = 1;ull PW = M;WH(EX != 0){(EX & 1)== 1?(prod *= PW)&= g_MN_base_minus:prod;EX >>= 1;(PW *= PW)&= g_MN_base_minus;}RE prod;} US MP = Mod

;US MNP = MN

;TE CE uint MN::Form(CRUI n)NE{ull n_copy = n;RE uint(MO(Reduction(n_copy *= COantsForMod::g_MN_base_square_mod)));}TE CE ull& MN::Reduction(ull& n)NE{ull n_sub = n & COantsForMod::g_MN_base_minus;RE ((n += ((n_sub *= COantsForMod::g_MN_M_neg_inverse)&= COantsForMod::g_MN_base_minus)*= M)>>= COantsForMod::g_MN_digit)< M?n:n -= M;}TE CE ull& MN::ReducedMU(ull& n,CRUI m)NE{RE Reduction(n *= m);}TE CE uint MN::MU(CRUI n0,CRUI n1)NE{ull n0_copy = n0;RE uint(MO(ReducedMU(ReducedMU(n0_copy,n1),COantsForMod::g_MN_base_square_mod)));}TE CE uint MN::BaseSquareTruncation(uint& n)NE{CO uint n_u = n >> COantsForMod::g_MN_digit_half;n &= COantsForMod::g_MN_base_sqrt_minus;RE n_u;}TE CE MN::MN()NE:Mod(){static_assert(! COantsForMod::g_even);}TE CE MN::MN(CO MN& n)NE:Mod(n){}TE CE MN::MN(MN& n)NE:Mod(n){}TE CE MN::MN(MN&& n)NE:Mod(MO(n)){}TE TE CE MN::MN(CO T& n)NE:Mod(n){static_assert(! COantsForMod::g_even);Mod::m_n = Form(Mod::m_n);}TE TE CE MN::MN(T&& n)NE:Mod(forward(n)){static_assert(! COantsForMod::g_even);Mod::m_n = Form(Mod::m_n);}TE CE MN& MN::OP=(CO MN& n)NE{RE Ref(Mod::OP=(n));}TE CE MN& MN::OP=(MN&& n)NE{RE Ref(Mod::OP=(MO(n)));}TE CE MN& MN::OP+=(CO MN& n)NE{RE Ref(Mod::OP+=(n));}TE CE MN& MN::OP-=(CO MN& n)NE{RE Ref(Mod::OP-=(n));}TE CE MN& MN::OP*=(CO MN& n)NE{ull m_n_copy = Mod::m_n;RE Ref(Mod::m_n = MO(ReducedMU(m_n_copy,n.m_n)));}TE IN MN& MN::OP/=(CO MN& n){RE OP*=(MN(n).Invert());}TE CE MN& MN::OP<<=(int n)NE{RE Ref(Mod::OP<<=(n));}TE CE MN& MN::OP>>=(int n)NE{RE Ref(Mod::OP>>=(n));}TE CE MN& MN::OP++()NE{RE Ref(Mod::Normalise(Mod::m_n += COantsForMod::g_MN_base_mod));}TE CE MN MN::OP++(int)NE{MN n{*TH};OP++();RE n;}TE CE MN& MN::OP--()NE{RE Ref(Mod::m_n < COantsForMod::g_MN_base_mod?((Mod::m_n += M)-= COantsForMod::g_MN_base_mod):Mod::m_n -= COantsForMod::g_MN_base_mod);}TE CE MN MN::OP--(int)NE{MN n{*TH};OP--();RE n;}DF_OF_AR_FOR_MN(+,MN(forward(n))+= *TH);DF_OF_AR_FOR_MN(-,MN(forward(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MN(*,MN(forward(n))*= *TH);DF_OF_AR_FOR_MN(/,MN(forward(n)).Invert()*= *TH);TE CE MN MN::OP<<(int n)CO NE{RE MO(MN(*TH)<<= n);}TE CE MN MN::OP>>(int n)CO NE{RE MO(MN(*TH)>>= n);}TE CE MN MN::OP-()CO NE{RE MO(MN(*TH).SignInvert());}TE CE MN& MN::SignInvert()NE{RE Ref(Mod::m_n > 0?Mod::m_n = M - Mod::m_n:Mod::m_n);}TE CE MN& MN::Double()NE{RE Ref(Mod::Double());}TE CE MN& MN::Halve()NE{RE Ref(Mod::Halve());}TE CE MN& MN::Invert(){assert(Mod::m_n > 0);RE PositivePW(uint(COantsForMod::g_M_minus_2));}TE TE CE MN& MN::PositivePW(T&& EX)NE{MN PW{*TH};(--EX)%= COantsForMod::g_M_minus_2;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE TE CE MN& MN::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(Mod::m_n = COantsForMod::g_MN_base_mod):PositivePW(forward(EX));}TE TE CE MN& MN::PW(T&& EX){bool neg = EX < 0;assert(!(neg && Mod::m_n == 0));RE neg?PositivePW(forward(EX *= COantsForMod::g_M_minus_2_neg)):NonNegativePW(forward(EX));}TE CE uint MN::RP()CO NE{ull m_n_copy = Mod::m_n;RE MO(Reduction(m_n_copy));}TE CE Mod MN::Reduce()CO NE{ull m_n_copy = Mod::m_n;RE Mod::DeRP(MO(Reduction(m_n_copy)));}TE CE MN MN::DeRP(CRUI n)NE{RE MN(Mod::DeRP(n));}TE IN CO MN& MN::Formise(CRUI n)NE{ST MN memory[COantsForMod::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = DeRP(LE_curr);LE_curr++;}RE memory[n];}TE IN CO MN& MN::Inverse(CRUI n)NE{ST MN memory[COantsForMod::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN(Mod::Inverse(LE_curr));LE_curr++;}RE memory[n];}TE IN CO MN& MN::Factorial(CRUI n)NE{ST MN memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN val_curr{one()};ST MN val_last{one()};WH(LE_curr <= n){memory[LE_curr++] = val_curr *= ++val_last;}RE memory[n];}TE IN CO MN& MN::FactorialInverse(CRUI n)NE{ST MN memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN val_curr{one()};ST MN val_last{one()};WH(LE_curr <= n){memory[LE_curr] = val_curr *= Inverse(LE_curr);LE_curr++;}RE memory[n];}TE IN MN MN::Combination(CRUI n,CRUI i)NE{RE i <= n?Factorial(n)*FactorialInverse(i)*FactorialInverse(n - i):zero();}TE IN CO MN& MN::zero()NE{ST CE CO MN z{};RE z;}TE IN CO MN& MN::one()NE{ST CE CO MN o{DeRP(1)};RE o;}TE TE CE MN& MN::Ref(T&& n)NE{RE *TH;}TE CE MN Twice(CO MN& n)NE{RE MO(MN(n).Double());}TE CE MN Half(CO MN& n)NE{RE MO(MN(n).Halve());}TE CE MN Inverse(CO MN& n){RE MO(MN(n).Invert());}TE CE MN PW(MN n,T EX){RE MO(n.PW(EX));}TE CE VO swap(MN& n0,MN& n1)NE{n0.swap(n1);}TE IN string to_string(CO MN& n)NE{RE to_string(n.RP())+ " + MZ";}TE IN basic_ostream& OP<<(basic_ostream& os,CO MN& n){RE os << n.RP();} TE CE Mod::Mod()NE:m_n(){}TE CE Mod::Mod(CO Mod& n)NE:m_n(n.m_n){}TE CE Mod::Mod(Mod& n)NE:m_n(n.m_n){}TE CE Mod::Mod(Mod&& n)NE:m_n(MO(n.m_n)){}TE TE CE Mod::Mod(CO T& n)NE:m_n(RS(n)){}TE TE CE Mod::Mod(T& n)NE:m_n(RS(decay_t(n))){}TE TE CE Mod::Mod(T&& n)NE:m_n(RS(forward(n))){}TE CE Mod& Mod::OP=(CO Mod& n)NE{RE Ref(m_n = n.m_n);}TE CE Mod& Mod::OP=(Mod&& n)NE{RE Ref(m_n = MO(n.m_n));}TE CE Mod& Mod::OP+=(CO Mod& n)NE{RE Ref(Normalise(m_n += n.m_n));}TE CE Mod& Mod::OP-=(CO Mod& n)NE{RE Ref(m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n);}TE CE Mod& Mod::OP*=(CO Mod& n)NE{RE Ref(m_n = COantsForMod::g_even?RS(ull(m_n)* n.m_n):MN::MU(m_n,n.m_n));}TE <> CE MP& MP::OP*=(CO MP& n)NE{ull m_n_copy = m_n;RE Ref(m_n = MO((m_n_copy *= n.m_n)< P?m_n_copy:RSP(m_n_copy)));}TE IN Mod& Mod::OP/=(CO Mod& n){RE OP*=(Mod(n).Invert());}TE CE Mod& Mod::OP<<=(int n)NE{WH(n-- > 0){Normalise(m_n <<= 1);}RE *TH;}TE CE Mod& Mod::OP>>=(int n)NE{WH(n-- > 0){((m_n & 1)== 0?m_n:m_n += M)>>= 1;}RE *TH;}TE CE Mod& Mod::OP++()NE{RE Ref(m_n < COantsForMod::g_M_minus?++m_n:m_n = 0);}TE CE Mod Mod::OP++(int)NE{Mod n{*TH};OP++();RE n;}TE CE Mod& Mod::OP--()NE{RE Ref(m_n == 0?m_n = COantsForMod::g_M_minus:--m_n);}TE CE Mod Mod::OP--(int)NE{Mod n{*TH};OP--();RE n;}DF_OF_CM_FOR_MOD(==);DF_OF_CM_FOR_MOD(!=);DF_OF_CM_FOR_MOD(>);DF_OF_CM_FOR_MOD(>=);DF_OF_CM_FOR_MOD(<);DF_OF_CM_FOR_MOD(<=);DF_OF_AR_FOR_MOD(+,Mod(forward(n))+= *TH);DF_OF_AR_FOR_MOD(-,Mod(forward(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MOD(*,Mod(forward(n))*= *TH);DF_OF_AR_FOR_MOD(/,Mod(forward(n)).Invert()*= *TH);TE CE Mod Mod::OP<<(int n)CO NE{RE MO(Mod(*TH)<<= n);}TE CE Mod Mod::OP>>(int n)CO NE{RE MO(Mod(*TH)>>= n);}TE CE Mod Mod::OP-()CO NE{RE MO(Mod(*TH).SignInvert());}TE CE Mod& Mod::SignInvert()NE{RE Ref(m_n > 0?m_n = M - m_n:m_n);}TE CE Mod& Mod::Double()NE{RE Ref(Normalise(m_n <<= 1));}TE CE Mod& Mod::Halve()NE{RE Ref(((m_n & 1)== 0?m_n:m_n += M)>>= 1);}TE IN Mod& Mod::Invert(){assert(m_n > 0);uint m_n_neg;RE m_n < COantsForMod::g_memory_LE?Ref(m_n = Inverse(m_n).m_n):(m_n_neg = M - m_n < COantsForMod::g_memory_LE)?Ref(m_n = M - Inverse(m_n_neg).m_n):PositivePW(uint(COantsForMod::g_M_minus_2));}TE <> IN Mod<2>& Mod<2>::Invert(){assert(m_n > 0);RE *TH;}TE TE CE Mod& Mod::PositivePW(T&& EX)NE{Mod PW{*TH};EX--;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <> TE CE Mod<2>& Mod<2>::PositivePW(T&& EX)NE{RE *TH;}TE TE CE Mod& Mod::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(m_n = 1):Ref(PositivePW(forward(EX)));}TE TE CE Mod& Mod::PW(T&& EX){bool neg = EX < 0;assert(!(neg && m_n == 0));neg?EX *= COantsForMod::g_M_minus_2_neg:EX;RE m_n == 0?*TH:(EX %= COantsForMod::g_M_minus)== 0?Ref(m_n = 1):PositivePW(forward(EX));}TE IN CO Mod& Mod::Inverse(CRUI n)NE{ST Mod memory[COantsForMod::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr].m_n = M - MN::MU(memory[M % LE_curr].m_n,M / LE_curr);LE_curr++;}RE memory[n];}TE IN CO Mod& Mod::Factorial(CRUI n)NE{ST Mod memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN::Factorial(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE IN CO Mod& Mod::FactorialInverse(CRUI n)NE{ST Mod memory[COantsForMod::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN::FactorialInverse(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE IN Mod Mod::Combination(CRUI n,CRUI i)NE{RE MN::Combination(n,i).Reduce();}TE CE VO Mod::swap(Mod& n)NE{std::swap(m_n,n.m_n);}TE CE CRUI Mod::RP()CO NE{RE m_n;}TE CE Mod Mod::DeRP(CRUI n)NE{Mod n_copy{};n_copy.m_n = n;RE n_copy;}TE CE uint& Mod::Normalise(uint& n)NE{RE n < M?n:n -= M;}TE IN CO Mod& Mod::zero()NE{ST CE CO Mod z{};RE z;}TE IN CO Mod& Mod::one()NE{ST CE CO Mod o{DeRP(1)};RE o;}TE TE CE Mod& Mod::Ref(T&& n)NE{RE *TH;}TE CE Mod Twice(CO Mod& n)NE{RE MO(Mod(n).Double());}TE CE Mod Half(CO Mod& n)NE{RE MO(Mod(n).Halve());}TE IN Mod Inverse(CO Mod& n){RE MO(Mod(n).Invert());}TE CE Mod Inverse_COrexpr(CRUI n)NE{RE MO(Mod::DeRP(RS(n)).NonNegativePW(M - 2));}TE CE Mod PW(Mod n,T EX){RE MO(n.PW(EX));}TE CE Mod<2> PW(Mod<2> n,const T& p){RE p == 0?Mod<2>::one():move(n);}TE CE VO swap(Mod& n0,Mod& n1)NE{n0.swap(n1);}TE IN string to_string(CO Mod& n)NE{RE to_string(n.RP())+ " + MZ";}TE IN basic_ostream& OP<<(basic_ostream& os,CO Mod& n){RE os << n.RP();} // AAA ライブラリは以上に挿入する。 // データ構造使用畤のNの上限 // inline CEXPR( int , bound_N , 10 ); inline DEXPR( int , bound_N , 100000 , 100 ); // 0が5個 // inline CEXPR( int , bound_N , 1000000000 ); // 0が9個 // inline CEXPR( ll , bound_N , 1000000000000000000 ); // 0が18個 // データ構造使用畤のMの上限 // inline CEXPR( TYPE_OF( bound_N ) , bound_M , bound_N ); // inline CEXPR( int , bound_M , 10 ); inline DEXPR( int , bound_M , 100000 , 100 ); // 0が5個 // inline CEXPR( int , bound_M , 1000000000 ); // 0が9個 // inline CEXPR( ll , bound_M , 1000000000000000000 ); // 0が18個 // データ構造や壁配列使用畤のH,Wの上限 inline DEXPR( int , bound_H , 1000 , 20 ); // inline DEXPR( int , bound_H , 100000 , 10 ); // 0が5個 // inline CEXPR( int , bound_H , 1000000000 ); // 0が9個 inline CEXPR( int , bound_W , bound_H ); static_assert( ll( bound_H ) * bound_W < ll( 1 ) << 31 ); inline CEXPR( int , bound_HW , bound_H * bound_W ); // CEXPR( int , bound_HW , 100000 ); // 0が5個 // CEXPR( int , bound_HW , 1000000 ); // 0が6個 inline void SetEdgeOnGrid( const string& Si , const int& i , list ( &e )[bound_HW] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back(v);}if(i+10){e[EnumHW_inv(i,j-1)].push_back(v);}if(j+1 > ( &e )[bound_HW] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){const int v=EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back({v,1});}if(i+10){e[EnumHW_inv(i,j-1)].push_back({v,1});}if(j+1; // CEXPR( int , bound_E , bound_M ); // bound_Mのデフォルト値は10^5。 // // CEXPR( int , bound_E , bound_HW ); // bound_HWのデフォルト値は10^6。 // list e[bound_E] = {}; // list E( const int& i ) // { // list answer{}; // list answer = e[i]; // // 入力によらない処理 // return answer; // } // ライブラリをここに挿入しない。 ll Guchoku( const int& M ) { int power = 1; while( power < M ){ power <<= 1; } ll answer = 0; ll dp[power+1][power][power] = {}; FOR( i , 0 , M ){ answer += dp[1][i][i] = 1; } FOREQ( L , 2 , power ){ FOR( i , 0 , power ){ FOR( j , L - 2 , power ){ FOR( k , j + 1 , power ){ ( j ^ k ) < M ? dp[L][j^k][k] += dp[L-1][i][j] : 0; } } } FOR( i , 0 , power ){ FOR( j , L - 1 , power ){ answer += dp[L][i][j]; } } } // M <= powerかつanswer <= 2^power - 1 // M == powerの時、answer == 2^M - 1 return answer; } ll Guchoku2( const int& M ) { int power = 1; while( power * 2 <= M ){ power <<= 1; } ll power2[power+1] = { 1 }; FOREQ( i , 1 , power ){ power2[i] = power2[i-1] * 2; } ll answer = ( power2[power] - power2[0] ) + ( power2[power * 2 - power] - power2[power * 2 - M] ); FOR( b0 , 0 , power ){ ll temp = 0; FOR( a1 , power , M ){ int b1 = b0 ^ a1; int diff = power * 2 - ( b1 + 1 ); temp += power2[diff]; } answer += temp *= power2[b0]; } return answer; } ll Guchoku3( const int& M ) { int power = 1; while( power * 2 <= M ){ power <<= 1; } ll power2[power*2+1] = { 1 }; FOREQ( i , 1 , power*2 ){ power2[i] = power2[i-1] * 2; } ll answer = ( power2[power] - power2[0] ) + ( power2[power * 2 - power] - power2[power * 2 - M] ); FOR( a1 , power , M ){ FOR( b0 , 0 , power ){ int b1 = b0 ^ a1; answer += power2[power * 2 - ( b1 - b0 + 1 )]; } } return answer; } ll Guchoku4( const int& M ) { int power = 1; while( power * 2 <= M ){ power <<= 1; } ll power2[power*2+1] = { 1 }; FOREQ( i , 1 , power*2 ){ power2[i] = power2[i-1] * 2; } ll answer = ( power2[power] - power2[0] ) + ( power2[power * 2 - power] - power2[power * 2 - M] ); int M_minus = M - power; FOR( a1_minus , 0 , M_minus ){ FOR( b0 , 0 , power ){ answer += power2[ ( power * 2 - power - 1 ) - ( ( b0 ^ a1_minus ) - b0 ) ]; } } return answer; } ll Guchoku5( const int& M ) { int power = 1; int D = 0; while( power * 2 <= M ){ D++; power <<= 1; } MP power2[power*2+1] = { 1 }; FOREQ( i , 1 , power*2 ){ power2[i] = power2[i-1] * 2; } MP answer = ( power2[power] - power2[0] ) + ( power2[power * 2 - power] - power2[power * 2 - M] ); int M_minus = M - power; FOR( a1_minus , 0 , M_minus ){ FOR( b0 , 0 , power ){ MP temp = power2[power * 2 - power - 1]; FOR( d , 0 , D ){ if( ( ( a1_minus >> d ) & 1 ) == 1 ){ ( ( b0 >> d ) & 1 ) == 0 ? temp /= power2[1 << d] : temp *= power2[1 << d]; } } answer += temp; } } return answer.RP(); } void Experiment() { FOR( M , 1 , 10 ){ cout << Guchoku( M ) << " \n"[M==9]; } FOR( M , 1 , 10 ){ cout << Guchoku2( M ) << " \n"[M==9]; } FOR( M , 1 , 10 ){ cout << Guchoku3( M ) << " \n"[M==9]; } FOR( M , 1 , 10 ){ cout << Guchoku4( M ) << " \n"[M==9]; } FOR( M , 1 , 10 ){ cout << Guchoku5( M ) << " \n"[M==9]; } // 1 3 9 15 55 99 169 255 1407 } int main() { UNTIE; AUTO_CHECK; // START_WATCH; TEST_CASE_NUM( 1 ); START_MAIN; // Experiment(); CIN( ll , M ); int D = -1; ll power2 = 1; while( power2 <= M ){ D++; power2 <<= 1; } ll power = power2 >> 1; constexpr MP two = MP::DeRP( 2 ); MP answer = ( PW( two , power ) - 1 ) + ( PW( two , power ) - PW( two , power2 - M ) ); int M_minus = M - power; MP ppower = two + 1 / two; MP full = PW( two , power - 1 ); MP less = ( ( M_minus >> 0 ) & 1 ) == 0 ? MP::zero() : full << 1; full *= 2 + ppower; FOR( d , 1 , D ){ ppower *= ppower; ( ( M_minus >> d ) & 1 ) == 0 ? less <<= 1 : ( less *= ppower - 2 ) += full << 1; full *= ppower; ppower -= 2; } answer += less; RETURN( answer ); FINISH_MAIN; }