// 愚直解チェック #ifndef INCLUDE_MODE #define INCLUDE_MODE // #define REACTIVE // #define USE_GETLINE #endif #ifdef INCLUDE_MAIN inline void Solve() { // Nの入力受け取り CEXPR( int , bound_N , 1e7 ); CIN_ASSERT( N , 1 , bound_N ); // Bの入力受け取り CEXPR( ll , bound_B , 1e9 ); CIN_ASSERT( B , 1 , bound_B ); // Qの入力受け取り CEXPR( int , bound_Q , 1e6 ); CIN_ASSERT( Q , 1 , bound_Q ); // 合同式での四則演算を扱う型の法をBに設定 QuotientRing::SetStaticModulo( &B ); // C_1,D_1の入力受け取りとAの初期値計算 CEXPR( ll , bound_CD1 , 1e9 ); CIN_ASSERT( C_1 , 0 , bound_CD1 ); CIN_ASSERT( D_1 , 0 , bound_CD1 ); vector> A( N , C_1 ); QuotientRing R_1 = D_1; FOR( i , 1 , N ){ A[i] = A[i-1] * R_1; } // C_2,D_2の入力受け取りとi_qの初期値計算 CEXPR( ll , bound_CD2 , 1e7 ); CIN_ASSERT( C_2 , 0 , bound_CD2 ); CIN_ASSERT( D_2 , 0 , bound_CD2 ); ll i_q = move( C_2 %= N ); // C_3,D_3の入力受け取りとj_qの初期値計算 CEXPR( ll , bound_CD3 , 1e7 ); CIN_ASSERT( C_3 , 0 , bound_CD3 ); CIN_ASSERT( D_3 , 0 , bound_CD3 ); ll j_q = move( C_3 %= N ); // C_4,D_4の入力受け取りとx_q mod Bの初期値計算 CEXPR( ll , bound_CD4 , 1e9 ); CIN_ASSERT( C_4 , 0 , bound_CD4 ); CIN_ASSERT( D_4 , 0 , bound_CD4 ); QuotientRing x_q = C_4; QuotientRing D_4_mod_B = D_4; // C_5,D_5の入力受け取りとy_q mod Bの初期値計算 CEXPR( ll , bound_CD5 , 1e9 ); CIN_ASSERT( C_5 , 0 , bound_CD5 ); CIN_ASSERT( D_5 , 0 , bound_CD5 ); QuotientRing y_q = C_5; QuotientRing D_5_mod_B = D_5; REPEAT( Q ){ A[i_q] = x_q; // f(j_q,y_q)を格納する変数 QuotientRing fjy{}; // y_q羃をBで割った余りを格納する変数 QuotientRing y_power{ 1 }; int j = j_q; while( j > 0 ){ int j_next = j - ( j & -j ); QuotientRing sum{}; FOREQ( k , j_next + 1 , j ){ sum += A[k]; } fjy += y_power * sum; // y羃を更新 y_power *= y_q; // jを更新 j = j_next; } // 最高次の寄与も加算 fjy += y_power * A[0]; // 最終的なfjyの値を出力 const ll& answer = fjy.Represent(); COUT( answer < 0 ? answer + B : answer ); // クエリを更新 ( i_q *= D_2 ) %= N; ( j_q *= D_3 ) %= N; x_q *= D_4_mod_B; y_q *= D_5_mod_B; } } REPEAT_MAIN(1); #else // INCLUDE_MAIN #ifdef INCLUDE_SUB // グラフ用 template typename V> inline auto Get( const V& a ) { return [&]( const int& i ){ return a[i]; }; } // VVV テンプレート引数用の関数は以下に挿入する。 // AAA テンプレート引数用の関数は以上に挿入する。 #define INCLUDE_MAIN #include __FILE__ #else // INCLUDE_SUB #ifdef INCLUDE_LIBRARY // https://github.com/p-adic/cpp // VVV ライブラリは以下に挿入する。 template class QuotientRing { protected: INT m_n; const INT* m_p_M; static const INT* g_p_M; public: inline QuotientRing() noexcept; inline QuotientRing( const INT& n , const INT* const& p_M = g_p_M ) noexcept; inline QuotientRing( const QuotientRing& n ) noexcept; inline QuotientRing& operator+=( const QuotientRing& n ) noexcept; template inline QuotientRing& operator+=( const T& n ) noexcept; // operator<が定義されていても負の数は正に直さず剰余を取ることに注意。 inline QuotientRing& operator-=( const QuotientRing& n ) noexcept; template inline QuotientRing& operator-=( const T& n ) noexcept; inline QuotientRing& operator*=( const QuotientRing& n ) noexcept; template inline QuotientRing& operator*=( const T& n ) noexcept; // *m_p_Mが素数でかつnの逆元が存在する場合のみサポート。 inline QuotientRing& operator/=( const QuotientRing& n ); template inline QuotientRing& operator/=( const T& n ); // m_nの正負やm_p_Mの一致込みの等号。 inline bool operator==( const QuotientRing& n ) const noexcept; // m_nの正負込みの等号。 template inline bool operator==( const T& n ) const noexcept; template inline bool operator!=( const T& n ) const noexcept; template inline QuotientRing operator+( const T& n1 ) const noexcept; inline QuotientRing operator-() const noexcept; template inline QuotientRing operator-( const T& n1 ) const noexcept; template inline QuotientRing operator*( const T& n1 ) const noexcept; // *m_p_Mが素数でかつn1の逆元が存在する場合のみサポート。 template inline QuotientRing operator/( const T& n1 ) const; inline const INT& Represent() const noexcept; inline const INT& GetModulo() const noexcept; inline void SetModulo( const INT* const& p_M = nullptr ) noexcept; static inline const INT& GetStaticModulo() noexcept; static inline void SetStaticModulo( const INT* const& p_M ) noexcept; template static QuotientRing Power( const QuotientRing& n , T exponent ); // *m_p_Mが素数でかつnの逆元が存在する場合のみサポート。 static QuotientRing Inverse( const QuotientRing& n ); }; template inline QuotientRing Power( const QuotientRing& n , T exponent ); // *(n.m_p_M)が素数でかつnの逆元が存在する場合のみサポート。 template inline QuotientRing Inverse( const QuotientRing& n ); template inline basic_istream& operator>>( basic_istream& is , QuotientRing& n ); template inline basic_ostream& operator<<( basic_ostream& os , const QuotientRing& n ); template const INT* QuotientRing::g_p_M = nullptr; template inline QuotientRing::QuotientRing() noexcept : m_n() , m_p_M( g_p_M ) {} template inline QuotientRing::QuotientRing( const INT& n , const INT* const& p_M ) noexcept : m_n( p_M == nullptr ? n : n % *p_M ) , m_p_M( p_M ) {} template inline QuotientRing::QuotientRing( const QuotientRing& n ) noexcept : m_n( n.m_n ) , m_p_M( n.m_p_M ) {} template inline QuotientRing& QuotientRing::operator+=( const QuotientRing& n ) noexcept { if( m_p_M == nullptr ){ m_p_M = n.m_p_M; } m_n += n.m_n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; } template template inline QuotientRing& QuotientRing::operator+=( const T& n ) noexcept { m_p_M == nullptr ? m_n += n : ( m_n += n % *m_p_M ) %= *m_p_M; return *this; } template inline QuotientRing& QuotientRing::operator-=( const QuotientRing& n ) noexcept { if( m_p_M == nullptr ){ m_p_M = n.m_p_M; } m_n -= n.m_n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; } template template inline QuotientRing& QuotientRing::operator-=( const T& n ) noexcept { m_p_M == nullptr ? m_n -= n : ( m_n -= n % *m_p_M ) %= *m_p_M; return *this; } template inline QuotientRing& QuotientRing::operator*=( const QuotientRing& n ) noexcept { if( m_p_M == nullptr ){ m_p_M = n.m_p_M; } m_n *= n.m_n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; } template template inline QuotientRing& QuotientRing::operator*=( const T& n ) noexcept { m_p_M == nullptr ? m_n *= n : ( m_n *= n % *m_p_M ) %= *m_p_M; return *this; } template inline QuotientRing& QuotientRing::operator/=( const QuotientRing& n ) { if( m_p_M == nullptr ){ if( n.m_p_M == nullptr ){ assert( n.m_n != 0 ); m_n /= n.m_n; return *this; } else { m_p_M = n.m_p_M; } } return operator*=( Inverse( QuotientRing( n.m_n , m_p_M ) ) ); } template template inline QuotientRing& QuotientRing::operator/=( const T& n ) { if( m_p_M == nullptr ){ assert( n.m_n != 0 ); m_n /= n.m_n; return *this; } return operator*=( Inverse( Q( n.m_n , m_p_M ) ) ); } template inline bool QuotientRing::operator==( const QuotientRing& n ) const noexcept { return m_p_M == n.m_p_M && m_n == n.m_n; } template template inline bool QuotientRing::operator==( const T& n ) const noexcept { return m_n == n; } template template inline bool QuotientRing::operator!=( const T& n ) const noexcept { return !operator==( n ); } template template inline QuotientRing QuotientRing::operator+( const T& n ) const noexcept { return QuotientRing( *this ).operator+=( n ); } template inline QuotientRing QuotientRing::operator-() const noexcept { return QuotientRing( -m_n , m_p_M ); } template template inline QuotientRing QuotientRing::operator-( const T& n ) const noexcept { return QuotientRing( *this ).operator-=( n ); } template template inline QuotientRing QuotientRing::operator*( const T& n ) const noexcept { return QuotientRing( *this ).operator*=( n ); } template template inline QuotientRing QuotientRing::operator/( const T& n ) const { return QuotientRing( *this ).operator/=( n ); } template inline const INT& QuotientRing::Represent() const noexcept { return m_n; } template inline const INT& QuotientRing::GetModulo() const noexcept { static const INT zero{ 0 }; return m_p_M == nullptr ? zero : *m_p_M; } template inline void QuotientRing::SetModulo( const INT* const& p_M ) noexcept { m_p_M = p_M; if( m_p_M != nullptr ){ m_n %= *m_p_M; } } template inline const INT& QuotientRing::GetStaticModulo() noexcept { static const INT zero{ 0 }; return g_p_M == nullptr ? zero : *g_p_M; } template inline void QuotientRing::SetStaticModulo( const INT* const& p_M ) noexcept { g_p_M = p_M; } template template QuotientRing QuotientRing::Power( const QuotientRing& n , T exponent ) { QuotientRing answer{ 1 , n.m_p_M }; QuotientRing power{ n }; while( exponent != 0 ){ if( exponent % 2 == 1 ){ answer *= power; } power *= power; exponent /= 2; } return answer; } template inline QuotientRing QuotientRing::Inverse( const QuotientRing& n ) { assert( n.m_p_M != nullptr ); return Power( n , *( n.m_p_M ) - 2 ); } template inline QuotientRing Power( const QuotientRing& n , T exponent ) { return QuotientRing::template Power( n , exponent ); } template inline QuotientRing Inverse( const QuotientRing& n ) { return QuotientRing::Inverse( n ); } template inline basic_istream& operator>>( basic_istream& is , QuotientRing& n ) { INT m; is >> m; n = m; return is; } template inline basic_ostream& operator<<( basic_ostream& os , const QuotientRing& n ) { return os << n.Represent(); } // AAA ライブラリは以上に挿入する。 #define INCLUDE_SUB #include __FILE__ #else // INCLUDE_LIBRARY #ifdef DEBUG #define _GLIBCXX_DEBUG #define SIGNAL signal( SIGABRT , &AlertAbort ); #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE ) #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック: " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) ) #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 #else #pragma GCC optimize ( "O3" ) #pragma GCC optimize ( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #define SIGNAL #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE ) #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #define CERR( ... ) #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL #define CERR_A( A , N ) #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL #define CERR_ITR( A ) #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL #endif #ifdef REACTIVE #define ENDL endl #else #define ENDL "\n" #endif #ifdef USE_GETLINE #define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); } #define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ ) #define GETLINE( ... ) GETLINE_SEPARATE( '\n' , __VA_ARGS__ ) #else #define SET_LL( A ) cin >> A #define CIN( LL , ... ) LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ ) #define SET_A( A , N ) FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; } #define CIN_A( LL , A , N ) vector A( N ); SET_A( A , N ); #endif #include using namespace std; #define REPEAT_MAIN( BOUND ) int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr ); SIGNAL; DEXPR( int , bound_test_case_num , BOUND , min( BOUND , 100 ) ); int test_case_num = 1; if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } REPEAT( test_case_num ){ if constexpr( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } } #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 CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE #define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX ) #define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( decldecay_t( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define FOREQ( VAR , INITIAL , FINAL ) for( decldecay_t( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define FOREQINV( VAR , INITIAL , FINAL ) for( decldecay_t( INITIAL ) VAR = INITIAL ; VAR + 1 > 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 RETURN( ... ) COUT( __VA_ARGS__ ); return // 型のエイリアス #define decldecay_t( VAR ) decay_t template using ret_t = decltype( declval()( declval()... ) ); template using inner_t = typename T::type; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using ld = long double; using lld = __float128; template using T2 = pair; template using T3 = tuple; template using T4 = tuple; // 入出力用 template inline basic_istream& VariadicCin( basic_istream& is ) { return is; } template inline basic_istream& VariadicCin( basic_istream& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); } template inline basic_istream& VariadicGetline( basic_istream& is , const char& separator ) { return is; } template inline basic_istream& VariadicGetline( basic_istream& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); } template inline basic_ostream& operator<<( basic_ostream& os , const vector& arg ) { auto begin = arg.begin() , end = arg.end(); auto itr = begin; while( itr != end ){ ( itr == begin ? os : os << " " ) << *itr; itr++; } return os; } 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... ); } // デバッグ用 #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 #define INCLUDE_LIBRARY #include __FILE__ #endif // INCLUDE_LIBRARY #endif // INCLUDE_SUB #endif // INCLUDE_MAIN