#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( MESSAGE ) cerr << MESSAGE << endl; #define COUT( ANSWER ) cout << ANSWER << endl #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック: " << ( MIN ) << ( ( MIN ) <= A ? "<=" : ">" ) << A << ( A <= ( MAX ) ? "<=" : ">" ) << ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) ) #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( MESSAGE ) #define COUT( ANSWER ) cout << ANSWER << "\n" #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #endif #include using namespace std; using ll = long long; #define MAIN main #define TYPE_OF( VAR ) decay_t #define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE #define CIN( LL , A ) LL A; cin >> A #define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define QUIT return 0 #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX ) #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。" ); } #endif template inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); } // 入力の範囲内で要件 // (1) (T,m_T:T^2->T,i_T:T->T)が群である。 // が成り立つ場合のみサポート。(単位元は引数に渡さなくてよい) template class CumulativeProd_Body { protected: int m_size; T m_a[size_max]; T m_a_reverse[size_max]; public: inline CumulativeProd_Body( const int& size ); // iからへのpathがi=v_0->...->v_k=jの時m_a[v_0]...m_a[v_k]を // Prodや逆順のProdに関して計算する。 inline T PathProd( const int& i , const int& j ); private: virtual int Parent( const int& i ) = 0; virtual int LCA( const int& i , const int& j ) = 0; }; // 通常の配列上の累積積。 // テンプレート引数に単位元e_T:1->Tも渡す。 template class CumulativeProd : public CumulativeProd_Body { public: inline CumulativeProd( const T ( &a )[size_max] , const int& size ); // 0 <= iかつi-1 <= j < m_sizeの場合のみサポート。 // m_a[i]...m_a[j]をm_Tに関して計算する。 inline T RightProd( const int& i , const int& j ); // m_a[j]...m_a[i]をm_Tに関して計算する。 inline T LeftProd( const int& i , const int& j ); private: inline int Parent( const int& i ); inline int LCA( const int& i , const int& j ); }; template inline CumulativeProd_Body::CumulativeProd_Body( const int& size ) : m_size( size ) , m_a() , m_a_reverse() { assert( size <= size_max ); } template inline CumulativeProd::CumulativeProd( const T ( &a )[size_max] , const int& size ) : CumulativeProd_Body( size ) { using base = CumulativeProd_Body; T temp , temp_reverse; base::m_a[0] = base::m_a_reverse[0] = temp = temp_reverse = a[0]; for( int i = 1 ; i < size ; i++ ){ base::m_a[i] = temp = m_T( temp , a[i] ); base::m_a_reverse[i] = temp_reverse = m_T( a[i] , temp_reverse ); } } template inline T CumulativeProd_Body::PathProd( const int& i , const int& j ) { const int k = LCA( i , j ); return m_T( m_T( m_a_reverse[i] , i_T( m_a_reverse[k] ) ) , k == 0 ? m_a[j] : m_T( i_T( m_a[Parent( k ) ] ) , m_a[j] )); } template inline T CumulativeProd::RightProd( const int& i , const int& j ) { assert( i - 1 <= j ); using base = CumulativeProd_Body; return i <= j ? i == 0 ? base::m_a[j] : m_T( i_T( base::m_a[i-1] ) , base::m_a[j] ) : e_T(); } template inline T CumulativeProd::LeftProd( const int& i , const int& j ) { assert( i - 1 <= j ); using base = CumulativeProd_Body; return i <= j ? i == 0 ? base::m_a_reverse[j] : m_T( base::m_a_reverse[j] , i_T( base::m_a_reverse[i - 1] ) ) : e_T(); } template inline int CumulativeProd::Parent( const int& i ) { return i - 1; } template inline int CumulativeProd::LCA( const int& i , const int& j ) { return min( i , j ); } #define OO first.first #define OI first.second #define IO second.first #define II second.second ll B; using Matrix = pair,pair >; inline Matrix m( const Matrix& M , const Matrix& N ) { return { { ( M.OO * N.OO + M.OI * N.IO ) % B , ( M.OO * N.OI + M.OI * N.II ) % B } , { ( M.IO * N.OO + M.II * N.IO ) % B , ( M.IO * N.OI + M.II * N.II ) % B } }; } inline const Matrix& e() { static const Matrix one{ { 1 , 0 } , { 0 , 1 } }; return one; } inline Matrix i( const Matrix& M ) { return { { M.II , -M.OI } , { -M.IO , M.OO } }; } int MAIN() { UNTIE; DEXPR( int , bound_N , 100000 , 100 ); // 0が5個 CIN_ASSERT( N , 1 , bound_N ); CEXPR( ll , bound_ABx , 1000000000 ); // 0が9個 SET_ASSERT( B , 1 , bound_ABx ); DEXPR( int , bound_Q , 100000 , 100 ); // 0が5個 CIN_ASSERT( Q , 1 , bound_Q ); Matrix temp = e(); Matrix A[bound_N + 1] = { temp }; FOREQ( n , 1 , N ){ CIN_ASSERT( AOO , -bound_ABx , bound_ABx ); CIN_ASSERT( AOI , -bound_ABx , bound_ABx ); CIN_ASSERT( AIO , -bound_ABx , bound_ABx ); CIN_ASSERT( AII , -bound_ABx , bound_ABx ); assert( AOO * AII - AOI * AIO == 1 ); A[n] = { { AOO , AOI } , { AIO , AII } }; } CumulativeProd cp{ A , N + 1 }; REPEAT( Q ){ CIN_ASSERT( Lq , 0 , N ); CIN_ASSERT( Rq , Lq , N ); CIN_ASSERT( x , -bound_ABx , bound_ABx ); CIN_ASSERT( y , -bound_ABx , bound_ABx ); Matrix temp = Lq < Rq ? cp.PathProd( Rq , Lq + 1 ) : A[0]; // Matrix temp = cp.LeftProd( Lq + 1 , Rq ); ll z = Residue( temp.OO * x + temp.OI * y , B ); ll w = Residue( temp.IO * x + temp.II * y , B ); COUT( z << " " << w ); } QUIT; }