#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 ); } #define OO first.first #define OI first.second #define IO second.first #define II second.second ll B; using Matrix = pair,pair >; inline Matrix operator*( 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 } }; } 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{ { 1 , 0 } , { 0 , 1 } }; Matrix prod[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 ); Matrix A = { { AOO , AOI } , { AIO , AII } }; prod[n] = temp = A * temp; } 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& prod_Lq = prod[Lq]; Matrix& prod_Rq = prod[Rq]; temp = { { prod_Lq.II , -prod_Lq.OI } , { -prod_Lq.IO , prod_Lq.OO } }; temp = prod_Rq * temp; ll z = Residue( temp.OO * x + temp.OI * y , B ); ll w = Residue( temp.IO * x + temp.II * y , B ); COUT( z << " " << w ); } QUIT; }