#pragma GCC optimize ( "O3" ) #pragma GCC target ( "avx" ) #include using namespace std; using uint = unsigned int; using ll = long long; #define TYPE_OF( VAR ) remove_const::type >::type #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define CEXPR( LL , BOUND , VALUE ) constexpr const 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 , MAX_I , LENGTH , MODULO ) \ ll ANSWER[LENGTH]; \ ll ANSWER_INV[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; \ } \ POWER_MOD( FACTORIAL_MAX_INV , ANSWER[MAX_I] , MODULO - 2 , MODULO ); \ ANSWER_INV[MAX_I] = FACTORIAL_MAX_INV; \ FOREQINV( i , MAX_I - 1 , 0 ){ \ ANSWER_INV[i] = ( FACTORIAL_MAX_INV *= i + 1 ) %= MODULO; \ } \ } \ \ // 通常の二分探索 #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 ){ \ VARIABLE_FOR_BINARY_SEARCH_L = ANSWER; \ 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 #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 inline T Absolute( const T& a ){ return a > 0 ? a : - a; } template inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - ( - a - 1 ) % p - 1; } // InitialSegmentSumで負の入力を扱うためにuintではなくintをテンプレート引数にする。 template class BIT { private: T m_fenwick[N + 1]; public: inline BIT(); inline BIT( const T ( & a )[N] ); inline void Set( const int& i , const T& n ); inline BIT& operator+=( const T ( & a )[N] ); void Add( const int& i , const T& n ); T InitialSegmentSum( const int& i_final ); inline T IntervalSum( const int& i_start , const int& i_final ); }; template inline BIT::BIT() : m_fenwick() {} template inline BIT::BIT( const T ( & a )[N] ) : m_fenwick() { operator+=( a ); } template inline void BIT::Set( const int& i , const T& n ) { Add( i , n - IntervalSum( i , i ) ); } template inline BIT& BIT::operator+=( const T ( & a )[N] ) { for( int i = 0 ; i < N ; i++ ){ Add( i , a[i] ); } return *this; } template void BIT::Add( const int& i , const T& n ) { int j = i + 1; while( j <= N ){ m_fenwick[j] += n; j += ( j & -j ); } return; } template T BIT::InitialSegmentSum( const int& i_final ) { T sum = 0; int j = ( i_final < N ? i_final : N - 1 ) + 1; while( j > 0 ){ sum += m_fenwick[j]; j -= j & -j; } return sum; } template inline T BIT::IntervalSum( const int& i_start , const int& i_final ) { return InitialSegmentSum( i_final ) - InitialSegmentSum( i_start - 1 ); } #define MULTIPLICATION( F0 , SIGN ) \ { \ FOR( i , 0 , N_half ){ \ CIN_ASSERT( Ai , 1 , bound ); \ CIN_ASSERT( Bi , 1 , bound ); \ FOREQINV( d0 , min( K , i ) , 0 ){ \ map,int>& fd0 = F0[d0]; \ map,int>& fd1 = F0[d0+1]; \ FOR_ITR( fd0 , itr , end ){ \ l0 = itr->first.second; \ l1 = l0 + Ai; \ if( l1 <= L ){ \ p0 = itr->first.first; \ p1 = p0 + ( SIGN ) * Bi; \ if( ( SIGN ) * p1 > P ){ \ p1 = ( SIGN ) * P; \ } \ fd1[c1] += fd0[c0]; \ } \ } \ } \ } \ } \ \ int main() { UNTIE; CEXPR( int , bound_N , 34 ); CIN_ASSERT( N , 1 , bound_N ); CIN_ASSERT( K , 1 , N ); CEXPR( int , bound , 1000000000 ); CIN_ASSERT( L , 1 , bound ); CIN_ASSERT( P , 1 , bound ); pair c0{}; pair c1{}; int& p0 = c0.first; int& l0 = c0.second; int& p1 = c1.first; int& l1 = c1.second; CEXPR( int , bound_N_half , bound_N / 2); map,int> f[2][bound_N_half + 1] = {}; map,int> ( &f0 )[bound_N_half + 1] = f[0]; map,int> ( &f1 )[bound_N_half + 1] = f[1]; f0[0][c1] = 1; f1[0][c1] = 1; int N_half = N / 2; MULTIPLICATION( f0 , 1 ); int K0 = min( K , N_half ); N_half = N - N_half; MULTIPLICATION( f1 , -1 ); int K1 = min( K , N_half ); map TheAtl1[bound_N_half + 1] = {}; int num; FOREQ( d1 , 0 , K1 ){ map,int>& f1d1 = f1[d1]; map& TheAtl1d1 = TheAtl1[d1]; FOR_ITR( f1d1 , itr1 , end1 ){ TheAtl1d1[- itr1->first.second] = 0; } num = 0; FOR_ITR( TheAtl1d1 , itr1 , end1 ){ itr1->second = num++; } } ll answer = 0; map::iterator itr_TheAtl1d1 , end_TheAtl1d1; map,int>::iterator itr1 , end1; CEXPR( int , length , 1 << bound_N_half ); FOREQINV( d0 , K0 , 0 ){ map,int>& f0d0 = f0[d0]; FOREQINV( d1 , min( K1 , K - d0 ) , 0 ){ map,int>& f1d1 = f1[d1]; map& TheAtl1d1 = TheAtl1[d1]; BIT S{}; itr1 = f1d1.begin(); end1 = f1d1.end(); end_TheAtl1d1 = TheAtl1d1.end(); c1 = itr1->first; FOR_ITR( f0d0 , itr0 , end0 ){ c0 = itr0->first; while( itr1 != end1 && p0 - p1 >= P ){ S.Add( TheAtl1d1[- c1.second] , itr1->second ); itr1++; c1 = itr1->first; } itr_TheAtl1d1 = TheAtl1d1.lower_bound( l0 - L ); if( itr_TheAtl1d1 != end_TheAtl1d1 ){ num = itr_TheAtl1d1->second; answer += itr0->second * S.IntervalSum( num , length - 1 ); } } } } RETURN( answer ); }