#871465 (C++17(gcc12)) No.2448 一次変換と面積

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問題	No.2448 一次変換と面積
コンテスト
ユーザー	👑 p-adic
提出日時	2023-05-23 21:24:48
言語	C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
結果	AC
実行時間	125 ms / 2,000 ms
コード長	11,143 bytes
コンパイル時間	1,825 ms
コンパイル使用メモリ	96,224 KB
最終ジャッジ日時	2025-02-13 04:17:07
ジャッジサーバーID （参考情報）	judge5 / judge3
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ファイルパターン	結果
other	AC * 30
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ソースコード

raw source code
#pragma GCC optimize ( "O3" )
#pragma GCC optimize( "unroll-loops" )
#pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
#include <iostream>
#include <stdio.h>
#include <stdint.h>
#include <cassert>
using namespace std;

using ll = long long;

#define MAIN main
#define TYPE_OF( VAR ) remove_const<remove_reference<decltype( VAR )>::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 FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT , 0 , HOW_MANY_TIMES )
#define QUIT return 0 
#define RETURN( ANSWER ) cout << ( 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;				\
    }									\
  }									\

template <typename T>
class TwoByTwoMatrix
{

public:
  // private:
  T m_M00;
  T m_M01;
  T m_M10;
  T m_M11;

public:
  inline TwoByTwoMatrix( const ll& n ) noexcept;
  inline TwoByTwoMatrix( const T& M00 , const T& M01 , const T& M10 , const T& M11 ) noexcept;
  inline TwoByTwoMatrix( const T& n = T() ) noexcept;
  inline TwoByTwoMatrix<T>& operator=( const TwoByTwoMatrix<T>& mat ) noexcept;
  inline TwoByTwoMatrix<T>& operator*=( const TwoByTwoMatrix<T>& mat ) noexcept;

  inline TwoByTwoMatrix<T> operator+( const TwoByTwoMatrix<T>& mat );
  inline TwoByTwoMatrix<T> operator*( const TwoByTwoMatrix<T>& mat );

};

template <typename T> inline TwoByTwoMatrix<T>::TwoByTwoMatrix( const ll& n ) noexcept : m_M00( n ) , m_M01( 0 ) , m_M10( 0 ) , m_M11( n ) {}
template <typename T> inline TwoByTwoMatrix<T>::TwoByTwoMatrix( const T& M00 , const T& M01 , const T& M10 , const T& M11 ) noexcept : m_M00( M00 ) , m_M01( M01 ) , m_M10( M10 ) , m_M11( M11 ) {}
template <typename T> inline TwoByTwoMatrix<T>::TwoByTwoMatrix( const T& n ) noexcept : m_M00( n ) , m_M01() , m_M10() , m_M11( n ) {}

template <typename T> inline TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator=( const TwoByTwoMatrix<T>& mat ) noexcept { if( &mat != this ){ m_M00 = mat.m_M00; m_M01 = mat.m_M01; m_M10 = mat.m_M10; m_M11 = mat.m_M11; } return *this; }

template <typename T> inline TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator*=( const TwoByTwoMatrix<T>& mat ) noexcept { return operator=( *this * mat ); }

template <typename T> inline TwoByTwoMatrix<T> TwoByTwoMatrix<T>::operator+( const TwoByTwoMatrix<T>& mat ) { return TwoByTwoMatrix<T>( m_M00 + mat.m_M00 , m_M01 + mat.m_M01 , m_M10 + mat.m_M10 , m_M11 + mat.m_M11 ); }
template <typename T> inline TwoByTwoMatrix<T> TwoByTwoMatrix<T>::operator*( const TwoByTwoMatrix<T>& mat ) { return TwoByTwoMatrix<T>( m_M00 * mat.m_M00 + m_M01 * mat.m_M10 , m_M00 * mat.m_M01 + m_M01 * mat.m_M11 , m_M10 * mat.m_M00 + m_M11 * mat.m_M10 , m_M10 * mat.m_M01 + m_M11 * mat.m_M11 ); }


template <typename INT>
class QuotientRing
{

protected:
  INT m_n;
  const INT* m_p_M;

public:
  inline QuotientRing() noexcept;
  inline QuotientRing( const INT& n , const INT* const & p_M = nullptr ) noexcept;
  inline QuotientRing( const QuotientRing<INT>& n ) noexcept;

  inline QuotientRing<INT>& operator+=( const QuotientRing<INT>& n ) noexcept;
  inline QuotientRing<INT>& operator+=( const INT& 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<INT>& operator-=( const QuotientRing<INT>& n ) noexcept;
  inline QuotientRing<INT>& operator-=( const INT& n ) noexcept;
  inline QuotientRing<INT>& operator*=( const QuotientRing<INT>& n ) noexcept;
  inline QuotientRing<INT>& operator*=( const INT& n ) noexcept;

  inline const INT& Represent() const noexcept;
  inline const INT& GetModulo() const noexcept;

  // m_nの正負やm_p_Mの一致込みの等号。
  static inline bool Equal( const QuotientRing<INT>& n0 , const QuotientRing<INT>& n1 ) noexcept;

  template <typename T> static QuotientRing<INT> Power( const QuotientRing<INT>& n , const T& exponent );
  
};

template <typename INT> inline bool operator==( const QuotientRing<INT>& n0 , const QuotientRing<INT>& n1 ) noexcept;
template <typename INT> inline bool operator!=( const QuotientRing<INT>& n0 , const QuotientRing<INT>& n1 ) noexcept;

template <typename INT , typename T> inline QuotientRing<INT> operator+( const QuotientRing<INT>& n0 , const T& n1 ) noexcept;
template <typename INT , typename T> inline QuotientRing<INT> operator-( const QuotientRing<INT>& n0 , const T& n1 ) noexcept;
template <typename INT , typename T> inline QuotientRing<INT> operator*( const QuotientRing<INT>& n0 , const T& n1 ) noexcept;

template <typename INT , typename T> inline QuotientRing<INT> Power( const QuotientRing<INT>& n , const T& exponent );


template <typename INT> inline QuotientRing<INT>::QuotientRing() noexcept : m_n() , m_p_M( nullptr ) {}
template <typename INT> inline QuotientRing<INT>::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 <typename INT> inline QuotientRing<INT>::QuotientRing( const QuotientRing<INT>& n ) noexcept : m_n( n.m_n ) , m_p_M( n.m_p_M ) {}

template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator+=( const QuotientRing<INT>& 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 <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator+=( const INT& n ) noexcept { m_n += n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator-=( const QuotientRing<INT>& 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 <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator-=( const INT& n ) noexcept { m_n -= n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator*=( const QuotientRing<INT>& 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 <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator*=( const INT& n ) noexcept { m_n *= n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
  
template <typename INT> inline const INT& QuotientRing<INT>::Represent() const noexcept { return m_n; }
template <typename INT> inline const INT& QuotientRing<INT>::GetModulo() const noexcept { static const INT zero{ 0 }; return m_p_M == nullptr ? zero : *m_p_M; }

template <typename INT> inline bool QuotientRing<INT>::Equal( const QuotientRing<INT>& n0 , const QuotientRing<INT>& n1 ) noexcept { return n0.m_n == n1.m_n && n0.m_p_M == n1.m_p_M; }

template <typename INT> template <typename T>
QuotientRing<INT> QuotientRing<INT>::Power( const QuotientRing<INT>& n , const T& exponent )
{

  QuotientRing<INT> answer{ 1 , n.m_p_M };
  QuotientRing<INT> power{ n };

  while( exponent != 0 ){

    if( exponent % 2 == 1 ){

      answer *= power;

    }

    power *= power;
    exponent /= 2;

  }

  return answer;

}

template <typename INT> inline bool operator==( const QuotientRing<INT>& n0 , const QuotientRing<INT>& n1 ) noexcept { return QuotientRing<INT>::Equal( n0 , n1 ); }
template <typename INT> inline bool operator!=( const QuotientRing<INT>& n0 , const QuotientRing<INT>& n1 ) noexcept { return ! QuotientRing<INT>::Equal( n0 , n1 ); }

template <typename INT , typename T> inline QuotientRing<INT> operator+( const QuotientRing<INT>& n0 , const T& n1 ) noexcept { return QuotientRing<INT>( n0 ).operator+=( n1 ); }
template <typename INT , typename T> inline QuotientRing<INT> operator-( const QuotientRing<INT>& n0 , const T& n1 ) noexcept { return QuotientRing<INT>( n0 ).operator-=( n1 ); }
template <typename INT , typename T> inline QuotientRing<INT> operator*( const QuotientRing<INT>& n0 , const T& n1 ) noexcept { return QuotientRing<INT>( n0 ).operator*=( n1 ); }

template <typename INT , typename T> inline QuotientRing<INT> Power( const QuotientRing<INT>& n , const T& exponent ) { return QuotientRing<INT>::template Power<T>( n , exponent ); }


inline ll sgn( const ll& n ) { return n == 0 ? 0 : n > 0 ? 1 : -1; }

inline int Solve()
{
  CEXPR( ll , bound_N , 1000000000000000000 );
  CIN_ASSERT( N , 1 , bound_N );
  CEXPR( ll , bound_B , 1000000000 );
  CIN_ASSERT( B , 1 , bound_B );
  CEXPR( ll , bound_Aij , 1000000000 );
  CEXPR( int , size , 2 );
  ll A00 , A01 , A10 , A11;
  ll* p_A[size][size] = { { &A00 , &A01 } , { &A10 , & A11 }  };
  FOR( i , 0 , size ){
    FOR( j , 0 , size ){
      CIN_ASSERT( Aij , -bound_Aij , bound_Aij );
      *( p_A[i][j] ) = Aij;
    }
  }
  ll det_A = A00 * A11 - A01 * A10;
  ll det_A_minus_E = ( A00 - 1 ) * ( A11 - 1 ) - A01 * A10;
  ll sgn_Delta;
  if( det_A_minus_E != 0 ){
    ll tr = A00 + A11;
    ll D = tr * tr - 4 * det_A;
    if( D >= 0 ){
      ll det_A_plus_E = ( A00 + 1 ) * ( A11 + 1 ) - A01 * A10;
      sgn_Delta = N % 2 == 0 ? sgn( det_A ) * sgn( det_A_plus_E ) : sgn( det_A );
    } else {
      sgn_Delta = sgn( det_A_minus_E );
    }
  } else {
    if( det_A == 1 ){
      N %= B;
      RETURN( ( N * N ) % B );
    } else if( det_A == 0 ){
      RETURN( 0 );
    } else if( N % 2 == 0 ){
      sgn_Delta = 1;
    } else {
      sgn_Delta = sgn( det_A );
    }
  }
  QuotientRing<ll> A00mod{ A00 , &B };
  QuotientRing<ll> A01mod{ A01 , &B };
  QuotientRing<ll> A10mod{ A10 , &B };
  QuotientRing<ll> A11mod{ A11 , &B };
  TwoByTwoMatrix<QuotientRing<ll> > A{ A00mod , A01mod , A10mod , A11mod };
  QuotientRing<ll> one{ 1 , &B };
  QuotientRing<ll> zero{ 0 , &B };
  TwoByTwoMatrix<QuotientRing<ll> > I{ one , zero , zero , one };
  TwoByTwoMatrix<QuotientRing<ll> > O{ zero , zero , zero , zero };
  TwoByTwoMatrix<TwoByTwoMatrix<QuotientRing<ll> > > AAOI{ A , A , O , I };
  POWER( power_AAOI , AAOI , N - 1 );
  TwoByTwoMatrix<QuotientRing<ll> > sum_power_A = power_AAOI.m_M00 * A + power_AAOI.m_M01;
  ll Delta = ( sum_power_A.m_M00 * sum_power_A.m_M11 - sum_power_A.m_M01 * sum_power_A.m_M10 ).Represent();
  Delta < 0 ? Delta += B : Delta;
  RETURN( sgn_Delta >= 0 ? Delta : B - Delta );
}

int MAIN()
{
  UNTIE;
  CEXPR( int , bound_T , 1000 );
  CIN_ASSERT( T , 1 , bound_T );
  REPEAT( T ){
    Solve();
  }
  QUIT;
}
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