#959231 (C++17(gcc12)) No.3170 [Cherry 7th Tune KY] Even if you could say "See you ..."

提出ソース
結果

問題	No.3170 [Cherry 7th Tune KY] Even if you could say "See you ..."
ユーザー	👑 p-adic
提出日時	2024-03-11 07:15:20
言語	C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
結果	AC
実行時間	573 ms / 4,000 ms
コード長	49,578 bytes
コンパイル時間	15,045 ms
コンパイル使用メモリ	245,768 KB
実行使用メモリ	7,848 KB
最終ジャッジ日時	2025-06-11 23:04:43
合計ジャッジ時間	18,376 ms
ジャッジサーバーID （参考情報）	judge2 / judge3
このコードへのチャレンジ
（要ログイン）
ファイルパターン	結果
sample	AC * 2
other	AC * 40
権限があれば一括ダウンロードができます
ソースコード

raw source code
#ifndef INCLUDE_MODE
  #define INCLUDE_MODE
  // #define REACTIVE
  // #define USE_GETLINE
#endif

#ifdef INCLUDE_MAIN

IN VO Solve()
{
  CEXPR( ll , bound_P , 3e5 ); CIN_ASSERT( P , 2 , bound_P );
  FOR( i , 2 , P ){
    assert( P % i != 0 );
    if( i * i > P ){
      break;
    }
  }
  U::SetStaticModulo( &P );
  CIN( U , A11 , A12 , A21 , A22 );
  CIN( U , B11 , B12 , B21 , B22 );
  RETURN( Answer( P , A11 , A12 , A21 , A22 , B11 , B12 , B21 , B22 ) );
}
REPEAT_MAIN(5);

#else // INCLUDE_MAIN

#ifdef INCLUDE_SUB

using U = QuotientRing<ll>;
using M = TwoByTwoMatrix<U>;

// COMPAREに使用。圧縮時は削除する。
ll Naive( const ll& P , const U& A11 , const U& A12 , const U& A21 , const U& A22 , const U& B11 , const U& B12 , const U& B21 , const U& B22 )
{
  M A( A11 , A12 , A21 , A22 );
  M B( B11 , B12 , B21 , B22 );
  ll bound = P * ( P * P - 1 );
  M E( 1 , 0 , 0 , 1 );
  M power_A = E;
  FOREQ( i , 0 , bound ){
    if( power_A == B ){
      return i;
    }
    power_A *= A;
  }
  return -1;
}

// COMPAREに使用。圧縮時は削除する。
ll Answer( const ll& P , const U& A11 , const U& A12 , const U& A21 , const U& A22 , const U& B11 , const U& B12 , const U& B21 , const U& B22 )
{
  M A( A11 , A12 , A21 , A22 );
  M B( B11 , B12 , B21 , B22 );
  M E( 1 , 0 , 0 , 1 );
  if( B == E ){
    CERR( "Solved at" , __LINE__ );
    return 0;
  }
  U det_A = A.det();
  U det_B = B.det();
  if( ( det_A == 0 ) != ( det_B == 0 ) ){
    CERR( "Solved at" , __LINE__ );
    return -1;
  }
  ll ord_A = det_A == 0 ? -2 : -1;
  M power_A = A;
  FOREQ( n , 1 , P ){
    if( power_A == B ){
      CERR( "Solved at" , __LINE__ );
      return n;
    }
    if( ord_A == -1 && power_A == E ){
      ord_A = n;
      CERR( "ord_A =" , n );
    }
    power_A *= A;
  }
  if( ord_A != -1 ){
    // ord_A > 0の場合は位数がP以下なのでP乗までで冪乗が全探策可能。
    // ord_A = -2の場合はdet_A = 0なので非正則だが、
    // 対角化可能ならばtrがFpに属すのでP-1乗まで、対角化不可能ならP乗までで
    // 羃乗が全探索可能。
    // 従っていずれの場合も羃乗がP乗までで全探索可能。
    return -1;
  }
  // ここから先はord_A = -1つまりdet_A != 0かつ位数がPより大きい。
  // #GL_2(F_P) = P^4 - ( P^2 + P - 1 ) * P = P^4 - P^3 - P^2 + P
  // = P(P-1)(P^2 - 1) = P(P-1)^2(P+1)
  // で位数は対角化可能ならばP^2-1の約数、対角化不可能ならP(P^2-1)の約数。
  // 従ってNはP(P^2-1)未満。N mod P,N mod P-1,N mod P+1を調べる。
  auto Power = [&]( const M& mat , ll e ){
    M answer = E;
    M power = mat;
    while( e > 0 ){
      ( e & 1 ) == 1 ? answer *= power : answer;
      power *= power;
      e >>= 1;
    }
    return answer;
  };
  ll mod[3] = { P * ( P - 1 ) , ( P - 1 ) * ( P + 1 ) , P * ( P + 1 ) };
  M A_P[3];
  M B_P[3];
  int ord_A_P[3] = {-1,-1,-1};
  ll e[3] = {-1,-1,-1};
  // A^N=BならばA^{(N mod (ord_A_P[i]))(P(P^2-1)/ord_A_P[i])}=B^{P(P^2-1)/ord_A_P[i]}
  // なのでN mod ord_A_P[i]の候補が調べられる。
  FOR( i , 0 , 3 ){
    A_P[i] = Power( A , mod[i] );
    B_P[i] = Power( B , mod[i] );
    power_A = E;
    FOREQ( n , 0 , P + 1 ){
      if( e[i] == -1 && power_A == B_P[i] ){
	// N mod ord_A_P[i] = e[i]
	e[i] = n;
      }
      if( n > 0 && power_A == E ){
	ord_A_P[i] = n;
	break;
      }
      power_A *= A_P[i];
    }
    if( e[i] == -1 ){
      CERR( "Solved at" , __LINE__ , "i =" , i );
      return -1;
    }
    if( ord_A_P[i] == -1 ){
      while( 1 ){
	COUT( "Error:" , i );
	CERR( P , A11 , A12 , A21 , A22 , B11 , B12 , B21 , B22 );
      }
    }
    CERR( "( P(P^1-1)/ord_A_P[" , i , "] , ord_A_P[" , i , "] , e[" , i , "] ) = (" , P*(P*P-1)/ord_A_P[i] , "," , ord_A_P[i] , "," , e[i] , ")" );
  }
  // 中国剰余定理によりN mod lcm(ord_A_O[i])_iを求められる。
  ll lcm = LCM( ll( ord_A_P[0] ) , ll( ord_A_P[1] ) );
  ll x = ChineseRemainderTheorem( ll( ord_A_P[0] ) , ll( e[0] ) , ll( ord_A_P[1] ) , ll( e[1] ) );
  if( x == -1 ){
    CERR( "Solved at" , __LINE__ );
    return -1;
  }
  x = ChineseRemainderTheorem( lcm , x , ll( ord_A_P[2] ) , ll( e[2] ) );
  if( x == -1 ){
    CERR( "Solved at" , __LINE__ );
    return -1;
  }
  lcm = LCM( lcm , ll( ord_A_P[2] ) );
  // N mod ord_A_P[i] = e[i]となるNをP(P^2 - 1)以下で全探策。
  power_A = Power( A , x );
  M A_lcm = Power( A , lcm );
  ll N = x;
  while( N <= P * ( P * P - 1 ) ){
    if( power_A == B ){
      CERR( "Solved at" , __LINE__ );
      return N;
    }
    N += lcm;
    power_A *= A_lcm;
  }
  CERR( "Solved at" , __LINE__ );
  return -1;
}

// 圧縮時は中身だけ削除する。
IN VO Experiment()
{
}

// 圧縮時は中身だけ削除する。
IN VO SmallTest()
{
  CEXPR( int , bound , 10 );
  ll P[bound+1] = {2,3,5,7,11,13,17,19,23};
  FOREQ( i , 0 , bound ){
    ll& p = P[i];
    ll p4 = p*p*p*p;
    U::SetStaticModulo( &p );
    M E( 1 , 0 , 0 , 1 );
    FOR( a , 0 , p4 ){
      ll A11 = a % p;
      ll A12 = a / p % p;
      ll A21 = a / p / p % p;
      ll A22 = a / p / p / p;
      FOR( b , 0 , p4 ){
	ll B11 = b % p;
	ll B12 = b / p % p;
	ll B21 = b / p / p % p;
	ll B22 = b / p / p / p;
    	COMPARE( p , A11 , A12 , A21 , A22 , B11 , B12 , B21 , B22 );
      }
    }
  }
}

#define INCLUDE_MAIN
#include __FILE__

#else // INCLUDE_SUB

#ifdef INCLUDE_LIBRARY

/*

C-x 3 C-x o C-x C-fによるファイル操作用

BFS (5KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt

CoordinateCompress (3KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txt

DFSOnTree (11KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepthFirstSearch/Tree/a.hpp

Divisor (4KB)
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt

IntervalAddBIT (9KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/IntervalAdd/compress.txt

Polynomial (21KB)
c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt

UnionFind (3KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/UnionFindForest/compress.txt

*/

// VVV 常設でないライブラリは以下に挿入する。

template <typename INT>
INT GCD( const INT& b_0 , const INT& b_1 )
{

  INT a_0 = abs( b_0 );
  INT a_1 = abs( b_1 );

  while( a_1 != 0 ){

    swap( a_0 %= a_1 , a_1 );

  }

  return a_0;

}

template <typename INT> inline INT LCM( const INT& b_0 , const INT& b_1 ) { return ( b_0 == 0 && b_1 == 0 ) ? 0 : ( b_0 / GCD( b_0 , b_1 ) ) * b_1; }

template <typename INT>
INT PartitionOfUnity( const INT& b_0 , const INT& b_1 , INT& u_0 ,  INT& u_1 )
{

  INT a[2][2] = { { 1 , 0 } , { 0 , 1 } };
  INT b[2] = { b_0 , b_1 };

  for( int i = 0 ; i < 2 ; i++ ){

    if( b[i] < 0 ){

      a[i][i] = -1;
      b[i] *= -1;

    }

  }
  
  int i_0 = ( b_0 >= b_1 ? 0 : 1 );
  int i_1 = 1 - i_0;

  while( b[i_1] != 0 ){

    INT& b_i_0 = b[i_0];
    const INT& b_i_1 = b[i_1];
    INT ( &a_i_0 )[2] = a[i_0];
    const INT ( &a_i_1 )[2] = a[i_1];
    const INT q = b_i_0 / b_i_1;
    a_i_0[i_0] -= q * a_i_1[i_0];
    a_i_0[i_1] -= q * a_i_1[i_1];
    b_i_0 -= q * b_i_1;
    swap( i_0 , i_1 );

  }

  INT ( &a_i_0 )[2] = a[i_0];
  u_0 = move( a_i_0[0] );
  u_1 = move( a_i_0[1] );
  return move( b[i_0] );

}

template <typename INT>
INT ChineseRemainderTheorem( const INT& b_0 , const INT& c_0 , const INT& b_1 , const INT& c_1 )
{

  INT u_0 , u_1;
  const INT gcd = PartitionOfUnity( b_0 , b_1 , u_0 , u_1 );
  const INT c = c_0 % gcd;

  if( c_1 % gcd != c ){

    return -1;

  }
  
  const INT lcm = ( b_0 / gcd ) * b_1;
  u_0 *= ( c_1 - c ) / gcd;
  Residue( u_0 , lcm );
  u_1 *= ( c_0 - c ) / gcd;
  u_1 = ( u_1 >= 0 ? u_1 % lcm : lcm - ( - u_1 - 1 ) % lcm - 1 );
  return ( c + u_0 * b_0 + u_1 * b_1 ) % lcm;

}

#define SFINAE_FOR_MATRIX(DEFAULT) TY Arg,enable_if_t<is_constructible<T,Arg>::value>* DEFAULT

template <typename T>
class TwoByTwoMatrix
{
  
private:
  T m_M00;
  T m_M01;
  T m_M10;
  T m_M11;

public:
  inline constexpr TwoByTwoMatrix( const T& M00 , const T& M01 , const T& M10 , const T& M11 ) noexcept;
  inline constexpr TwoByTwoMatrix( T&& M00 , T&& M01 , T&& M10 , T&& M11 ) noexcept;
  inline constexpr TwoByTwoMatrix( const T& n = T() ) noexcept;
  template <SFINAE_FOR_MATRIX( = nullptr )> inline constexpr TwoByTwoMatrix( const Arg& n ) noexcept;
  inline constexpr TwoByTwoMatrix( const TwoByTwoMatrix<T>& mat ) noexcept;
  inline constexpr TwoByTwoMatrix( TwoByTwoMatrix<T>&& mat ) noexcept;
  
  inline constexpr TwoByTwoMatrix<T>& operator=( const TwoByTwoMatrix<T>& mat ) noexcept;
  inline constexpr TwoByTwoMatrix<T>& operator=( TwoByTwoMatrix<T>&& mat ) 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 ) noexcept;
  inline constexpr TwoByTwoMatrix<T>& operator*=( const T& scalar ) noexcept;
  template <SFINAE_FOR_MATRIX( = nullptr )> inline constexpr TwoByTwoMatrix<T>& operator*=( const Arg& scalar ) noexcept;
  inline TwoByTwoMatrix<T>& operator/=( const TwoByTwoMatrix<T>& mat );
  inline TwoByTwoMatrix<T>& operator/=( const T& scalar );
  template <SFINAE_FOR_MATRIX( = nullptr )> inline constexpr TwoByTwoMatrix<T>& operator/=( const Arg& scalar );
  inline TwoByTwoMatrix<T>& operator%=( const T& scalar );
  template <SFINAE_FOR_MATRIX( = nullptr )> inline constexpr TwoByTwoMatrix<T>& operator%=( const Arg& scalar );

  inline TwoByTwoMatrix<T>& Invert();

  inline constexpr bool operator==( const TwoByTwoMatrix<T>& mat ) const noexcept;
  inline constexpr bool operator!=( const TwoByTwoMatrix<T>& mat ) const noexcept;

  inline TwoByTwoMatrix<T> operator*( const TwoByTwoMatrix<T>& mat ) const noexcept;
  // inline TwoByOneMatrix<T> operator*( const TwoByOneMatrix<T>& mat ) const noexcept;
  inline TwoByTwoMatrix<T> operator/( const TwoByTwoMatrix<T>& mat ) const;
  inline constexpr TwoByTwoMatrix<T> Square() const noexcept;

  inline constexpr T det() const noexcept;
  inline constexpr const T& GetEntry( const uint& y , const uint& x ) const noexcept;
  inline constexpr T& RefEntry( const uint& y , const uint& x ) noexcept;
  
};

template <typename T> inline TwoByTwoMatrix<T> operator+( const TwoByTwoMatrix<T>& mat1 , const TwoByTwoMatrix<T>& mat2 ) noexcept;
template <typename T> inline TwoByTwoMatrix<T> operator-( const TwoByTwoMatrix<T>& mat1 , const TwoByTwoMatrix<T>& mat2 ) noexcept;
template <typename T> inline constexpr TwoByTwoMatrix<T> operator*( const T& scalar , const TwoByTwoMatrix<T>& mat ) noexcept;
template <typename T , SFINAE_FOR_MATRIX( = nullptr )> inline constexpr TwoByTwoMatrix<T> operator*( const Arg& scalar , const TwoByTwoMatrix<T>& mat ) noexcept;
template <typename T> inline constexpr TwoByTwoMatrix<T> operator*( const TwoByTwoMatrix<T>& mat , const T& scalar ) noexcept;
template <typename T , SFINAE_FOR_MATRIX( = nullptr )> inline constexpr TwoByTwoMatrix<T> operator*( const TwoByTwoMatrix<T>& mat , const T& scalar ) noexcept;
template <typename T> inline TwoByTwoMatrix<T> operator/( const TwoByTwoMatrix<T>& mat , const T& scalar );
template <typename T , SFINAE_FOR_MATRIX( = nullptr )> inline TwoByTwoMatrix<T> operator/( const TwoByTwoMatrix<T>& mat , const Arg& scalar );
template <typename T> inline TwoByTwoMatrix<T> operator%( const TwoByTwoMatrix<T>& mat , const T& scalar );
template <typename T , SFINAE_FOR_MATRIX( = nullptr )> inline TwoByTwoMatrix<T> operator%( const TwoByTwoMatrix<T>& mat , const Arg& scalar );

template <typename T> inline constexpr 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 constexpr TwoByTwoMatrix<T>::TwoByTwoMatrix( T&& M00 , T&& M01 , T&& M10 , T&& M11 ) noexcept : m_M00( move( M00 ) ) , m_M01( move( M01 ) ) , m_M10( move( M10 ) ) , m_M11( move( M11 ) ) {}
template <typename T> inline constexpr TwoByTwoMatrix<T>::TwoByTwoMatrix( const T& n ) noexcept : m_M00( n ) , m_M01() , m_M10() , m_M11( n ) {}
template <typename T> template <SFINAE_FOR_MATRIX()> inline constexpr TwoByTwoMatrix<T>::TwoByTwoMatrix( const Arg& n ) noexcept : TwoByTwoMatrix( T( n ) ) {}
template <typename T> inline constexpr TwoByTwoMatrix<T>::TwoByTwoMatrix( const TwoByTwoMatrix<T>& mat ) noexcept : m_M00( mat.m_M00 ) , m_M01( mat.m_M01 ) , m_M10( mat.m_M10 ) , m_M11( mat.m_M11 ) {}
template <typename T> inline constexpr TwoByTwoMatrix<T>::TwoByTwoMatrix( TwoByTwoMatrix<T>&& mat ) noexcept : m_M00( move( mat.m_M00 ) ) , m_M01( move( mat.m_M01 ) ) , m_M10( move( mat.m_M10 ) ) , m_M11( move( mat.m_M11 ) ) {}


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

template <typename T> inline TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator+=( const TwoByTwoMatrix<T>& mat ) noexcept { 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 { 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 constexpr TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator*=( const T& scalar ) noexcept { m_M00 *= scalar; m_M01 *= scalar; m_M10 *= scalar; m_M11 *= scalar; return *this; }
template <typename T> template <SFINAE_FOR_MATRIX()> inline constexpr TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator*=( const Arg& scalar ) noexcept { return operator*=( T( scalar ) ); }
template <typename T> inline TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator/=( const TwoByTwoMatrix<T>& mat ) { return operator=( *this / mat ); }
template <typename T> inline TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator/=( const T& scalar ) { return operator*=( T( 1 ) / scalar ); }
template <typename T> template <SFINAE_FOR_MATRIX()> inline constexpr TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator/=( const Arg& scalar ) { return operator/=( T( scalar ) ); }
template <typename T> inline TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator%=( const T& scalar ) { m_M00 %= scalar; m_M01 %= scalar; m_M10 %= scalar; m_M11 %= scalar; return *this; }
template <typename T> template <SFINAE_FOR_MATRIX()> inline constexpr TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator%=( const Arg& scalar ) { return operator%=( T( scalar ) ); }

template <typename T> inline TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::Invert() { const T det_inv{ T( 1 ) / ( m_M00 * m_M11 - m_M01 * m_M10 ) }; swap( m_M00 , m_M11 ); m_M01 = T() - m_M01; m_M10 = T() - m_M10; return operator*=( det_inv ); }

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

template <typename T> inline TwoByTwoMatrix<T> TwoByTwoMatrix<T>::operator*( const TwoByTwoMatrix<T>& mat ) const noexcept { 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 T> inline TwoByOneMatrix<T> TwoByTwoMatrix<T>::operator*( const TwoByOneMatrix<T>& mat ) const noexcept { return TwoByOneMatrix<T>( m_M00 * mat.m_M0 + m_M01 * mat.m_M1 , m_M10 * mat.m_M0 + m_M11 * mat.m_M1 ); }

template <typename T> inline TwoByTwoMatrix<T> TwoByTwoMatrix<T>::operator/( const TwoByTwoMatrix<T>& mat ) const { const T det_inv{ T( 1 ) / ( mat.m_M00 * mat.m_M11 - mat.m_M01 * mat.m_M10 ) }; return TwoByTwoMatrix<T>( ( m_M00 * mat.m_M11 - m_M01 * mat.m_M10 ) * det_inv , ( m_M01 * mat.m_M00 - m_M00 * mat.m_M01 ) * det_inv , ( m_M10 * mat.m_M11 - m_M11 * mat.m_M10 ) * det_inv , ( m_M11 * mat.m_M00 - m_M10 * mat.m_M01 ) * det_inv ); }

template <typename T> inline constexpr TwoByTwoMatrix<T> TwoByTwoMatrix<T>::Square() const noexcept { return TwoByTwoMatrix<T>( m_M00 * m_M00 + m_M01 * m_M10 , ( m_M00 + m_M11 ) * m_M01 , m_M10 * ( m_M00 + m_M11 ) , m_M10 * m_M01 + m_M11 * m_M11 ); }

template <typename T> inline constexpr T TwoByTwoMatrix<T>::det() const noexcept { return m_M00 * m_M11 - m_M01 * m_M10; }
template <typename T> inline constexpr const T& TwoByTwoMatrix<T>::GetEntry( const uint& y , const uint& x ) const noexcept { return y == 0 ? x == 0 ? m_M00 : m_M01 : x == 0 ? m_M10 : m_M11; }
template <typename T> inline constexpr T& TwoByTwoMatrix<T>::RefEntry( const uint& y , const uint& x ) noexcept { return y == 0 ? x == 0 ? m_M00 : m_M01 : x == 0 ? m_M10 : m_M11; }

template <typename T> inline TwoByTwoMatrix<T> operator+( const TwoByTwoMatrix<T>& mat1 , const TwoByTwoMatrix<T>& mat2 ) noexcept { return move( TwoByTwoMatrix<T>( mat1 ) += mat2 ); }
template <typename T> inline TwoByTwoMatrix<T> operator-( const TwoByTwoMatrix<T>& mat1 , const TwoByTwoMatrix<T>& mat2 ) noexcept { return move( TwoByTwoMatrix<T>( mat1 ) -= mat2 ); }
template <typename T> inline constexpr TwoByTwoMatrix<T> operator*( const T& scalar , const TwoByTwoMatrix<T>& mat ) noexcept { return move( TwoByTwoMatrix<T>( mat ) *= scalar ); }
template <typename T , SFINAE_FOR_MATRIX()> inline constexpr TwoByTwoMatrix<T> operator*( const Arg& scalar , const TwoByTwoMatrix<T>& mat ) noexcept { return T( scalar ) * mat; }
template <typename T> inline constexpr TwoByTwoMatrix<T> operator*( const TwoByTwoMatrix<T>& mat , const T& scalar ) noexcept { return move( TwoByTwoMatrix<T>( mat ) *= scalar ); }
template <typename T , SFINAE_FOR_MATRIX()> inline constexpr TwoByTwoMatrix<T> operator*( const TwoByTwoMatrix<T>& mat , const Arg& scalar ) noexcept { return mat * T( scalar ); }
template <typename T> inline TwoByTwoMatrix<T> operator/( const TwoByTwoMatrix<T>& mat , const T& scalar ) { return move( TwoByTwoMatrix<T>( mat ) /= scalar ); }
template <typename T , SFINAE_FOR_MATRIX()> inline TwoByTwoMatrix<T> operator/( const TwoByTwoMatrix<T>& mat , const Arg& scalar ) { return mat / T( scalar ); }
template <typename T> inline TwoByTwoMatrix<T> operator%( const TwoByTwoMatrix<T>& mat , const T& scalar ) { return move( TwoByTwoMatrix<T>( mat ) %= scalar ); }
template <typename T , SFINAE_FOR_MATRIX()> inline TwoByTwoMatrix<T> operator%( const TwoByTwoMatrix<T>& mat , const Arg& scalar ) { return mat % T( scalar ); }

template <typename INT>
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<INT>& n ) noexcept;

  inline QuotientRing<INT>& operator+=( const QuotientRing<INT>& n ) noexcept;
  template <typename T> inline QuotientRing<INT>& 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<INT>& operator-=( const QuotientRing<INT>& n ) noexcept;
  template <typename T> inline QuotientRing<INT>& operator-=( const T& n ) noexcept;
  inline QuotientRing<INT>& operator*=( const QuotientRing<INT>& n ) noexcept;
  template <typename T> inline QuotientRing<INT>& 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<INT>& operator/=( const QuotientRing<INT>& n );
  template <typename T> inline QuotientRing<INT>& 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<INT>& n ) const noexcept;
  // m_nの正負込みの等号。
  template <typename T> inline bool operator==( const T& n ) const noexcept;
  template <typename T> inline bool operator!=( const T& n ) const noexcept;

  template <typename T> inline QuotientRing<INT> operator+( const T& n1 ) const noexcept;
  inline QuotientRing<INT> operator-() const noexcept;
  template <typename T> inline QuotientRing<INT> operator-( const T& n1 ) const noexcept;
  template <typename T> inline QuotientRing<INT> 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 <typename T> inline QuotientRing<INT> 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 <typename T> static QuotientRing<INT> Power( const QuotientRing<INT>& 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<INT> Inverse( const QuotientRing<INT>& n );
  
};

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

template <typename INT , class Traits> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , QuotientRing<INT>& n );
template <typename INT , class Traits> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const QuotientRing<INT>& n );

template <typename INT> const INT* QuotientRing<INT>::g_p_M = nullptr;
template <typename INT> inline QuotientRing<INT>::QuotientRing() noexcept : m_n() , m_p_M( g_p_M ) {}
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> template <typename T> inline QuotientRing<INT>& QuotientRing<INT>::operator+=( const T& n ) noexcept { m_p_M == nullptr ? m_n += n : ( m_n += n % *m_p_M ) %= *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> template <typename T> inline QuotientRing<INT>& QuotientRing<INT>::operator-=( const T& n ) noexcept { m_p_M == nullptr ? m_n -= n : ( m_n -= n % *m_p_M ) %= *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> template <typename T> inline QuotientRing<INT>& QuotientRing<INT>::operator*=( const T& n ) noexcept { m_p_M == nullptr ? m_n *= n : ( m_n *= n % *m_p_M ) %= *m_p_M; return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator/=( const QuotientRing<INT>& 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<INT>( n.m_n , m_p_M ) ) ); }
template <typename INT> template <typename T> inline QuotientRing<INT>& QuotientRing<INT>::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 <typename INT> inline bool QuotientRing<INT>::operator==( const QuotientRing<INT>& n ) const noexcept { return m_p_M == n.m_p_M && m_n == n.m_n; }
template <typename INT> template <typename T> inline bool QuotientRing<INT>::operator==( const T& n ) const noexcept { return m_n == n; }
template <typename INT> template <typename T> inline bool QuotientRing<INT>::operator!=( const T& n ) const noexcept { return !operator==( n ); }

template <typename INT> template<typename T> inline QuotientRing<INT> QuotientRing<INT>::operator+( const T& n ) const noexcept { return QuotientRing<INT>( *this ).operator+=( n ); }
template <typename INT> inline QuotientRing<INT> QuotientRing<INT>::operator-() const noexcept { return QuotientRing<INT>( -m_n , m_p_M ); }
template <typename INT> template<typename T> inline QuotientRing<INT> QuotientRing<INT>::operator-( const T& n ) const noexcept { return QuotientRing<INT>( *this ).operator-=( n ); }
template <typename INT> template<typename T> inline QuotientRing<INT> QuotientRing<INT>::operator*( const T& n ) const noexcept { return QuotientRing<INT>( *this ).operator*=( n ); }
template <typename INT> template<typename T> inline QuotientRing<INT> QuotientRing<INT>::operator/( const T& n ) const { return QuotientRing<INT>( *this ).operator/=( n ); }
  
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 void QuotientRing<INT>::SetModulo( const INT* const& p_M ) noexcept { m_p_M = p_M; if( m_p_M != nullptr ){ m_n %= *m_p_M; } }
template <typename INT> inline const INT& QuotientRing<INT>::GetStaticModulo() noexcept { static const INT zero{ 0 }; return g_p_M == nullptr ? zero : *g_p_M; }
template <typename INT> inline void QuotientRing<INT>::SetStaticModulo( const INT* const& p_M ) noexcept { g_p_M = p_M; }

template <typename INT> template <typename T>
QuotientRing<INT> QuotientRing<INT>::Power( const QuotientRing<INT>& n , 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 QuotientRing<INT> QuotientRing<INT>::Inverse( const QuotientRing<INT>& n ) { assert( n.m_p_M != nullptr ); return Power( n , *( n.m_p_M ) - 2 ); }

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

template <typename INT , class Traits> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , QuotientRing<INT>& n ) { INT m; is >> m; n = m; return is; }
template <typename INT , class Traits> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const QuotientRing<INT>& n ) { return os << n.Represent(); }

// AAA 常設でない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 REPEAT_MAIN( BOUND ) START_MAIN; signal( SIGABRT , &AlertAbort ); AutoCheck( exec_mode , use_getline ); if( exec_mode == sample_debug_mode || exec_mode == submission_debug_mode || exec_mode == library_search_mode ){ RE 0; } else if( exec_mode == experiment_mode ){ Experiment(); RE 0; } else if( exec_mode == small_test_mode ){ SmallTest(); RE 0; }; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if( exec_mode == solve_mode ){ if CE( bound_test_case_num > 1 ){ CERR( "テストケースの個数を入力してください。" ); SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } } else if( exec_mode == random_test_mode ){ CERR( "ランダムテストを行う回数を指定してください。" ); SET_LL( test_case_num ); } FINISH_MAIN
  #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); AS( ( MIN ) <= A && A <= ( MAX ) )
  #define SET_ASSERT( A , MIN , MAX ) if( exec_mode == solve_mode ){ SET_LL( A ); ASSERT( A , MIN , MAX ); } else if( exec_mode == random_test_mode ){ CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ); } else { AS( false ); }
  #define SOLVE_ONLY ST_AS( __FUNCTION__[0] == 'S' )
  #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 REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if CE( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN
  #define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) )
  #define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX )
  #define SOLVE_ONLY 
  #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 , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
  #define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#else
  #define SET_LL( A ) cin >> A
  #define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
  #define SET_A( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_SET_A , 0 , N ){ cin >> A[VARIABLE_FOR_SET_A]; }
  #define CIN_A( LL , A , N ) VE<LL> A( N ); SET_A( A , N );
#endif
#include <bits/stdc++.h>
using namespace std;
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define FINISH_MAIN REPEAT( test_case_num ){ if CE( 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<double>( chrono::duration_cast<chrono::microseconds>( chrono::system_clock::now() - watch ).count() / 1000.0 )
#define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 )
#define CEXPR( LL , BOUND , VALUE ) CE LL BOUND = VALUE
#define SET_A_ASSERT( A , N , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A] , MIN , MAX ); }
#define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define CIN_A_ASSERT( A , N , MIN , MAX ) vector<decldecay_t( MAX )> A( N ); SET_A_ASSERT( A , N , 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 .BE() , end_ ## ARRAY = ARRAY .EN()
#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.BE() , EN_FOR_OUTPUT_ITR = A.EN(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; WH( 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( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); RE
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ RE; }

// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#define AS assert
#define IN inline
#define CL class
#define PU public
#define OP operator
#define CE constexpr
#define CO const
#define NE noexcept
#define RE return 
#define WH while
#define VO void
#define VE vector
#define LI list
#define BE begin
#define EN end
#define SZ size
#define LE length
#define PW Power
#define MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&
#define VI virtual 
#define ST_AS static_assert
#define reMO_CO remove_const
#define is_COructible_v is_constructible_v
#define rBE rbegin
#define reSZ resize

// 型のエイリアス
#define decldecay_t( VAR ) decay_t<decltype( VAR )>
TE <TY F , TY...Args> US ret_t = decltype( declval<F>()( declval<Args>()... ) );
TE <TY T> US inner_t = TY T::type;
US uint = unsigned int;
US ll = long long;
US ull = unsigned long long;
US ld = long double;
US lld = __float128;
TE <TY INT> US T2 = pair<INT,INT>;
TE <TY INT> US T3 = tuple<INT,INT,INT>;
TE <TY INT> US T4 = tuple<INT,INT,INT,INT>;
US path = pair<int,ll>;

// 入出力用
TE <CL Traits> IN basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is ) { RE is; }
TE <CL Traits , TY Arg , TY... ARGS> IN basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is , Arg& arg , ARGS&... args ) { RE VariadicCin( is >> arg , args... ); }
TE <CL Traits> IN basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , CO char& separator ) { RE is; }
TE <CL Traits , TY Arg , TY... ARGS> IN basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , CO char& separator , Arg& arg , ARGS&... args ) { RE VariadicGetline( getline( is , arg , separator ) , separator , args... ); }
TE <CL Traits , TY Arg> IN basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , CO VE<Arg>& arg ) { auto BE = arg.BE() , EN = arg.EN(); auto itr = BE; WH( itr != EN ){ ( itr == BE ? os : os << " " ) << *itr; itr++; } RE os; }
TE <CL Traits , TY Arg1 , TY Arg2> IN basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , CO pair<Arg1,Arg2>& arg ) { RE os << arg.first << " " << arg.second; }
TE <CL Traits , TY Arg> IN basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , CO Arg& arg ) { RE os << arg; }
TE <CL Traits , TY Arg1 , TY Arg2 , TY... ARGS> IN basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , CO Arg1& arg1 , CO Arg2& arg2 , CO ARGS&... args ) { RE VariadicCout( os << arg1 << " " , arg2 , args... ); }

// 算術用
TE <TY T> CE T PositiveBaseResidue( CO T& a , CO T& p ){ RE a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }
TE <TY T> CE T Residue( CO T& a , CO T& p ){ RE PositiveBaseResidue( a , p < 0 ? -p : p ); }
TE <TY T> CE T PositiveBaseQuotient( CO T& a , CO T& p ){ RE ( a - PositiveBaseResidue( a , p ) ) / p; }
TE <TY T> CE T Quotient( CO T& a , CO T& p ){ RE p < 0 ? PositiveBaseQuotient( -a , -p ) : PositiveBaseQuotient( a , p ); }

#define POWER( ANSWER , ARGUMENT , EXPONENT )				\
  ST_AS( ! is_same<decldecay_t( ARGUMENT ),int>::value && ! is_same<decldecay_t( ARGUMENT ),uint>::value ); \
  decldecay_t( ARGUMENT ) ANSWER{ 1 };					\
  {									\
    decldecay_t( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT ); \
    decldecay_t( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \
    WH( 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 )		\
  ll ANSWER{ 1 };							\
  {									\
    ll ARGUMENT_FOR_SQUARE_FOR_POWER = ( ( ARGUMENT ) % ( MODULO ) ) % ( MODULO ); \
    ARGUMENT_FOR_SQUARE_FOR_POWER < 0 ? ARGUMENT_FOR_SQUARE_FOR_POWER += ( MODULO ) : ARGUMENT_FOR_SQUARE_FOR_POWER; \
    decldecay_t( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \
    WH( 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 , INVERSE , MAX_INDEX , CE_LENGTH , MODULO ) \
  ll ANSWER[CE_LENGTH];							\
  ll ANSWER_INV[CE_LENGTH];						\
  ll INVERSE[CE_LENGTH];						\
  {									\
    ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1;				\
    ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL;			\
    FOREQ( i , 1 , MAX_INDEX ){						\
      ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \
    }									\
    ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \
    FOREQ( i , 2 , MAX_INDEX ){						\
      ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \
    }									\
  }									\

// 二分探索用
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CO_TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , CO_TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
  ST_AS( ! is_same<decldecay_t( CO_TARGET ),uint>::value && ! is_same<decldecay_t( CO_TARGET ),ull>::value ); \
  ll ANSWER = MINIMUM;							\
  {									\
    ll L_BS = MINIMUM;							\
    ll U_BS = MAXIMUM;							\
    ANSWER = UPDATE_ANSWER;						\
    ll EXPRESSION_BS;							\
    CO ll CO_TARGET_BS = ( CO_TARGET );			\
    ll DIFFERENCE_BS;							\
    WH( L_BS < U_BS ){						\
      DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CO_TARGET_BS; \
      CERR( "二分探索中：" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS :" , #EXPRESSION , "=" , EXPRESSION_BS , DIFFERENCE_BS > 0 ? ">" : DIFFERENCE_BS < 0 ? "<" : "=" , CO_TARGET_BS , "=" , #CO_TARGET ); \
      if( DIFFERENCE_BS INEQUALITY_FOR_CHECK 0 ){			\
	U_BS = UPDATE_U;						\
      } else {								\
	L_BS = UPDATE_L;						\
      }									\
      ANSWER = UPDATE_ANSWER;						\
    }									\
    if( L_BS > U_BS ){							\
      CERR( "二分探索失敗：" , "L_BS =" , L_BS , ">" , U_BS , "= U_BS :" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1  ); \
      CERR( "二分探索マクロにミスがある可能性があります。変更前の版に戻してください。" ); \
      ANSWER = MAXIMUM + 1;						\
    } else {								\
      CERR( "二分探索終了：" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS" ); \
      CERR( "二分探索が成功したかを確認するために" , #EXPRESSION , "を計算します。" ); \
      CERR( "成功判定が不要な場合はこの計算を削除しても構いません。" );	\
      EXPRESSION_BS = ( EXPRESSION );					\
      CERR( "二分探索結果：" , #EXPRESSION , "=" , EXPRESSION_BS , ( EXPRESSION_BS > CO_TARGET_BS ? ">" : EXPRESSION_BS < CO_TARGET_BS ? "<" : "=" ) , CO_TARGET_BS ); \
      if( EXPRESSION_BS DESIRED_INEQUALITY CO_TARGET_BS ){		\
	CERR( "二分探索成功：" , #ANSWER , ":=" , ANSWER );		\
      } else {								\
	CERR( "二分探索失敗：" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \
	CERR( "単調でないか、単調増加性と単調減少性を逆にしてしまったか、探索範囲内に解が存在しません。" ); \
	ANSWER = MAXIMUM + 1;						\
      }									\
    }									\
  }									\

// 単調増加の時にEXPRESSION >= CO_TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , >= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 )
// 単調増加の時にEXPRESSION <= CO_TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , > , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 )
// 単調減少の時にEXPRESSION >= CO_TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , < , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 )
// 単調減少の時にEXPRESSION <= CO_TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , <= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 )
// t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。
TE <TY T> IN TY set<T>::iterator MaximumLeq( set<T>& S , CO T& t ) { CO auto EN = S.EN(); if( S.empty() ){ RE EN; } auto itr = S.upper_bound( t ); RE itr == EN ? S.find( *( S.rBE() ) ) : itr == S.BE() ? EN : --itr; }
// t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。
TE <TY T> IN TY set<T>::iterator MaximumLt( set<T>& S , CO T& t ) { CO auto EN = S.EN(); if( S.empty() ){ RE EN; } auto itr = S.lower_bound( t ); RE itr == EN ? S.find( *( S.rBE() ) ) : itr == S.BE() ? EN : --itr; }
// t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。
TE <TY T> IN TY set<T>::iterator MinimumGeq( set<T>& S , CO T& t ) { RE S.lower_bound( t ); }
// tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。
TE <TY T> IN TY set<T>::iterator MinimumGt( set<T>& S , CO T& t ) { RE S.upper_bound( t ); }

// 尺取り法用
// VAR_TPAがINITからUPDATEを繰り返しCONTINUE_CONDITIONを満たす限り、ON_CONDITIONを判定して
// trueならON、falseならOFFとなる。直近のONの区間を[VAR_TPA_L,VAR_TPA_R)で管理する。
#define TPA( VAR_TPA , INIT , UPDATE , CONTINUE_CONDITION , ON_CONDITION , ONON , ONOFF , OFFON , OFFOFF , FINISH ) \
  {									\
    auto VAR_TPA = INIT;						\
    auto VAR_TPA ## _L = VAR_TPA;					\
    auto VAR_TPA ## _R = VAR_TPA;					\
    bool on_TPA = false;						\
    int state_TPA = 3;							\
    WH( CONTINUE_CONDITION ){						\
      bool on_TPA_next = ON_CONDITION;					\
      state_TPA = ( ( on_TPA ? 1 : 0 ) << 1 ) | ( on_TPA_next ? 1 : 0 ); \
      CERR( "尺取り中： [L,R) = [" , VAR_TPA ## _L , "," , VAR_TPA ## _R , ") ," , #VAR_TPA , "=" , VAR_TPA , "," , ( ( state_TPA >> 1 ) & 1 ) == 1 ? "on" : "off" , " ->" , ( state_TPA & 1 ) == 1 ? "on" : "off" ); \
      if( state_TPA == 0 ){						\
	OFFOFF; VAR_TPA ## _L = VAR_TPA ## _R = VAR_TPA; UPDATE;	\
      } else if( state_TPA == 1 ){					\
	OFFON; VAR_TPA ## _L = VAR_TPA; UPDATE; VAR_TPA ## _R = VAR_TPA; \
      } else if( state_TPA == 2 ){					\
	ONOFF; VAR_TPA ## _L = VAR_TPA ## _R = VAR_TPA; UPDATE;		\
      } else {								\
	ONON; UPDATE; VAR_TPA ## _R = VAR_TPA;				\
      }									\
      on_TPA = on_TPA_next;						\
    }									\
    CERR( "尺取り終了： [L,R) = [" , VAR_TPA ## _L , "," , VAR_TPA ## _R , ") ," , #VAR_TPA , "=" , VAR_TPA ); \
    FINISH;								\
  }									\

// データ構造用
// TE <TY T , TE <TY...> TY V> IN V<T> OP+( CO V<T>& a0 , CO V<T>& a1 ) { if( a0.empty() ){ RE a1; } if( a1.empty() ){ RE a0; } AS( a0.SZ() == a1.SZ() ); V<T> answer{}; for( auto itr0 = a0.BE() , itr1 = a1.BE() , EN0 = a0.EN(); itr0 != EN0 ; itr0++ , itr1++ ){ answer.push_back( *itr0 + *itr1 ); } RE answer; }
TE <TY T , TY U> IN pair<T,U> OP+( CO pair<T,U>& t0 , CO pair<T,U>& t1 ) { RE { t0.first + t1.first , t0.second + t1.second }; }
TE <TY T , TY U , TY V> IN tuple<T,U,V> OP+( CO tuple<T,U,V>& t0 , CO tuple<T,U,V>& t1 ) { RE { get<0>( t0 ) + get<0>( t1 ) , get<1>( t0 ) + get<1>( t1 ) , get<2>( t0 ) + get<2>( t1 ) }; }
TE <TY T , TY U , TY V , TY W> IN tuple<T,U,V,W> OP+( CO tuple<T,U,V,W>& t0 , CO tuple<T,U,V,W>& t1 ) { RE { get<0>( t0 ) + get<0>( t1 ) , get<1>( t0 ) + get<1>( t1 ) , get<2>( t0 ) + get<2>( t1 ) , get<3>( t0 ) + get<3>( t1 ) }; }
TE <TY T> IN T Add( CO T& t0 , CO T& t1 ) { RE t0 + t1; }
TE <TY T> IN T XorAdd( CO T& t0 , CO T& t1 ){ RE t0 ^ t1; }
TE <TY T> IN T Multiply( CO T& t0 , CO T& t1 ) { RE t0 * t1; }
TE <TY T> IN CO T& Zero() { ST CO T z{}; RE z; }
TE <TY T> IN CO T& One() { ST CO T o = 1; RE o; }\
TE <TY T> IN T AddInv( CO T& t ) { RE -t; }
TE <TY T> IN T Id( CO T& v ) { RE v; }
TE <TY T> IN T Min( CO T& a , CO T& b ){ RE a < b ? a : b; }
TE <TY T> IN T Max( CO T& a , CO T& b ){ RE a < b ? b : a; }
TE <TY T , TE <TY...> TY V> IN auto Get( CO V<T>& a ) { return [&]( CRI i = 0 ){ RE a[i]; }; }

// グリッド問題用
int H , W , H_minus , W_minus , HW;
VE<VE<bool>> non_wall;
IN T2<int> EnumHW( CRI v ) { RE { v / W , v % W }; }
IN int EnumHW_inv( CO T2<int>& ij ) { auto& [i,j] = ij; RE i * W + j; }
CO string direction[4] = {"U","R","D","L"};
// (i,j)->(k,h)の方向番号を取得
IN int DirectionNumberOnGrid( CRI i , CRI j , CRI k , CRI h ){RE i<k?2:i>k?0:j<h?1:j>h?3:(AS(false),-1);}
// v->wの方向番号を取得
IN int DirectionNumberOnGrid( CRI v , CRI w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);RE DirectionNumberOnGrid(i,j,k,h);}
// 方向番号の反転U<->D、R<->L
IN int ReverseDirectionNumberOnGrid( CRI n ){AS(0<=n&&n<4);RE(n+2)%4;}
IN VO SetEdgeOnGrid( CO string& Si , CRI i , VE<LI<int>>& e , CO char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv({i,j});if(i>0){e[EnumHW_inv({i-1,j})].push_back(v);}if(i+1<H){e[EnumHW_inv({i+1,j})].push_back(v);}if(j>0){e[EnumHW_inv({i,j-1})].push_back(v);}if(j+1<W){e[EnumHW_inv({i,j+1})].push_back(v);}}}}
IN VO SetEdgeOnGrid( CO string& Si , CRI i , VE<LI<path>>& e , CO char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){CO int v=EnumHW_inv({i,j});if(i>0){e[EnumHW_inv({i-1,j})].push_back({v,1});}if(i+1<H){e[EnumHW_inv({i+1,j})].push_back({v,1});}if(j>0){e[EnumHW_inv({i,j-1})].push_back({v,1});}if(j+1<W){e[EnumHW_inv({i,j+1})].push_back({v,1});}}}}
IN VO SetWallOnGrid( CO string& Si , CRI i , VE<VE<bool>>& non_wall , CO char& walkable = '.'  , CO char& unwalkable = '#' ){non_wall.push_back(VE<bool>(W));auto& non_wall_i=non_wall[i];FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]==unwalkable),false);}}

// デバッグ用
#ifdef DEBUG
  IN VO 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。" ); }
  VO AutoCheck( int& exec_mode , CO bool& use_getline );
  IN VO Solve();
  IN VO Experiment();
  IN VO SmallTest();
  IN VO RandomTest();
  ll GetRand( CRL Rand_min , CRL Rand_max );
  IN VO BreakPoint( CRI LINE ) {}
  int exec_mode;
  CEXPR( int , solve_mode , 0 );
  CEXPR( int , sample_debug_mode , 1 );
  CEXPR( int , submission_debug_mode , 2 );
  CEXPR( int , library_search_mode , 3 );
  CEXPR( int , experiment_mode , 4 );
  CEXPR( int , small_test_mode , 5 );
  CEXPR( int , random_test_mode , 6 );
  #ifdef USE_GETLINE
    CEXPR( bool , use_getline , true );
  #else
    CEXPR( bool , use_getline , false );
  #endif
#else
  ll GetRand( CRL Rand_min , CRL Rand_max ) { ll answer = time( NULL ); RE answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; }
#endif

// VVV 常設ライブラリは以下に挿入する。

// AAA 常設ライブラリは以上に挿入する。

#define INCLUDE_LIBRARY
#include __FILE__

#endif // INCLUDE_LIBRARY

#endif // INCLUDE_SUB

#endif // INCLUDE_MAIN
yukicoder

結果

ソースコード
