#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 << "出力： " << 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 ) )
  #define AUTO_CHECK bool auto_checked = true; AutoCheck( auto_checked ); if( auto_checked ){ return 0; };
#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 ) )
  #define AUTO_CHECK
#endif
// #define RANDOM_TEST
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define TYPE_OF( VAR ) decay_t<decltype( VAR )>
#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 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 AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end()
#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( IS_FIXED , DECIMAL_DIGITS ) if constexpr( IS_FIXED ){ cout << fixed; } cout << setprecision( DECIMAL_DIGITS )
#define QUIT goto END_MAIN
#define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = 1; if constexpr( bound_T > 1 ){ SET_ASSERT( T , 1 , bound_T ); }
#define START_MAIN REPEAT( T ){ if constexpr( bound_T > 1 ){ CERR( "testcase " << VARIABLE_FOR_REPEAT_T << ":" ); }
#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 FINISH_MAIN QUIT; } END_MAIN: CERR( "" );

#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。" ); }
  void AutoCheck( bool& auto_checked );
#endif
#if defined( DEBUG ) && defined( RANDOM_TEST )
  ll GetRand( const ll& Rand_min , const ll& Rand_max );
  #define SET_ASSERT( A , MIN , MAX ) CERR( #A << " = " << ( A = GetRand( MIN , MAX ) ) )
  #define RETURN( ANSWER ) if( ( ANSWER ) == guchoku ){ CERR( ( ANSWER ) << " == " << guchoku ); goto END_MAIN; } else { CERR( ( ANSWER ) << " != " << guchoku ); QUIT; }
#else
  #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX )
  #define RETURN( ANSWER ) COUT( ( ANSWER ) ); QUIT
#endif

// 算術的関数
template <typename T> inline T Absolute( const T& a ){ return a > 0 ? a : -a; }
template <typename T> inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }
inline ll MIN( const ll& a , const ll& b ){ return min( a , b ); }
inline ull MIN( const ull& a , const ull& b ){ return min( a , b ); }
inline ll MAX( const ll& a , const ll& b ){ return max( a , b ); }
inline ull MAX( const ull& a , const ull& b ){ return max( a , b ); }

#define POWER( ANSWER , ARGUMENT , EXPONENT )				\
  static_assert( ! is_same<TYPE_OF( ARGUMENT ),int>::value && ! is_same<TYPE_OF( ARGUMENT ),uint>::value ); \
  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 )		\
  ll ANSWER{ 1 };							\
  {									\
    ll 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 , INVERSE , MAX_INDEX , CONSTEXPR_LENGTH , MODULO ) \
  static ll ANSWER[CONSTEXPR_LENGTH];					\
  static ll ANSWER_INV[CONSTEXPR_LENGTH];				\
  static ll INVERSE[CONSTEXPR_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 ); \
    }									\
  }									\

// 二分探索テンプレート
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
  static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \
  ll ANSWER = MINIMUM;							\
  if( MINIMUM <= MAXIMUM ){						\
    ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM;				\
    ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM;				\
    ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
    ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH;			\
    while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \
      VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \
      CERR( "二分探索中： " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << "=" << VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ); \
      if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH INEQUALITY_FOR_CHECK 0 ){	\
	VARIABLE_FOR_BINARY_SEARCH_U = UPDATE_U;			\
      } else {								\
	VARIABLE_FOR_BINARY_SEARCH_L = UPDATE_L;			\
      }									\
      ANSWER = UPDATE_ANSWER;						\
    }									\
    CERR( "二分探索終了： " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << ( EXPRESSION > TARGET ? ">" : EXPRESSION < TARGET ? "<" : "=" ) << TARGET ); \
    CERR( ( EXPRESSION DESIRED_INEQUALITY TARGET ? "二分探索成功" : "二分探索失敗" ) ); \
    assert( EXPRESSION DESIRED_INEQUALITY TARGET );			\
  } else {								\
    CERR( "二分探索失敗： " << MINIMUM << ">" << MAXIMUM );		\
    assert( MINIMUM <= MAXIMUM );					\
  }									\

// 単調増加の時にEXPRESSION >= TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , >= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調増加の時にEXPRESSION <= TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , > , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調減少の時にEXPRESSION >= TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , < , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調減少の時にEXPRESSION <= TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , <= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 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。
template <typename T> inline typename set<T>::iterator MaximumLeq( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.upper_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --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。
template <typename T> inline typename set<T>::iterator MaximumLt( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.lower_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --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。
template <typename T> inline typename set<T>::iterator MinimumGeq( set<T>& S , const T& t ) { return 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。
template <typename T> inline typename set<T>::iterator MinimumGt( set<T>& S , const T& t ) { return S.upper_bound( t ); }

// データ構造用関数
template <typename T> inline T add( const T& t0 , const T& t1 ) { return t0 + t1; }
template <typename T> inline T xor_add( const T& t0 , const T& t1 ){ return t0 ^ t1; }
template <typename T> inline T multiply( const T& t0 , const T& t1 ) { return t0 * t1; }
template <typename T> inline const T& zero() { static const T z = 0; return z; }
template <typename T> inline const T& one() { static const T o = 1; return o; }\
template <typename T> inline T add_inv( const T& t ) { return -t; }
template <typename T> inline T id( const T& v ) { return v; }

// グリッド問題用関数
int H , W , H_minus , W_minus , HW;
inline pair<int,int> EnumHW( const int& v ) { return { v / W , v % W }; }
inline int EnumHW_inv( const int& h , const int& w ) { return h * W + w; }
const string direction[4] = {"U","R","D","L"};
// (i,j)->(k,h)の方向番号を取得
inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return i<k?2:i>k?0:j<h?1:j>h?3:(assert(false),-1);}
// v->wの方向番号を取得
inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);return DirectionNumberOnGrid(i,j,k,h);}
// 方向番号の反転U<->D、R<->L
inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;}

// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#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 MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&

// 大きな素数
// inline CEXPR( ll , P , 998244353 );
// // inline CEXPR( ll , P2 , 1000000007 );

// データ構造使用畤のNの上限
// inline CEXPR( int , bound_N , 10 );
inline DEXPR( int , bound_N , 100000 , 100 ); // 0が5個
// inline CEXPR( int , bound_N , 1000000000 ); // 0が9個
// inline CEXPR( ll , bound_N , 1000000000000000000 ); // 0が18個

// データ構造使用畤のMの上限
// inline CEXPR( TYPE_OF( bound_N ) , bound_M , bound_N );
// inline CEXPR( int , bound_M , 10 );
inline DEXPR( int , bound_M , 100000 , 100 ); // 0が5個
// inline CEXPR( int , bound_M , 1000000000 ); // 0が9個
// inline CEXPR( ll , bound_M , 1000000000000000000 ); // 0が18個

// データ構造や壁配列使用畤のH,Wの上限
inline DEXPR( int , bound_H , 1000 , 10 );
// inline DEXPR( int , bound_H , 100000 , 10 ); // 0が5個
// inline CEXPR( int , bound_H , 1000000000 ); // 0が9個
inline CEXPR( int , bound_W , bound_H );
static_assert( ll( bound_H ) * bound_W < ll( 1 ) << 31 );
inline CEXPR( int , bound_HW , bound_H * bound_W );
// CEXPR( int , bound_HW , 100000 ); // 0が5個
// CEXPR( int , bound_HW , 1000000 ); // 0が6個
inline void SetEdgeOnGrid( const string& Si , const int& i , list<int> ( &e )[bound_HW] , const 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);}}}}
inline void SetWallOnGrid( const string& Si , const int& i , bool ( &non_wall )[bound_H+1][bound_W+1] , const char& walkable = '.' ){bool(&non_wall_i)[bound_W+1]=non_wall[i];FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]=='#'),false);}}

// using path_type = int;
// // using path_type = pair<int,ll>;
// list<path_type> e[bound_M]; // bound_Mのデフォルト値は10^5
// // list<path_type> e[bound_HW]; // bound_HWのデフォルト値は10^6
// list<path_type> E( const int& i )
// {
//   list<path_type> answer = e[i];
//   // 入力によらない処理
//   return answer;
// }


template <typename UINT , int digit> class Extended_ull;

template <typename UINT , int digit>
class ConstantsForExtended_ull
{

  friend class Extended_ull<UINT,digit>;
  
private:
  ConstantsForExtended_ull() = delete;
  static constexpr const int g_digit_half = digit >> 1;
  static constexpr const int g_full_digit = digit << 1;
  static constexpr const int g_full_digit_minus = g_full_digit - 1;
  static constexpr const UINT g_low_bit = ( UINT( 1 ) << g_digit_half ) - 1;

};

#define SFINAE_FOR_EXTENDED_ULL( DEFAULT )				\
  typename T , enable_if_t<is_constructible<UINT,decay_t<T> >::value>* DEFAULT \

template <typename UINT , int digit>
class Extended_ull
{

private:
  UINT m_n[2];

public:
  inline constexpr Extended_ull() noexcept;
  template <SFINAE_FOR_EXTENDED_ULL( = nullptr )> inline constexpr Extended_ull( T n0 ) noexcept;
  template <SFINAE_FOR_EXTENDED_ULL( = nullptr )> inline constexpr Extended_ull( T n0 , T n1 ) noexcept;
  inline constexpr Extended_ull( const UINT ( &n )[2] ) noexcept;
  inline constexpr Extended_ull( UINT ( &&n )[2] ) noexcept;
  inline constexpr Extended_ull( const Extended_ull<UINT,digit>& n ) noexcept;
  inline constexpr Extended_ull( Extended_ull<UINT,digit>&& n ) noexcept;

  inline constexpr Extended_ull<UINT,digit>& operator=( const Extended_ull<UINT,digit>& n ) noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator=( Extended_ull<UINT,digit>&& n ) noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator+=( const Extended_ull<UINT,digit>& n ) noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator-=( const Extended_ull<UINT,digit>& n ) noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator*=( const Extended_ull<UINT,digit>& n ) noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator/=( const Extended_ull<UINT,digit>& n );
  inline constexpr Extended_ull<UINT,digit>& operator%=( const Extended_ull<UINT,digit>& n );
  inline constexpr Extended_ull<UINT,digit>& operator&=( const Extended_ull<UINT,digit>& n ) noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator|=( const Extended_ull<UINT,digit>& n ) noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator<<=( const int& n ) noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator>>=( const int& n ) noexcept;

  inline constexpr Extended_ull<UINT,digit>& operator++() noexcept;
  inline constexpr Extended_ull<UINT,digit>& operator--() noexcept;
  inline constexpr Extended_ull<UINT,digit> operator++( int ) noexcept;
  inline constexpr Extended_ull<UINT,digit> operator--( int ) noexcept;

  inline constexpr Extended_ull<UINT,digit> operator+( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr Extended_ull<UINT,digit> operator-() const noexcept;
  inline constexpr Extended_ull<UINT,digit> operator-( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr Extended_ull<UINT,digit> operator*( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr Extended_ull<UINT,digit> operator/( const Extended_ull<UINT,digit>& n ) const;
  inline constexpr Extended_ull<UINT,digit> operator%( const Extended_ull<UINT,digit>& n ) const;
  inline constexpr Extended_ull<UINT,digit> operator~() const noexcept;
  inline constexpr Extended_ull<UINT,digit> operator&( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr Extended_ull<UINT,digit> operator|( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr Extended_ull<UINT,digit> operator<<( const int& n ) const noexcept;
  inline constexpr Extended_ull<UINT,digit> operator>>( const int& n ) const noexcept;

  inline constexpr bool operator==( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator!=( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator<=( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator>=( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator<( const Extended_ull<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator>( const Extended_ull<UINT,digit>& n ) const noexcept;

  inline constexpr const UINT& GetLowerDigit() const noexcept;
  inline constexpr const UINT& GetUpperDigit() const noexcept;

  inline constexpr Extended_ull<UINT,digit> Quotient( const Extended_ull<UINT,digit>& n );
  inline constexpr UINT Sqrt() const noexcept;

  static inline constexpr Extended_ull<UINT,digit> Sum( const UINT& n0 , const UINT& n1 ) noexcept;
  static inline constexpr Extended_ull<UINT,digit> Prod( const UINT& n0 , const UINT& n1 ) noexcept;
  static inline constexpr void swap( Extended_ull<UINT,digit>& n0 , Extended_ull<UINT,digit>& n1 ) noexcept;

  using base = UINT;

};

template <typename UINT , int digit> inline constexpr void swap( Extended_ull<UINT,digit>& n0 , Extended_ull<UINT,digit>& n1 ) noexcept;

template <typename ULL> inline ULL stoeull( string s );
template <typename UINT , int digit , class Traits> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , Extended_ull<UINT,digit>& n );

template <typename UINT , int digit> inline string to_string( Extended_ull<UINT,digit> n );
template <typename UINT , int digit , class Traits> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const Extended_ull<UINT,digit>& n );


template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>::Extended_ull() noexcept : m_n() {}
template <typename UINT , int digit> template <SFINAE_FOR_EXTENDED_ULL()> inline constexpr Extended_ull<UINT,digit>::Extended_ull( T n0 ) noexcept : m_n{ UINT( n0 ) , UINT( 0 ) } {}
template <typename UINT , int digit> template <SFINAE_FOR_EXTENDED_ULL()> inline constexpr Extended_ull<UINT,digit>::Extended_ull( T n0 , T n1 ) noexcept : m_n{ UINT( n0 ) , UINT( n1 ) } {}
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>::Extended_ull( const UINT ( &n )[2] ) noexcept : m_n{ n[0] , n[1] } {}
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>::Extended_ull( UINT ( &&n )[2] ) noexcept : m_n{ move( n[0] ) , move( n[1] ) } {}
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>::Extended_ull( const Extended_ull<UINT,digit>& n ) noexcept : m_n{ n.m_n[0] , n.m_n[1] } {}
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>::Extended_ull( Extended_ull<UINT,digit>&& n ) noexcept : m_n{ move( n.m_n[0] ) , move( n.m_n[1] ) } {}

template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator=( const Extended_ull<UINT,digit>& n ) noexcept { m_n[0] = n.m_n[0]; m_n[1] = n.m_n[1]; return *this; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator=( Extended_ull<UINT,digit>&& n ) noexcept { m_n[0] = move( n.m_n[0] ); m_n[1] = move( n.m_n[1] ); return *this; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator+=( const Extended_ull<UINT,digit>& n ) noexcept { return operator=( operator+( n ) ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator-=( const Extended_ull<UINT,digit>& n ) noexcept { return operator=( operator-( n ) ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator*=( const Extended_ull<UINT,digit>& n ) noexcept { return operator=( operator*( n ) ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator/=( const Extended_ull<UINT,digit>& n ) { return *this = Quotient( n ); }

template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator%=( const Extended_ull<UINT,digit>& n )
{

  assert( n != 0 );
  constexpr const Extended_ull<UINT,digit> full_power = Extended_ull<UINT,digit>( 1 ) << ConstantsForExtended_ull<UINT,digit>::g_full_digit_minus;
  Extended_ull<UINT,digit> power = full_power;
  
  for( int d = ConstantsForExtended_ull<UINT,digit>::g_full_digit_minus ; d >= 0 ; d-- ){

    if( ( *this >> d ) >= n ){

      *this -= ( n << d );

    }

    power >>= 1;

  }
  
  return *this;

}

template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator&=( const Extended_ull<UINT,digit>& n ) noexcept { m_n[0] &= n.m_n[0]; m_n[1] &= n.m_n[1]; return *this; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator|=( const Extended_ull<UINT,digit>& n ) noexcept { m_n[0] |= n.m_n[0]; m_n[1] |= n.m_n[1]; return *this; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator<<=( const int& n ) noexcept
{ n == 0 ? m_n[1] : n < digit ? ( ( m_n[1] <<= n ) |= ( m_n[0] >> ( digit - n ) ) , m_n[0] <<= n ) : n < ConstantsForExtended_ull<UINT,digit>::g_full_digit ? ( m_n[1] = ( m_n[0] << ( n - digit ) ) , m_n[0] = 0 ) : ( m_n[1] = m_n[0] = 0 ); return *this; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator>>=( const int& n ) noexcept { n == 0 ? m_n[0] : n < digit ? ( ( m_n[0] >>= n ) |= ( m_n[1] << ( digit - n ) ) , m_n[1] >>= n ) : n < ConstantsForExtended_ull<UINT,digit>::g_full_digit ? ( m_n[0] = ( m_n[1] >> ( n - digit ) ) , m_n[1] = 0 ) : ( m_n[0] = m_n[1] = 0 ); return *this; }


template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator++() noexcept { if( ++m_n[0] == 0 ){ ++m_n[1]; } return *this; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit>& Extended_ull<UINT,digit>::operator--() noexcept { if( m_n[0]-- == 0 ){ m_n[1]--; } return *this; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator++( int ) noexcept { const Extended_ull<UINT,digit> answer = *this; if( ++m_n[0] == 0 ){ ++m_n[1]; } return answer; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator--( int ) noexcept { const Extended_ull<UINT,digit> answer = *this; if( m_n[0]-- == 0 ){ m_n[1]--; } return answer; }


template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator+( const Extended_ull<UINT,digit>& n ) const noexcept { Extended_ull<UINT,digit> answer = Sum( m_n[0] , n.m_n[0] ); answer.m_n[1] += m_n[1] + n.m_n[1]; return answer; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator-() const noexcept { return ++( operator~() ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator-( const Extended_ull<UINT,digit>& n ) const noexcept { return operator+( -n ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator*( const Extended_ull<UINT,digit>& n ) const noexcept { Extended_ull<UINT,digit> answer = Prod( m_n[0] , n.m_n[0] ); answer.m_n[1] += m_n[1] * n.m_n[0] + m_n[0] * n.m_n[1]; return answer; }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator/( const Extended_ull<UINT,digit>& n ) const { return move( Extended_ull<UINT,digit>( *this ) /= n ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator%( const Extended_ull<UINT,digit>& n ) const { return move( Extended_ull<UINT,digit>( *this ) %= n ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator~() const noexcept { return Extended_ull<UINT,digit>( ~m_n[0] , ~m_n[1] ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator&( const Extended_ull<UINT,digit>& n ) const noexcept { Extended_ull<UINT,digit> answer = *this; return move( answer &= n ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator|( const Extended_ull<UINT,digit>& n ) const noexcept { Extended_ull<UINT,digit> answer = *this; return move( answer |= n ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator<<( const int& n ) const noexcept { Extended_ull<UINT,digit> answer = *this; return move( answer <<= n ); }
template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::operator>>( const int& n ) const noexcept { Extended_ull<UINT,digit> answer = *this; return move( answer >>= n ); }


template <typename UINT , int digit> inline constexpr bool Extended_ull<UINT,digit>::operator==( const Extended_ull<UINT,digit>& n ) const noexcept { return m_n[0] == n.m_n[0] && m_n[1] == n.m_n[1]; }
template <typename UINT , int digit> inline constexpr bool Extended_ull<UINT,digit>::operator!=( const Extended_ull<UINT,digit>& n ) const noexcept { return !( *this == n ); }
template <typename UINT , int digit> inline constexpr bool Extended_ull<UINT,digit>::operator<=( const Extended_ull<UINT,digit>& n ) const noexcept { return !( n < *this ); }
template <typename UINT , int digit> inline constexpr bool Extended_ull<UINT,digit>::operator>=( const Extended_ull<UINT,digit>& n ) const noexcept { return !( *this < n ); }
template <typename UINT , int digit> inline constexpr bool Extended_ull<UINT,digit>::operator<( const Extended_ull<UINT,digit>& n ) const noexcept { return m_n[1] < n.m_n[1] || ( m_n[1] == n.m_n[1] && m_n[0] < n.m_n[0] ); }
template <typename UINT , int digit> inline constexpr bool Extended_ull<UINT,digit>::operator>( const Extended_ull<UINT,digit>& n ) const noexcept { return n < *this; }

template <typename UINT , int digit> inline constexpr const UINT& Extended_ull<UINT,digit>::GetLowerDigit() const noexcept { return m_n[0]; }
template <typename UINT , int digit> inline constexpr const UINT& Extended_ull<UINT,digit>::GetUpperDigit() const noexcept { return m_n[1]; }

template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::Quotient( const Extended_ull<UINT,digit>& n )
{

  assert( n != 0 );
  constexpr const Extended_ull<UINT,digit> full_power = Extended_ull<UINT,digit>( 1 ) << ConstantsForExtended_ull<UINT,digit>::g_full_digit_minus;
  Extended_ull<UINT,digit> answer{};
  Extended_ull<UINT,digit> power = full_power;
  
  for( int d = ConstantsForExtended_ull<UINT,digit>::g_full_digit_minus ; d >= 0 ; d-- ){

    if( ( *this >> d ) >= n ){

      *this -= ( n << d );
      answer |= power;

    }

    power >>= 1;

  }
  
  return answer;

}

template <typename UINT , int digit> inline constexpr UINT Extended_ull<UINT,digit>::Sqrt() const noexcept {

  constexpr const UINT UINT_max = ~( UINT( 0 ) ); 
  constexpr const Extended_ull<UINT,digit> threshold{ 1 , UINT_max - 1 };
  
  if( threshold <= *this ){

    return UINT_max;

  }
  
  UINT l = 0;
  UINT r = UINT_max;

  while( l + 1 < r ){

    UINT m = ( ( l + r ) >> 1 );
    ( Extended_ull<UINT,digit>::Prod( m , m ) <= *this ? l : r ) = move( m );

  }
  
  return l;

}


template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::Sum( const UINT& n0 , const UINT& n1 ) noexcept
{

  UINT temp[2] = {
    ( n0 & ConstantsForExtended_ull<UINT,digit>::g_low_bit ) + ( n1 & ConstantsForExtended_ull<UINT,digit>::g_low_bit ) ,
    ( n0 >> ConstantsForExtended_ull<UINT,digit>::g_digit_half ) + ( n1 >> ConstantsForExtended_ull<UINT,digit>::g_digit_half )
  };
  temp[1] += ( temp[0] >> ConstantsForExtended_ull<UINT,digit>::g_digit_half );
  ( temp[0] &= ConstantsForExtended_ull<UINT,digit>::g_low_bit ) |= ( temp[1] << ConstantsForExtended_ull<UINT,digit>::g_digit_half );
  temp[1] >>= ConstantsForExtended_ull<UINT,digit>::g_digit_half;
  return Extended_ull<UINT,digit>( move( temp ) );

}

template <typename UINT , int digit> inline constexpr Extended_ull<UINT,digit> Extended_ull<UINT,digit>::Prod( const UINT& n0 , const UINT& n1 ) noexcept
{

  const UINT n0_copy[2] = { n0 & ConstantsForExtended_ull<UINT,digit>::g_low_bit , n0 >> ConstantsForExtended_ull<UINT,digit>::g_digit_half };
  const UINT n1_copy[2] = { n1 & ConstantsForExtended_ull<UINT,digit>::g_low_bit , n1 >> ConstantsForExtended_ull<UINT,digit>::g_digit_half };
  UINT temp0[2] = {
    n0_copy[0] * n1_copy[0] ,
    n0_copy[1] * n1_copy[1]
  };
  UINT temp1[2] = {
    n0_copy[0] * n1_copy[1] ,
    n0_copy[1] * n1_copy[0] ,
  };
  temp0[1] += ( temp1[0] >> ConstantsForExtended_ull<UINT,digit>::g_digit_half ) + ( temp1[1] >> ConstantsForExtended_ull<UINT,digit>::g_digit_half );
  ( temp1[1] &= ConstantsForExtended_ull<UINT,digit>::g_low_bit ) += ( temp1[0] &= ConstantsForExtended_ull<UINT,digit>::g_low_bit ) + ( temp0[0] >> ConstantsForExtended_ull<UINT,digit>::g_digit_half );
  temp0[1] += temp1[1] >> ConstantsForExtended_ull<UINT,digit>::g_digit_half;
  ( temp0[0] &= ConstantsForExtended_ull<UINT,digit>::g_low_bit ) |= ( temp1[1] << ConstantsForExtended_ull<UINT,digit>::g_digit_half );
  return Extended_ull<UINT,digit>( move( temp0 ) );

}

template <typename UINT , int digit> inline constexpr void Extended_ull<UINT,digit>::swap( Extended_ull<UINT,digit>& n0 , Extended_ull<UINT,digit>& n1 ) noexcept { swap( n0.m_n , n1.m_n ); }

template <typename UINT , int digit> inline constexpr void swap( Extended_ull<UINT,digit>& n0 , Extended_ull<UINT,digit>& n1 ) noexcept { Extended_ull<UINT,digit>::swap( n0 , n1 ); }


template <typename ULL> inline ULL stoeull( string s )
{

  if constexpr ( is_same<ULL,ull>::value ){

      return stoull( s );

    } else {

    using UINT = typename ULL::base;
    static vector<UINT> ten_power = { 1 };
    static int length = 1;
    const int size = s.size();
    const int size_half0 = size / 2;
    const int size_half1 = size - size_half0;

    while( size_half0 >= length ){

      ten_power.push_back( ten_power.back() * 10 );
      length++;

    }
    
    return size_half0 > 0 ? ULL::Prod( stoeull<UINT>( s.substr( 0 , size_half1 ) ) , ten_power[size_half0] ) + stoeull<UINT>( s.substr( size_half1 ) ) : ULL( stoeull<UINT>( move( s ) ) );

  }

}

template <typename UINT , int digit , class Traits> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , Extended_ull<UINT,digit>& n )
{

  string temp;
  is >> temp;
  n = stoeull<Extended_ull<UINT,digit> >( move( temp ) );
  return is;

}

template <typename UINT , int digit> inline string to_string( Extended_ull<UINT,digit> n )
{

  list<char> temp{};
  static const Extended_ull<UINT,digit> zero{ 0 };
  static const Extended_ull<UINT,digit> ten{ 10 };

  while( n != zero ){

    Extended_ull<UINT,digit> n_div = n / ten;
    Extended_ull<UINT,digit> n_res = n - ( n_div * ten );
    temp.push_front( to_string( n_res.GetLowerDigit() )[0] );
    n = move( n_div );

  }

  if( temp.empty() ){

    temp.push_back( '0' );

  }

  string answer = "";

  for( auto itr = temp.begin() , end = temp.end() ; itr != end ; itr++ ){

    answer += *itr;

  }

  return answer;

}

template <typename UINT , int digit , class Traits> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const Extended_ull<UINT,digit>& n ) { return os << to_string( n ); }




template <typename UINT , int digit> class Extended_udouble;
template <typename UINT , int digit> inline string to_string( Extended_udouble<UINT,digit> n );

template <typename UINT , int digit>
class ConstantsForExtended_udouble
{

  friend class Extended_udouble<UINT,digit>;
  friend string to_string<>( Extended_udouble<UINT,digit> n );

private:
  static constexpr UINT g_full_bit = UINT( 1 ) << ( digit - 1 );
  static constexpr UINT g_ten_power = UINT( 1000000000000000000 );
  static constexpr int g_ten_exponent = 18;

};

template <typename UINT , int digit>
class Extended_udouble
{

private:
  UINT m_n;
  // 2羃の指数
  int m_exponent;

public:
  inline constexpr Extended_udouble( const UINT& n = 0 , const int& exponent = 0 ) noexcept;
  inline constexpr Extended_udouble( const Extended_udouble<UINT,digit>& n ) noexcept;
  inline constexpr Extended_udouble( Extended_udouble<UINT,digit>&& n ) noexcept;
  inline constexpr Extended_udouble( Extended_ull<UINT,digit> n , const int exponent = 0 ) noexcept;

  inline constexpr Extended_udouble<UINT,digit>& operator=( const Extended_udouble<UINT,digit>& n ) noexcept;
  inline constexpr Extended_udouble<UINT,digit>& operator=( Extended_udouble<UINT,digit>&& n ) noexcept;
  inline constexpr Extended_udouble<UINT,digit>& operator+=( const Extended_udouble<UINT,digit>& n ) noexcept;
  inline constexpr Extended_udouble<UINT,digit>& operator*=( const Extended_udouble<UINT,digit>& n ) noexcept;
  inline constexpr Extended_udouble<UINT,digit>& operator/=( const Extended_udouble<UINT,digit>& n );
  inline constexpr Extended_udouble<UINT,digit>& operator<<=( const int& n ) noexcept;
  inline constexpr Extended_udouble<UINT,digit>& operator>>=( const int& n ) noexcept;

  inline constexpr Extended_udouble<UINT,digit> operator+( const Extended_udouble<UINT,digit>& n ) const noexcept;
  inline constexpr Extended_udouble<UINT,digit> operator*( const Extended_udouble<UINT,digit>& n ) const noexcept;
  inline constexpr Extended_udouble<UINT,digit> operator/( const Extended_udouble<UINT,digit>& n ) const;
  inline constexpr Extended_udouble<UINT,digit> operator<<( const int& n ) const noexcept;
  inline constexpr Extended_udouble<UINT,digit> operator>>( const int& n ) const noexcept;

  // 近似的等号
  inline constexpr bool operator==( const Extended_udouble<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator!=( const Extended_udouble<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator<=( const Extended_udouble<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator>=( const Extended_udouble<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator<( const Extended_udouble<UINT,digit>& n ) const noexcept;
  inline constexpr bool operator>( const Extended_udouble<UINT,digit>& n ) const noexcept;

  inline constexpr const UINT& GetDigit() const noexcept;
  inline constexpr const int& GetExponent() const noexcept;

  inline constexpr Extended_udouble<UINT,digit> Sqrt() const noexcept;

};

template <typename UINT , int digit> inline string to_string( Extended_udouble<UINT,digit> n );
template <typename UINT , int digit , class Traits> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const Extended_udouble<UINT,digit>& n );



template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>::Extended_udouble( const UINT& n , const int& exponent ) noexcept : m_n( n ) , m_exponent( exponent ) {}

template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>::Extended_udouble( const Extended_udouble<UINT,digit>& n ) noexcept : m_n( n.m_n ) , m_exponent( n.m_exponent ) {}
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>::Extended_udouble( Extended_udouble<UINT,digit>&& n ) noexcept : m_n( move( n.m_n ) ) , m_exponent( n.m_exponent ) {}
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>::Extended_udouble( Extended_ull<UINT,digit> n , const int exponent ) noexcept : m_n() , m_exponent()
{

  const UINT& n1 = n.GetUpperDigit();

  int l = 0;
  int r = digit;

  while( l + 1 < r ){

    int m = ( l + r ) / 2;
    ( ( n1 >> m ) == 0 ? r : l ) = m;

  }

  m_n = ( n >>= r ).GetLowerDigit();
  m_exponent = exponent + r;

}

template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>& Extended_udouble<UINT,digit>::operator=( const Extended_udouble<UINT,digit>& n ) noexcept { m_n = n.m_n; m_exponent = n.m_exponent; return *this; }
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>& Extended_udouble<UINT,digit>::operator=( Extended_udouble<UINT,digit>&& n ) noexcept { m_n = move( n.m_n ); m_exponent = n.m_exponent; return *this; }
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>& Extended_udouble<UINT,digit>::operator+=( const Extended_udouble<UINT,digit>& n ) noexcept { return operator=( *this + n ); }
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>& Extended_udouble<UINT,digit>::operator*=( const Extended_udouble<UINT,digit>& n ) noexcept { return operator=( *this * n ); }
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>& Extended_udouble<UINT,digit>::operator/=( const Extended_udouble<UINT,digit>& n ) { return operator=( *this / n ); }
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>& Extended_udouble<UINT,digit>::operator<<=( const int& n ) noexcept { m_exponent += n; return *this; }
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit>& Extended_udouble<UINT,digit>::operator>>=( const int& n ) noexcept { m_exponent -= n; return *this; }

template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit> Extended_udouble<UINT,digit>::operator+( const Extended_udouble<UINT,digit>& n ) const noexcept
{

  if( m_exponent < n.m_exponent ){

    return n + *this;

  }

  if( m_exponent >= n.m_exponent + digit ){

    return *this;

  }

  Extended_ull<UINT,digit> sum{ this->m_n };
  ( sum <<= ( m_exponent - n.m_exponent ) ) += Extended_ull<UINT,digit>( n.m_n );
  return Extended_udouble<UINT,digit>( sum , n.m_exponent );

}

template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit> Extended_udouble<UINT,digit>::operator*( const Extended_udouble<UINT,digit>& n ) const noexcept { return Extended_udouble<UINT,digit>( Extended_ull<UINT,digit>::Prod( m_n , n.m_n ) , m_exponent + n.m_exponent ); }

template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit> Extended_udouble<UINT,digit>::operator/( const Extended_udouble<UINT,digit>& n ) const
{

  Extended_ull<UINT,digit> div{ this->m_n };
  ( div <<= digit ) /= Extended_ull<UINT,digit>( n.m_n );
  return Extended_udouble<UINT,digit>( div , -digit );

}

template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit> Extended_udouble<UINT,digit>::operator<<( const int& n ) const noexcept { return Extended_udouble<UINT,digit>( m_n , m_exponent + n ); }
template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit> Extended_udouble<UINT,digit>::operator>>( const int& n ) const noexcept { return Extended_udouble<UINT,digit>( m_n , m_exponent - n ); }

template <typename UINT , int digit> inline constexpr bool Extended_udouble<UINT,digit>::operator==( const Extended_udouble<UINT,digit>& n ) const noexcept { return m_exponent + digit <= n.m_exponent ? false : m_exponent >= n.m_exponent + digit ? false : m_exponent < n.m_exponent ? Extended_ull<UINT,digit>( *this ) == ( Extended_ull<UINT,digit>( n ) << ( n.m_exponent - m_exponent ) ) : ( Extended_ull<UINT,digit>( *this ) << ( m_exponent - n.m_exponent ) ) == Extended_ull<UINT,digit>( n ); }
template <typename UINT , int digit> inline constexpr bool Extended_udouble<UINT,digit>::operator!=( const Extended_udouble<UINT,digit>& n ) const noexcept { return !( *this == n ); }
template <typename UINT , int digit> inline constexpr bool Extended_udouble<UINT,digit>::operator<=( const Extended_udouble<UINT,digit>& n ) const noexcept { return !( n < *this ); }
template <typename UINT , int digit> inline constexpr bool Extended_udouble<UINT,digit>::operator>=( const Extended_udouble<UINT,digit>& n ) const noexcept { return !( *this < n ); }
template <typename UINT , int digit> inline constexpr bool Extended_udouble<UINT,digit>::operator<( const Extended_udouble<UINT,digit>& n ) const noexcept { return m_exponent + digit <= n.m_exponent ? true : m_exponent >= n.m_exponent + digit ? false : m_exponent < n.m_exponent ? Extended_ull<UINT,digit>( *this ) < ( Extended_ull<UINT,digit>( n ) << ( n.m_exponent - m_exponent ) ) : ( Extended_ull<UINT,digit>( *this ) << ( m_exponent - n.m_exponent ) ) < Extended_ull<UINT,digit>( n ); }
template <typename UINT , int digit> inline constexpr bool Extended_udouble<UINT,digit>::operator>( const Extended_udouble<UINT,digit>& n ) const noexcept { return n < *this; }


template <typename UINT , int digit> inline constexpr const UINT& Extended_udouble<UINT,digit>::GetDigit() const noexcept { return m_n; }
template <typename UINT , int digit> inline constexpr const int& Extended_udouble<UINT,digit>::GetExponent() const noexcept { return m_exponent; }


template <typename UINT , int digit> inline constexpr Extended_udouble<UINT,digit> Extended_udouble<UINT,digit>::Sqrt() const noexcept
{

  Extended_ull<UINT,digit> this_copy{ this->m_n };
  int exponent = m_exponent - digit;
  return exponent % 2 == 0 ? Extended_udouble<UINT,digit>( ( this_copy <<= digit ).Sqrt() , exponent >>= 1 ) : Extended_udouble<UINT,digit>( ( this_copy <<= ( digit - 1 ) ).Sqrt() , ( ++exponent ) >>= 1 );

}

template <typename UINT , int digit> inline string to_string( Extended_udouble<UINT,digit> n )
{

  static const Extended_udouble<UINT,digit> ten_power{ ConstantsForExtended_udouble<UINT,digit>::g_ten_power };

  if( n.GetDigit() == 0 ){

    return "0";

  }
  
  const int& exponent = n.GetExponent();

  int ten_digit = 0;
  
  while( exponent < 0 ){

    n *= ten_power;
    ten_digit++;

  }

  Extended_ull<UINT,digit> n_copy{ n.GetDigit() };
  n_copy <<= exponent;

  string answer = to_string( n_copy );

  if( ten_digit > 0 ){ 

    ten_digit *= ConstantsForExtended_udouble<UINT,digit>::g_ten_exponent;
    int size = answer.size();

    if( size <= ten_digit ){
      
      string leading = "";

      for( int d = size ; d < ten_digit ; d++ ){

	leading += "0";
    
      }

      answer = "0." + leading + answer;

    } else {

      size -= ten_digit;
      answer = answer.substr( 0 , size ) + "." + answer.substr( size );
      
    }

  }

  return answer;

}

template <typename UINT , int digit , class Traits> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const Extended_udouble<UINT,digit>& n ) { return os << to_string( n ); }


using ulll = Extended_ull<ull,64>;
using ullll = Extended_ull<ulll,128>;
using ulllll = Extended_ull<ullll,256>;
using udouble = Extended_udouble<ull,64>;

int main()
{
  UNTIE;
  AUTO_CHECK;
  TEST_CASE_NUM( 1 );
  START_MAIN;

  CIN( ulllll , A );
  CIN( ulllll , B );
  RETURN( A + B );

  FINISH_MAIN;
}