#945636 (C++17) No.2354 Poor Sight in Winter

提出ソース
結果

問題	No.2354 Poor Sight in Winter
ユーザー	👑 p-adic
提出日時	2024-01-21 16:18:13
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	155 ms / 2,000 ms
コード長	62,858 bytes
コンパイル時間	3,790 ms
コンパイル使用メモリ	249,108 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-09-28 06:14:47
合計ジャッジ時間	5,247 ms
ジャッジサーバーID （参考情報）	judge4 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	1 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	2 ms 5,376 KB
testcase_11	AC	4 ms 5,376 KB
testcase_12	AC	90 ms 5,376 KB
testcase_13	AC	81 ms 5,376 KB
testcase_14	AC	155 ms 5,376 KB
testcase_15	AC	26 ms 5,376 KB
testcase_16	AC	137 ms 5,376 KB
testcase_17	AC	113 ms 5,376 KB
testcase_18	AC	20 ms 5,376 KB
testcase_19	AC	45 ms 5,376 KB
testcase_20	AC	7 ms 5,376 KB
testcase_21	AC	4 ms 5,376 KB
testcase_22	AC	25 ms 5,376 KB
testcase_23	AC	9 ms 5,376 KB
testcase_24	AC	52 ms 5,376 KB
testcase_25	AC	11 ms 5,376 KB
testcase_26	AC	11 ms 5,376 KB
testcase_27	AC	3 ms 5,376 KB
testcase_28	AC	5 ms 5,376 KB
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ソースコード

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

#ifdef INCLUDE_MAIN

inline void Solve()
{
  CIN( int , N , K );
  N += 2;
  gA<T2<int>>.resize( N );
  FOR( i , 0 , N ){
    CIN( ll , x , y );
    gA<T2<int>>[i] = { x + y , x - y };
  }
  auto k = [&]( const int& D ){
    auto edge = [&]( const int& i ){
      list<path> answer{};
      FOR( j , 0 , N ){
	int x = abs( gA<T2<int>>[i].first - gA<T2<int>>[j].first );
	int y = abs( gA<T2<int>>[i].second - gA<T2<int>>[j].second );
	if( x < y ){
	  swap( x , y );
	}
	answer.push_back( { j , ( x - 1 ) / D } );
      }
      return answer;
    };
    Graph graph{ N , edge };
    // EnumerationGraph graph{ N , Id<int> , Id<int> , edge };
    // MemorisationGraph<int,decltype(edge)> graph{ N , edge };
    Dijkstra d{ move( graph ) };
    // AbstractDijkstra d{ move( graph ) , AdditiveMonoid<>::Object() , 1LL<<62 };
    return d.GetDistance( 0 , 1 );
  };
  BS4( answer , 1 , 1e5 , k( answer ) , K );  
  RETURN( answer );
}
REPEAT_MAIN(1);

#else // INCLUDE_MAIN

#ifdef INCLUDE_SUB

// グラフ用
template <typename T> Map<T,T> gF;
template <typename T> inline T GetgF( const T& t ){ return gF<T>[t]; }

template <typename T> vector<T> gA;
template <typename T> inline T GetgA( const int& i ){ return gA<T>[i]; }

template <typename PATH> vector<list<PATH> > gE;
template <typename PATH> list<PATH> GetgE( const int& i )
{
  // list<PATH> answer{};
  list<PATH> answer = gE<PATH>[i];
  // VVV 入力によらない処理は以下に挿入する。

  // AAA 入力によらない処理は以上に挿入する。
  return answer;
}

// COMPAREに使用。圧縮時は削除する。
ll Naive( int N , int M , int K )
{
  ll answer = N + M + K;
  return answer;
}

// COMPAREに使用。圧縮時は削除する。
ll Answer( ll N , ll M , ll K )
{
  // START_WATCH;
  ll answer = N + M + K;

  // // TLに準じる乱択や全探索。デフォルトの猶予は100.0[ms]。
  // CEXPR( double , TL , 2000.0 );
  // while( CHECK_WATCH( TL ) ){

  // }
  return answer;
}

// 圧縮時は中身だけ削除する。
inline void Experiment()
{
  // CEXPR( int , bound , 10 );
  // FOREQ( N , 0 , bound ){
  //   FOREQ( M , 0 , bound ){
  //     FOREQ( K , 0 , bound ){
  //   	COUT( N , M , K , ":" , Naive( N , M , K ) );
  //     }
  //   }
  //   // cout << Naive( N ) << ",\n"[N==bound];
  // }
}

// 圧縮時は中身だけ削除する。
inline void SmallTest()
{
  // CEXPR( int , bound , 10 );
  // FOREQ( N , 0 , bound ){
  //   FOREQ( M , 0 , bound ){
  //     FOREQ( K , 0 , bound ){
  //   	COMPARE( N , M , K );
  //     }
  //   }
  //   // COMPARE( N );
  // }
}

#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:
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt

CoordinateCompress:
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txt

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

Divisor:
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt

Polynomial
c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt

UnionFind
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 U>
class VirtualPointedSet
{

public:
  virtual const U& Point() const noexcept = 0;
  inline const U& Unit() const noexcept;
  inline const U& Zero() const noexcept;
  inline const U& One() const noexcept;
  inline const U& Infty() const noexcept;
  inline const U& size() const noexcept;

};

template <typename U>
class PointedSet :
  virtual public VirtualPointedSet<U>
{

private:
  U m_b_U;

public:
  inline PointedSet( const U& b_u = U() );
  inline const U& Point() const noexcept;

};

template <typename U>
class VirtualNSet
{

public:
  virtual U Transfer( const U& u ) = 0;
  inline U Inverse( const U& u );

};

template <typename U , typename F_U>
class AbstractNSet :
  virtual public VirtualNSet<U>
{

private:
  F_U m_f_U;

public:
  inline AbstractNSet( F_U f_U );
  inline U Transfer( const U& u );

};

template <typename U>
class VirtualMagma
{

public:
  virtual U Product( const U& u0 , const U& u1 ) = 0;
  inline U Sum( const U& u0 , const U& u1 );

};

template <typename U , typename M_U>
class AbstractMagma :
  virtual public VirtualMagma<U>
{

private:
  M_U m_m_U;

public:
  inline AbstractMagma( M_U m_U );
  inline U Product( const U& u0 , const U& u1 );

};

template <typename U> inline PointedSet<U>::PointedSet( const U& b_U ) : m_b_U( b_U ) {}
template <typename U> inline const U& PointedSet<U>::Point() const noexcept { return m_b_U; }
template <typename U> inline const U& VirtualPointedSet<U>::Unit() const noexcept { return Point(); }
template <typename U> inline const U& VirtualPointedSet<U>::Zero() const noexcept { return Point(); }
template <typename U> inline const U& VirtualPointedSet<U>::One() const noexcept { return Point(); }
template <typename U> inline const U& VirtualPointedSet<U>::Infty() const noexcept { return Point(); }
template <typename U> inline const U& VirtualPointedSet<U>::size() const noexcept { return Point(); }

template <typename U , typename F_U> inline AbstractNSet<U,F_U>::AbstractNSet( F_U f_U ) : m_f_U( move( f_U ) ) { static_assert( is_invocable_r_v<U,F_U,U> ); }
template <typename U , typename F_U> inline U AbstractNSet<U,F_U>::Transfer( const U& u ) { return m_f_U( u ); }
template <typename U> inline U VirtualNSet<U>::Inverse( const U& u ) { return Transfer( u ); }

template <typename U , typename M_U> inline AbstractMagma<U,M_U>::AbstractMagma( M_U m_U ) : m_m_U( move( m_U ) ) { static_assert( is_invocable_r_v<U,M_U,U,U> ); }
template <typename U , typename M_U> inline U AbstractMagma<U,M_U>::Product( const U& u0 , const U& u1 ) { return m_m_U( u0 , u1 ); }
template <typename U> inline U VirtualMagma<U>::Sum( const U& u0 , const U& u1 ) { return Product( u0 , u1 ); }


template <typename U>
class VirtualMonoid :
  virtual public VirtualMagma<U> ,
  virtual public VirtualPointedSet<U>
{};

template <typename U = ll>
class AdditiveMonoid :
  virtual public VirtualMonoid<U> ,
  public PointedSet<U>
{

public:
  inline U Product( const U& u0 , const U& u1 );
  static inline AdditiveMonoid<U>& Object();

};

template <typename U = ll>
class MultiplicativeMonoid :
  virtual public VirtualMonoid<U> ,
  public PointedSet<U>
{

public:
  inline MultiplicativeMonoid( const U& e_U );
  inline U Product( const U& u0 , const U& u1 );
  static inline MultiplicativeMonoid<U>& Object();

};

template <typename U , typename M_U>
class AbstractMonoid :
  virtual public VirtualMonoid<U> ,
  public AbstractMagma<U,M_U> ,
  public PointedSet<U>
{

public:
  inline AbstractMonoid( M_U m_U , const U& e_U );
  inline U Product( const U& u0 , const U& u1 );

};

template <typename U> inline MultiplicativeMonoid<U>::MultiplicativeMonoid( const U& e_U ) : PointedSet<U>( e_U ) {}
template <typename U , typename M_U> inline AbstractMonoid<U,M_U>::AbstractMonoid( M_U m_U , const U& e_U ) : AbstractMagma<U,M_U>( move( m_U ) ) , PointedSet<U>( e_U ) {}

template <typename U> inline U AdditiveMonoid<U>::Product( const U& u0 , const U& u1 ) { return u0 + u1; }
template <typename U> inline U MultiplicativeMonoid<U>::Product( const U& u0 , const U& u1 ) { return u0 * u1; }
template <typename U , typename M_U> inline U AbstractMonoid<U,M_U>::Product( const U& u0 , const U& u1 ) { return m_m_U( u0 , u1 ); }

template <typename U> inline AdditiveMonoid<U>& AdditiveMonoid<U>::Object() { static AdditiveMonoid<U> obj{}; return obj; }


#ifndef RET_TYPE
  #define RET_TYPE
  template <typename F , typename...Args> using ret_t = decltype( declval<F>()( declval<Args>()... ) );
#endif
#ifndef INNER_TYPE
  #define INNER_TYPE
  template <typename T> using inner_t = typename T::type;
#endif
#ifndef decldecay_t
  #define decldecay_t( VAR ) decay_t<decltype( VAR )>
#endif

// Enumeration:N->R1-->TとEnumeration_inv:T->R2-->Nは互いに逆写像である仮想関数。
template <typename T , typename R1 , typename R2 , typename E>
class VirtualGraph :
  public PointedSet<int>
{

private:
  E m_edge;

public:
  inline VirtualGraph( const int& size , E edge );
  virtual R1 Enumeration( const int& i ) = 0;
  virtual R2 Enumeration_inv( const T& t ) = 0;
  inline void Reset();
  ret_t<E,T> Edge( const T& t );
  using type = T;

};

template <typename E>
class Graph :
  virtual public VirtualGraph<int,const int&,const int&,E>
{
  
public:
  inline Graph( const int& size , E edge );
  inline const int& Enumeration( const int& i );
  inline const int& Enumeration_inv( const int& t );
  template <typename F> inline Graph<F> GetGraph( F edge ) const;

};

template <typename T , typename Enum_T , typename Enum_T_inv , typename E>
class EnumerationGraph :
  virtual public VirtualGraph<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>
{

private:
  Enum_T m_enum_T;
  Enum_T_inv m_enum_T_inv;
  
public:
  inline EnumerationGraph( const int& size , Enum_T enum_T , Enum_T_inv enum_T_inv , E edge );
  inline ret_t<Enum_T,int> Enumeration( const int& i );
  inline ret_t<Enum_T_inv,T> Enumeration_inv( const T& t );
  template <typename F> inline EnumerationGraph<T,Enum_T,Enum_T_inv,F> GetGraph( F edge ) const;

};
template <typename Enum_T , typename Enum_T_inv , typename E> EnumerationGraph( const int& size , Enum_T enum_T , Enum_T_inv enum_T_inv , E edge ) -> EnumerationGraph<decldecay_t(get<0>(declval<E>()(0).front())),Enum_T,Enum_T_inv,E>;

// 推論補助のためにE::operator()はデフォルト引数が必要。
template <typename T , typename E>
class MemorisationGraph :
  virtual public VirtualGraph<T,T,const int&,E>
{

private:
  int m_length;
  vector<T> m_memory;
  Map<T,int> m_memory_inv;
  
public:
  inline MemorisationGraph( const int& size , E edge );
  // push_backする可能性のあるvectorなので参照にしないように注意
  inline T Enumeration( const int& i );
  inline const int& Enumeration_inv( const T& t );
  inline void Reset();
  template <typename F> inline MemorisationGraph<T,F> GetGraph( F edge ) const;

};
template <typename E> MemorisationGraph( const int& size , E edge ) -> MemorisationGraph<decldecay_t(get<0>(declval<E>()().front())),E>;

template <typename T , typename R1 , typename R2 , typename E> inline VirtualGraph<T,R1,R2,E>::VirtualGraph( const int& size , E edge ) : PointedSet<int>( size ) , m_edge( move( edge ) ) { static_assert( is_constructible_v<T,R1> && is_constructible_v<int,R2> && is_invocable_v<E,T> ); }
template <typename E> inline Graph<E>::Graph( const int& size , E edge ) : VirtualGraph<int,const int&,const int&,E>( size , move( edge ) ) {}
template <typename T , typename Enum_T , typename Enum_T_inv , typename E> inline EnumerationGraph<T,Enum_T,Enum_T_inv,E>::EnumerationGraph( const int& size , Enum_T enum_T , Enum_T_inv enum_T_inv , E edge ) : VirtualGraph<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>( size , move( edge ) ) , m_enum_T( move( enum_T ) ) , m_enum_T_inv( move( enum_T_inv ) ) {}
template <typename T , typename E> inline MemorisationGraph<T,E>::MemorisationGraph( const int& size , E edge ) : VirtualGraph<T,T,const int&,E>( size , move( edge ) ) , m_length() , m_memory() , m_memory_inv() {}

template <typename T , typename R1 , typename R2 , typename E> inline ret_t<E,T> VirtualGraph<T,R1,R2,E>::Edge( const T& t ) { return m_edge( t ); }

template <typename E> inline const int& Graph<E>::Enumeration( const int& i ) { return i; }
template <typename T , typename Enum_T , typename Enum_T_inv , typename E> inline ret_t<Enum_T,int> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration( const int& i ) { return m_enum_T( i ); }
template <typename T , typename E> inline T MemorisationGraph<T,E>::Enumeration( const int& i ) { assert( 0 <= i && i < m_length ); return m_memory[i]; }

template <typename E> inline const int& Graph<E>::Enumeration_inv( const int& i ) { return i; }
template <typename T , typename Enum_T , typename Enum_T_inv , typename E> inline ret_t<Enum_T_inv,T> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration_inv( const T& t ) { return m_enum_T_inv( t ); }
template <typename T , typename E> inline const int& MemorisationGraph<T,E>::Enumeration_inv( const T& t )
{

  if( m_memory_inv.count( t ) == 0 ){

    assert( m_length < this->size() );
    m_memory.push_back( t );
    return m_memory_inv[t] = m_length++;

  }
  
  return m_memory_inv[t];

}

template <typename T , typename R1 , typename R2 , typename E> void VirtualGraph<T,R1,R2,E>::Reset() {}
template <typename T , typename E> inline void MemorisationGraph<T,E>::Reset() { m_length = 0; m_memory.clear(); m_memory_inv.clear(); }

template <typename E> template <typename F> inline Graph<F> Graph<E>::GetGraph( F edge ) const { return Graph<F>( this->size() , move( edge ) ); }
template <typename T , typename Enum_T , typename Enum_T_inv , typename E> template <typename F> inline EnumerationGraph<T,Enum_T,Enum_T_inv,F> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::GetGraph( F edge ) const { return EnumerationGraph( this->size() , m_enum_T , m_enum_T_inv , move( edge ) ); }
template <typename T , typename E> template <typename F> inline MemorisationGraph<T,F> MemorisationGraph<T,E>::GetGraph( F edge ) const { return MemorisationGraph( this->size() , move( edge ) ); }


#define DIJKSTRA_BODY( INITIALISE_PREV , CHECK_FINAL , SET_PREV )	\
  const U& zero = m_M.Zero();						\
  const U& infty = this->Infty();					\
  assert( zero < infty );						\
  const int& size = m_G.size();						\
  auto&& i_start = m_G.Enumeration_inv( t_start );			\
  assert( 0 <= i_start && i_start < size );				\
  set<pair<U,int>> vertex{};						\
  vector<bool> found( size );						\
  vector<U> weight( size , infty );					\
  vertex.insert( pair<U,int>( weight[i_start] = zero , i_start ) );	\
  INITIALISE_PREV;							\
									\
  while( ! vertex.empty() ){						\
									\
    auto begin = vertex.begin();					\
    auto [weight_i,i] = *begin;						\
    CHECK_FINAL;							\
    found[i] = true;							\
    vertex.erase( begin );						\
    auto&& edge_i = m_G.Edge( m_G.Enumeration( i ) );			\
    list<pair<U,int> > changed_vertex{};				\
									\
    for( auto itr = edge_i.begin() , end = edge_i.end() ; itr != end ; itr++ ){ \
									\
      auto&& j = m_G.Enumeration_inv( itr->first );		\
      									\
      if( !found[j] ){							\
									\
	const U& edge_ij = itr->second;				\
	U temp = m_M.Sum( weight_i , edge_ij );				\
	assert( !( temp < edge_ij ) && temp < infty ); \
	U& weight_j = weight[j];					\
									\
	if( weight_j > temp ){						\
									\
	  if( weight_j != infty ){					\
									\
	    vertex.erase( pair<U,int>( weight_j , j ) );		\
									\
	  }								\
									\
	  SET_PREV;							\
	  changed_vertex.push_back( pair<U,int>( weight_j = move( temp ) , j ) ); \
									\
	}								\
									\
      }									\
									\
    }									\
									\
    for( auto itr_changed = changed_vertex.begin() , end_changed = changed_vertex.end() ; itr_changed != end_changed ; itr_changed++ ){ \
									\
      vertex.insert( *itr_changed );					\
									\
    }									\
									\
  }									\

// GRAPHはグラフG=(V_G,E_G:T->(T \times U)^{< \omega})に相当する型。

// 入力の範囲内で要件
// (0) Mは全順序可換モノイド構造である。
// (1) E_Gの値の各成分の第2成分がM.Zero()以上である。
// (2) inftyがE_Gの値の各成分の第2成分|V_G|個以下の和で表せるいかなる数よりも大きい。
// (3) Vの各要素u,vに対し、辺u->vが複数存在する場合は重みが最小のものが前にpushされている。
// が成り立つ場合にのみサポート。

// 単一始点単一終点最短経路探索／経路復元なしO((|V_G|+|E_G|)log |V_G|)
// 単一始点単一終点最短経路探索／経路復元ありO((|V_G|+|E_G|)log |V_G|)
// 単一始点全終点最短経路探索／経路復元なしO((|V_G|+|E_G|)log |V_G|)
// 単一始点全終点最短経路探索／経路復元ありO(|V_G|^2 + |E_G| log |V_G|)

// O((|V_G|+|E_G|)log |V_G|)が間に合わない場合は、
// 始点からの距離を格納して一番近い未訪問点を全探策で探し距離を更新するO(|V_G|^2)版を検討。
template <typename GRAPH , typename MONOID , typename U>
class AbstractDijkstra :
  public PointedSet<U>
{

private:
  GRAPH m_G;
  MONOID m_M;

public:
  inline AbstractDijkstra( GRAPH G , MONOID M , const U& infty );

  // 経路が存在しない場合の返り値はinfty
  U GetDistance( const inner_t<GRAPH>& t_start , const inner_t<GRAPH>& t_final );
  vector<U> GetDistance( const inner_t<GRAPH>& t_start );
  pair<U,list<inner_t<GRAPH>>> GetPath( const inner_t<GRAPH>& t_start , const inner_t<GRAPH>& t_final );
  pair<vector<U>,vector<list<inner_t<GRAPH>>>> GetPath( const inner_t<GRAPH>& t_start );

};

template <typename GRAPH>
class Dijkstra :
  public AbstractDijkstra<GRAPH,AdditiveMonoid<>,ll>
{

public:
  inline Dijkstra( GRAPH G );

};

template <typename GRAPH , typename MONOID , typename U> inline AbstractDijkstra<GRAPH,MONOID,U>::AbstractDijkstra( GRAPH G , MONOID M , const U& infty ) : PointedSet<U>( infty ) , m_G( move( G ) ) , m_M( move( M ) ) { static_assert( ! is_same_v<U,int> ); }
template <typename GRAPH> inline Dijkstra<GRAPH>::Dijkstra( GRAPH G ) : AbstractDijkstra<GRAPH,AdditiveMonoid<>,ll>( G , AdditiveMonoid<>::Object() , 4611686018427387904 ) {}

template <typename GRAPH , typename MONOID , typename U>
U AbstractDijkstra<GRAPH,MONOID,U>::GetDistance( const inner_t<GRAPH>& t_start , const inner_t<GRAPH>& t_final )
{

  auto&& i_final = m_G.Enumeration_inv( t_final );
  DIJKSTRA_BODY( , if( i == i_final ){ break; } , );
  U answer = move( weight[i_final] );
  m_G.Reset();
  return answer;

}

template <typename GRAPH , typename MONOID , typename U>
vector<U> AbstractDijkstra<GRAPH,MONOID,U>::GetDistance( const inner_t<GRAPH>& t_start )
{

  DIJKSTRA_BODY( , , );
  m_G.Reset();
  return weight;

}

template <typename GRAPH , typename MONOID , typename U>
pair<U,list<inner_t<GRAPH>>> AbstractDijkstra<GRAPH,MONOID,U>::GetPath( const inner_t<GRAPH>& t_start , const inner_t<GRAPH>& t_final )
{

  auto&& i_final = m_G.Enumeration_inv( t_final );
  DIJKSTRA_BODY( vector<int> prev( size ) , if( i == i_final ){ break; } , prev[j] = i );
  int i = i_final;
  list<inner_t<GRAPH>> path{};

  while( i != i_start ){

    path.push_front( m_G.Enumeration( i ) );
    i = prev[i];

  }

  path.push_front( t_start );
  U answer = move( weight[i_final] );
  m_G.Reset();
  return { move( answer ) , move( path ) };

}

template <typename GRAPH , typename MONOID , typename U>
pair<vector<U>,vector<list<inner_t<GRAPH>>>> AbstractDijkstra<GRAPH,MONOID,U>::GetPath( const inner_t<GRAPH>& t_start )
{

  DIJKSTRA_BODY( vector<int> prev( size ) , , prev[j] = i );
  vector<list<inner_t<GRAPH>>> path( size );

  for( int j = 0 ; j < size ; j++ ){

    auto& path_j = path[j];
    int i = j;

    while( i != i_start ){

      path_j.push_front( m_G.Enumeration( i ) );
      i = prev[i];

    }

    path_j.push_front( t_start );

  }

  m_G.Reset();
  return { move( weight ) , move( path ) };

}


// 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 ){ return 0; } else if( exec_mode == experiment_mode ){ Experiment(); return 0; } else if( exec_mode == small_test_mode ){ SmallTest(); return 0; }; DEXPR( int , bound_test_case_num , BOUND , min( BOUND , 100 ) ); int test_case_num = 1; if( exec_mode == solve_mode ){ if constexpr( bound_test_case_num > 1 ){ 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 DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE )
  #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( 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 { assert( false ); }
  #define SOLVE_ONLY static_assert( __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 constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE )
  #define ASSERT( A , MIN , MAX ) assert( ( 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_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; }
  #define CIN_A( LL , A , N ) vector<LL> A( N ); SET_A( A , N );
#endif
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using lld = __float128;
template <typename INT> using T2 = pair<INT,INT>;
template <typename INT> using T3 = tuple<INT,INT,INT>;
template <typename INT> using T4 = tuple<INT,INT,INT,INT>;
using path = pair<int,ll>;
#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 constexpr( 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 decldecay_t( VAR ) decay_t<decltype( VAR )>
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , 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 .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( 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.begin() , END_FOR_OUTPUT_ITR = A.end(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; while( 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__ ); return
#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 ){ return; }

// 入出力用
template <class Traits> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); }
template <class Traits> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const vector<Arg>& arg ) { auto begin = arg.begin() , end = arg.end(); auto itr = begin; while( itr != end ){ ( itr == begin ? os : os << " " ) << *itr; itr++; } return os; }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg& arg ) { return os << arg; }
template <class Traits , typename Arg1 , typename Arg2 , typename... ARGS> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); }

// 算術用
template <typename T> constexpr T PositiveBaseResidue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }
template <typename T> constexpr T Residue( const T& a , const T& p ){ return PositiveBaseResidue( a , p < 0 ? -p : p ); }
template <typename T> constexpr T PositiveBaseQuotient( const T& a , const T& p ){ return ( a - PositiveBaseResidue( a , p ) ) / p; }
template <typename T> constexpr T Quotient( const T& a , const T& p ){ return p < 0 ? PositiveBaseQuotient( -a , -p ) : PositiveBaseQuotient( a , p ); }

#define POWER( ANSWER , ARGUMENT , EXPONENT )				\
  static_assert( ! 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 );	\
    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 = ( ( 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 );	\
    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 ) \
  ll ANSWER[CONSTEXPR_LENGTH];						\
  ll ANSWER_INV[CONSTEXPR_LENGTH];					\
  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 ); \
    }									\
  }									\

// 二分探索用
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CONST_TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , CONST_TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
  static_assert( ! is_same<decldecay_t( CONST_TARGET ),uint>::value && ! is_same<decldecay_t( CONST_TARGET ),ull>::value ); \
  ll ANSWER = MINIMUM;							\
  {									\
    ll L_BS = MINIMUM;							\
    ll U_BS = MAXIMUM;							\
    ANSWER = UPDATE_ANSWER;						\
    ll EXPRESSION_BS;							\
    const ll CONST_TARGET_BS = ( CONST_TARGET );			\
    ll DIFFERENCE_BS;							\
    while( L_BS < U_BS ){						\
      DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CONST_TARGET_BS; \
      CERR( "二分探索中：" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS :" , #EXPRESSION , "-" , #CONST_TARGET , "=" , EXPRESSION_BS , "-" , CONST_TARGET_BS , "=" , DIFFERENCE_BS ); \
      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 > CONST_TARGET_BS ? ">" : EXPRESSION_BS < CONST_TARGET_BS ? "<" : "=" ) , CONST_TARGET_BS ); \
      if( EXPRESSION_BS DESIRED_INEQUALITY CONST_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 >= CONST_TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET )	\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CONST_TARGET , >= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) \

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

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

// 単調減少の時にEXPRESSION <= CONST_TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET )	\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CONST_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。
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
template <typename T , template <typename...> typename V> inline V<T> operator+( const V<T>& a0 , const V<T>& a1 ) { if( a0.empty() ){ return a1; } if( a1.empty() ){ return a0; } assert( a0.size() == a1.size() ); V<T> answer{}; for( auto itr0 = a0.begin() , itr1 = a1.begin() , end0 = a0.end(); itr0 != end0 ; itr0++ , itr1++ ){ answer.push_back( *itr0 + *itr1 ); } return answer; }
template <typename T , typename U> inline pair<T,U> operator+( const pair<T,U>& t0 , const pair<T,U>& t1 ) { return { t0.first + t1.first , t0.second + t1.second }; }
template <typename T , typename U , typename V> inline tuple<T,U,V> operator+( const tuple<T,U,V>& t0 , const tuple<T,U,V>& t1 ) { return { get<0>( t0 ) + get<0>( t1 ) , get<1>( t0 ) + get<1>( t1 ) , get<2>( t0 ) + get<2>( t1 ) }; }
template <typename T , typename U , typename V , typename W> inline tuple<T,U,V,W> operator+( const tuple<T,U,V,W>& t0 , const tuple<T,U,V,W>& t1 ) { return { get<0>( t0 ) + get<0>( t1 ) , get<1>( t0 ) + get<1>( t1 ) , get<2>( t0 ) + get<2>( t1 ) , get<3>( t0 ) + get<3>( t1 ) }; }
template <typename T> inline T Add( const T& t0 , const T& t1 ) { return t0 + t1; }
template <typename T> inline T XorAdd( 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{}; return z; }
template <typename T> inline const T& One() { static const T o = 1; return o; }\
template <typename T> inline T AddInv( const T& t ) { return -t; }
template <typename T> inline T Id( const T& v ) { return v; }
template <typename T> inline T Min( const T& a , const T& b ){ return a < b ? a : b; }
template <typename T> inline T Max( const T& a , const T& b ){ return a < b ? b : a; }

// グリッド問題用
int H , W , H_minus , W_minus , HW;
vector<vector<bool> > non_wall;
inline T2<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;}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<int> ( &e )[] , 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 SetEdgeOnGrid( const string& Si , const int& i , list<path> ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){const 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});}}}}
inline void SetWallOnGrid( const string& Si , const int& i , vector<vector<bool> >& non_wall , const char& walkable = '.'  , const char& unwalkable = '#' ){non_wall.push_back(vector<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
  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( int& exec_mode , const bool& use_getline );
  inline void Solve();
  inline void Experiment();
  inline void SmallTest();
  inline void RandomTest();
  ll GetRand( const ll& Rand_min , const ll& Rand_max );
  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( const ll& Rand_min , const ll& Rand_max ) { ll answer = time( NULL ); return answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; }
#endif

// 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&

// VVV 常設ライブラリは以下に挿入する。
// Map
// c:/Users/user/Documents/Programming/Mathematics/Function/Map
CL is_ordered{PU:is_ordered()= delete;TE <TY T> ST CE auto Check(CO T& t)-> decltype(t < t,true_type());ST CE false_type Check(...);TE <TY T> ST CE CO bool value = is_same_v< decltype(Check(declval<T>())),true_type >;};
TE <TY T , TY U>US Map = conditional_t<is_constructible_v<unordered_map<T,int>>,unordered_map<T,U>,conditional_t<is_ordered::value<T>,map<T,U>,void>>;

// ConstexprModulo
// c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/ConstexprModulo/a.hpp
CEXPR(uint,P,998244353);TE <uint M,TY INT> CE INT& RS(INT& n)NE{RE n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n %= M;}TE <uint M> CE uint& RS(uint& n)NE{RE n %= M;}TE <uint M> CE ull& RS(ull& n)NE{RE n %= M;}TE <TY INT> CE INT& RSP(INT& n)NE{CE CO uint trunc =(1 << 23)- 1;INT n_u = n >> 23;n &= trunc;INT n_uq =(n_u / 7)/ 17;n_u -= n_uq * 119;n += n_u << 23;RE n < n_uq?n += P - n_uq:n -= n_uq;}TE <> CE ull& RS<P,ull>(ull& n)NE{CE CO ull Pull = P;CE CO ull Pull2 =(Pull - 1)*(Pull - 1);RE RSP(n > Pull2?n -= Pull2:n);}TE <uint M,TY INT> CE INT RS(INT&& n)NE{RE MO(RS<M>(n));}TE <uint M,TY INT> CE INT RS(CO INT& n)NE{RE RS<M>(INT(n));}

#define SFINAE_FOR_MOD(DEFAULT)TY T,enable_if_t<is_constructible<uint,decay_t<T> >::value>* DEFAULT
#define DC_OF_CM_FOR_MOD(FUNC)CE bool OP FUNC(CO Mod<M>& n)CO NE
#define DC_OF_AR_FOR_MOD(FUNC)CE Mod<M> OP FUNC(CO Mod<M>& n)CO NE;TE <SFINAE_FOR_MOD(= nullptr)> CE Mod<M> OP FUNC(T&& n)CO NE;
#define DF_OF_CM_FOR_MOD(FUNC)TE <uint M> CE bool Mod<M>::OP FUNC(CO Mod<M>& n)CO NE{RE m_n FUNC n.m_n;}
#define DF_OF_AR_FOR_MOD(FUNC,FORMULA)TE <uint M> CE Mod<M> Mod<M>::OP FUNC(CO Mod<M>& n)CO NE{RE MO(Mod<M>(*TH)FUNC ## = n);}TE <uint M> TE <SFINAE_FOR_MOD()> CE Mod<M> Mod<M>::OP FUNC(T&& n)CO NE{RE FORMULA;}TE <uint M,SFINAE_FOR_MOD(= nullptr)> CE Mod<M> OP FUNC(T&& n0,CO Mod<M>& n1)NE{RE MO(Mod<M>(forward<T>(n0))FUNC ## = n1);}

TE <uint M>CL Mod{PU:uint m_n;CE Mod()NE;CE Mod(CO Mod<M>& n)NE;CE Mod(Mod<M>& n)NE;CE Mod(Mod<M>&& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> CE Mod(CO T& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> CE Mod(T& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> CE Mod(T&& n)NE;CE Mod<M>& OP=(CO Mod<M>& n)NE;CE Mod<M>& OP=(Mod<M>&& n)NE;CE Mod<M>& OP+=(CO Mod<M>& n)NE;CE Mod<M>& OP-=(CO Mod<M>& n)NE;CE Mod<M>& OP*=(CO Mod<M>& n)NE;IN Mod<M>& OP/=(CO Mod<M>& n);CE Mod<M>& OP<<=(int n)NE;CE Mod<M>& OP>>=(int n)NE;CE Mod<M>& OP++()NE;CE Mod<M> OP++(int)NE;CE Mod<M>& OP--()NE;CE Mod<M> OP--(int)NE;DC_OF_CM_FOR_MOD(==);DC_OF_CM_FOR_MOD(!=);DC_OF_CM_FOR_MOD(<);DC_OF_CM_FOR_MOD(<=);DC_OF_CM_FOR_MOD(>);DC_OF_CM_FOR_MOD(>=);DC_OF_AR_FOR_MOD(+);DC_OF_AR_FOR_MOD(-);DC_OF_AR_FOR_MOD(*);DC_OF_AR_FOR_MOD(/);CE Mod<M> OP<<(int n)CO NE;CE Mod<M> OP>>(int n)CO NE;CE Mod<M> OP-()CO NE;CE Mod<M>& SignInvert()NE;CE Mod<M>& Double()NE;CE Mod<M>& Halve()NE;IN Mod<M>& Invert();TE <TY T> CE Mod<M>& PositivePW(T&& EX)NE;TE <TY T> CE Mod<M>& NonNegativePW(T&& EX)NE;TE <TY T> CE Mod<M>& PW(T&& EX);CE VO swap(Mod<M>& n)NE;CE CRUI RP()CO NE;ST CE Mod<M> DeRP(CRUI n)NE;ST CE uint& Normalise(uint& n)NE;ST IN CO Mod<M>& Inverse(CRUI n)NE;ST IN CO Mod<M>& Factorial(CRUI n)NE;ST IN CO Mod<M>& FactorialInverse(CRUI n)NE;ST IN Mod<M> Combination(CRUI n,CRUI i)NE;ST IN CO Mod<M>& zero()NE;ST IN CO Mod<M>& one()NE;TE <TY T> CE Mod<M>& Ref(T&& n)NE;};

#define SFINAE_FOR_MN(DEFAULT)TY T,enable_if_t<is_constructible<Mod<M>,decay_t<T> >::value>* DEFAULT
#define DC_OF_AR_FOR_MN(FUNC)IN MN<M> OP FUNC(CO MN<M>& n)CO NE;TE <SFINAE_FOR_MOD(= nullptr)> IN MN<M> OP FUNC(T&& n)CO NE;
#define DF_OF_CM_FOR_MN(FUNC)TE <uint M> IN bool MN<M>::OP FUNC(CO MN<M>& n)CO NE{RE m_n FUNC n.m_n;}
#define DF_OF_AR_FOR_MN(FUNC,FORMULA)TE <uint M> IN MN<M> MN<M>::OP FUNC(CO MN<M>& n)CO NE{RE MO(MN<M>(*TH)FUNC ## = n);}TE <uint M> TE <SFINAE_FOR_MOD()> IN MN<M> MN<M>::OP FUNC(T&& n)CO NE{RE FORMULA;}TE <uint M,SFINAE_FOR_MOD(= nullptr)> IN MN<M> OP FUNC(T&& n0,CO MN<M>& n1)NE{RE MO(MN<M>(forward<T>(n0))FUNC ## = n1);}

TE <uint M>CL MN:PU Mod<M>{PU:CE MN()NE;CE MN(CO MN<M>& n)NE;CE MN(MN<M>& n)NE;CE MN(MN<M>&& n)NE;TE <SFINAE_FOR_MN(= nullptr)> CE MN(CO T& n)NE;TE <SFINAE_FOR_MN(= nullptr)> CE MN(T&& n)NE;CE MN<M>& OP=(CO MN<M>& n)NE;CE MN<M>& OP=(MN<M>&& n)NE;CE MN<M>& OP+=(CO MN<M>& n)NE;CE MN<M>& OP-=(CO MN<M>& n)NE;CE MN<M>& OP*=(CO MN<M>& n)NE;IN MN<M>& OP/=(CO MN<M>& n);CE MN<M>& OP<<=(int n)NE;CE MN<M>& OP>>=(int n)NE;CE MN<M>& OP++()NE;CE MN<M> OP++(int)NE;CE MN<M>& OP--()NE;CE MN<M> OP--(int)NE;DC_OF_AR_FOR_MN(+);DC_OF_AR_FOR_MN(-);DC_OF_AR_FOR_MN(*);DC_OF_AR_FOR_MN(/);CE MN<M> OP<<(int n)CO NE;CE MN<M> OP>>(int n)CO NE;CE MN<M> OP-()CO NE;CE MN<M>& SignInvert()NE;CE MN<M>& Double()NE;CE MN<M>& Halve()NE;CE MN<M>& Invert();TE <TY T> CE MN<M>& PositivePW(T&& EX)NE;TE <TY T> CE MN<M>& NonNegativePW(T&& EX)NE;TE <TY T> CE MN<M>& PW(T&& EX);CE uint RP()CO NE;CE Mod<M> Reduce()CO NE;ST CE MN<M> DeRP(CRUI n)NE;ST IN CO MN<M>& Formise(CRUI n)NE;ST IN CO MN<M>& Inverse(CRUI n)NE;ST IN CO MN<M>& Factorial(CRUI n)NE;ST IN CO MN<M>& FactorialInverse(CRUI n)NE;ST IN MN<M> Combination(CRUI n,CRUI i)NE;ST IN CO MN<M>& zero()NE;ST IN CO MN<M>& one()NE;ST CE uint Form(CRUI n)NE;ST CE ull& Reduction(ull& n)NE;ST CE ull& ReducedMU(ull& n,CRUI m)NE;ST CE uint MU(CRUI n0,CRUI n1)NE;ST CE uint BaseSquareTruncation(uint& n)NE;TE <TY T> CE MN<M>& Ref(T&& n)NE;};TE <uint M> CE MN<M> Twice(CO MN<M>& n)NE;TE <uint M> CE MN<M> Half(CO MN<M>& n)NE;TE <uint M> CE MN<M> Inverse(CO MN<M>& n);TE <uint M,TY T> CE MN<M> PW(MN<M> n,T EX);TE <TY T> CE MN<2> PW(CO MN<2>& n,CO T& p);TE <TY T> CE T Square(CO T& t);TE <> CE MN<2> Square<MN<2> >(CO MN<2>& t);TE <uint M> CE VO swap(MN<M>& n0,MN<M>& n1)NE;TE <uint M> IN string to_string(CO MN<M>& n)NE;TE<uint M,CL Traits> IN basic_istream<char,Traits>& OP>>(basic_istream<char,Traits>& is,MN<M>& n);TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO MN<M>& n);

TE <uint M>CL COantsForMod{PU:COantsForMod()= delete;ST CE CO bool g_even =((M & 1)== 0);ST CE CO uint g_memory_bound = 1000000;ST CE CO uint g_memory_LE = M < g_memory_bound?M:g_memory_bound;ST CE ull MNBasePW(ull&& EX)NE;ST CE uint g_M_minus = M - 1;ST CE uint g_M_minus_2 = M - 2;ST CE uint g_M_minus_2_neg = 2 - M;ST CE CO int g_MN_digit = 32;ST CE CO ull g_MN_base = ull(1)<< g_MN_digit;ST CE CO uint g_MN_base_minus = uint(g_MN_base - 1);ST CE CO uint g_MN_digit_half =(g_MN_digit + 1)>> 1;ST CE CO uint g_MN_base_sqrt_minus =(1 << g_MN_digit_half)- 1;ST CE CO uint g_MN_M_neg_inverse = uint((g_MN_base - MNBasePW((ull(1)<<(g_MN_digit - 1))- 1))& g_MN_base_minus);ST CE CO uint g_MN_base_mod = uint(g_MN_base % M);ST CE CO uint g_MN_base_square_mod = uint(((g_MN_base % M)*(g_MN_base % M))% M);};TE <uint M> CE ull COantsForMod<M>::MNBasePW(ull&& EX)NE{ull prod = 1;ull PW = M;WH(EX != 0){(EX & 1)== 1?(prod *= PW)&= g_MN_base_minus:prod;EX >>= 1;(PW *= PW)&= g_MN_base_minus;}RE prod;}

US MP = Mod<P>;US MNP = MN<P>;TE <uint M> CE uint MN<M>::Form(CRUI n)NE{ull n_copy = n;RE uint(MO(Reduction(n_copy *= COantsForMod<M>::g_MN_base_square_mod)));}TE <uint M> CE ull& MN<M>::Reduction(ull& n)NE{ull n_sub = n & COantsForMod<M>::g_MN_base_minus;RE((n +=((n_sub *= COantsForMod<M>::g_MN_M_neg_inverse)&= COantsForMod<M>::g_MN_base_minus)*= M)>>= COantsForMod<M>::g_MN_digit)< M?n:n -= M;}TE <uint M> CE ull& MN<M>::ReducedMU(ull& n,CRUI m)NE{RE Reduction(n *= m);}TE <uint M> CE uint MN<M>::MU(CRUI n0,CRUI n1)NE{ull n0_copy = n0;RE uint(MO(ReducedMU(ReducedMU(n0_copy,n1),COantsForMod<M>::g_MN_base_square_mod)));}TE <uint M> CE uint MN<M>::BaseSquareTruncation(uint& n)NE{CO uint n_u = n >> COantsForMod<M>::g_MN_digit_half;n &= COantsForMod<M>::g_MN_base_sqrt_minus;RE n_u;}TE <uint M> CE MN<M>::MN()NE:Mod<M>(){static_assert(! COantsForMod<M>::g_even);}TE <uint M> CE MN<M>::MN(CO MN<M>& n)NE:Mod<M>(n){}TE <uint M> CE MN<M>::MN(MN<M>& n)NE:Mod<M>(n){}TE <uint M> CE MN<M>::MN(MN<M>&& n)NE:Mod<M>(MO(n)){}TE <uint M> TE <SFINAE_FOR_MN()> CE MN<M>::MN(CO T& n)NE:Mod<M>(n){static_assert(! COantsForMod<M>::g_even);Mod<M>::m_n = Form(Mod<M>::m_n);}TE <uint M> TE <SFINAE_FOR_MN()> CE MN<M>::MN(T&& n)NE:Mod<M>(forward<T>(n)){static_assert(! COantsForMod<M>::g_even);Mod<M>::m_n = Form(Mod<M>::m_n);}TE <uint M> CE MN<M>& MN<M>::OP=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP=(n));}TE <uint M> CE MN<M>& MN<M>::OP=(MN<M>&& n)NE{RE Ref(Mod<M>::OP=(MO(n)));}TE <uint M> CE MN<M>& MN<M>::OP+=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP+=(n));}TE <uint M> CE MN<M>& MN<M>::OP-=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP-=(n));}TE <uint M> CE MN<M>& MN<M>::OP*=(CO MN<M>& n)NE{ull m_n_copy = Mod<M>::m_n;RE Ref(Mod<M>::m_n = MO(ReducedMU(m_n_copy,n.m_n)));}TE <uint M> IN MN<M>& MN<M>::OP/=(CO MN<M>& n){RE OP*=(MN<M>(n).Invert());}TE <uint M> CE MN<M>& MN<M>::OP<<=(int n)NE{RE Ref(Mod<M>::OP<<=(n));}TE <uint M> CE MN<M>& MN<M>::OP>>=(int n)NE{RE Ref(Mod<M>::OP>>=(n));}TE <uint M> CE MN<M>& MN<M>::OP++()NE{RE Ref(Mod<M>::Normalise(Mod<M>::m_n += COantsForMod<M>::g_MN_base_mod));}TE <uint M> CE MN<M> MN<M>::OP++(int)NE{MN<M> n{*TH};OP++();RE n;}TE <uint M> CE MN<M>& MN<M>::OP--()NE{RE Ref(Mod<M>::m_n < COantsForMod<M>::g_MN_base_mod?((Mod<M>::m_n += M)-= COantsForMod<M>::g_MN_base_mod):Mod<M>::m_n -= COantsForMod<M>::g_MN_base_mod);}TE <uint M> CE MN<M> MN<M>::OP--(int)NE{MN<M> n{*TH};OP--();RE n;}DF_OF_AR_FOR_MN(+,MN<M>(forward<T>(n))+= *TH);DF_OF_AR_FOR_MN(-,MN<M>(forward<T>(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MN(*,MN<M>(forward<T>(n))*= *TH);DF_OF_AR_FOR_MN(/,MN<M>(forward<T>(n)).Invert()*= *TH);TE <uint M> CE MN<M> MN<M>::OP<<(int n)CO NE{RE MO(MN<M>(*TH)<<= n);}TE <uint M> CE MN<M> MN<M>::OP>>(int n)CO NE{RE MO(MN<M>(*TH)>>= n);}TE <uint M> CE MN<M> MN<M>::OP-()CO NE{RE MO(MN<M>(*TH).SignInvert());}TE <uint M> CE MN<M>& MN<M>::SignInvert()NE{RE Ref(Mod<M>::m_n > 0?Mod<M>::m_n = M - Mod<M>::m_n:Mod<M>::m_n);}TE <uint M> CE MN<M>& MN<M>::Double()NE{RE Ref(Mod<M>::Double());}TE <uint M> CE MN<M>& MN<M>::Halve()NE{RE Ref(Mod<M>::Halve());}TE <uint M> CE MN<M>& MN<M>::Invert(){assert(Mod<M>::m_n > 0);RE PositivePW(uint(COantsForMod<M>::g_M_minus_2));}TE <uint M> TE <TY T> CE MN<M>& MN<M>::PositivePW(T&& EX)NE{MN<M> PW{*TH};(--EX)%= COantsForMod<M>::g_M_minus_2;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <uint M> TE <TY T> CE MN<M>& MN<M>::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(Mod<M>::m_n = COantsForMod<M>::g_MN_base_mod):PositivePW(forward<T>(EX));}TE <uint M> TE <TY T> CE MN<M>& MN<M>::PW(T&& EX){bool neg = EX < 0;assert(!(neg && Mod<M>::m_n == 0));RE neg?PositivePW(forward<T>(EX *= COantsForMod<M>::g_M_minus_2_neg)):NonNegativePW(forward<T>(EX));}TE <uint M> CE uint MN<M>::RP()CO NE{ull m_n_copy = Mod<M>::m_n;RE MO(Reduction(m_n_copy));}TE <uint M> CE Mod<M> MN<M>::Reduce()CO NE{ull m_n_copy = Mod<M>::m_n;RE Mod<M>::DeRP(MO(Reduction(m_n_copy)));}TE <uint M> CE MN<M> MN<M>::DeRP(CRUI n)NE{RE MN<M>(Mod<M>::DeRP(n));}TE <uint M> IN CO MN<M>& MN<M>::Formise(CRUI n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = DeRP(LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::Inverse(CRUI n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>(Mod<M>::Inverse(LE_curr));LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::Factorial(CRUI n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN<M> val_curr{one()};ST MN<M> val_last{one()};WH(LE_curr <= n){memory[LE_curr++] = val_curr *= ++val_last;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::FactorialInverse(CRUI n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN<M> val_curr{one()};ST MN<M> val_last{one()};WH(LE_curr <= n){memory[LE_curr] = val_curr *= Inverse(LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN MN<M> MN<M>::Combination(CRUI n,CRUI i)NE{RE i <= n?Factorial(n)*FactorialInverse(i)*FactorialInverse(n - i):zero();}TE <uint M> IN CO MN<M>& MN<M>::zero()NE{ST CE CO MN<M> z{};RE z;}TE <uint M> IN CO MN<M>& MN<M>::one()NE{ST CE CO MN<M> o{DeRP(1)};RE o;}TE <uint M> TE <TY T> CE MN<M>& MN<M>::Ref(T&& n)NE{RE *TH;}TE <uint M> CE MN<M> Twice(CO MN<M>& n)NE{RE MO(MN<M>(n).Double());}TE <uint M> CE MN<M> Half(CO MN<M>& n)NE{RE MO(MN<M>(n).Halve());}TE <uint M> CE MN<M> Inverse(CO MN<M>& n){RE MO(MN<M>(n).Invert());}TE <uint M,TY T> CE MN<M> PW(MN<M> n,T EX){RE MO(n.PW(EX));}TE <uint M> CE VO swap(MN<M>& n0,MN<M>& n1)NE{n0.swap(n1);}TE <uint M> IN string to_string(CO MN<M>& n)NE{RE to_string(n.RP())+ " + MZ";}TE<uint M,CL Traits> IN basic_istream<char,Traits>& OP>>(basic_istream<char,Traits>& is,MN<M>& n){ll m;is >> m;n = m;RE is;}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO MN<M>& n){RE os << n.RP();}

TE <uint M> CE Mod<M>::Mod()NE:m_n(){}TE <uint M> CE Mod<M>::Mod(CO Mod<M>& n)NE:m_n(n.m_n){}TE <uint M> CE Mod<M>::Mod(Mod<M>& n)NE:m_n(n.m_n){}TE <uint M> CE Mod<M>::Mod(Mod<M>&& n)NE:m_n(MO(n.m_n)){}TE <uint M> TE <SFINAE_FOR_MOD()> CE Mod<M>::Mod(CO T& n)NE:m_n(RS<M>(n)){}TE <uint M> TE <SFINAE_FOR_MOD()> CE Mod<M>::Mod(T& n)NE:m_n(RS<M>(decay_t<T>(n))){}TE <uint M> TE <SFINAE_FOR_MOD()> CE Mod<M>::Mod(T&& n)NE:m_n(RS<M>(forward<T>(n))){}TE <uint M> CE Mod<M>& Mod<M>::OP=(CO Mod<M>& n)NE{RE Ref(m_n = n.m_n);}TE <uint M> CE Mod<M>& Mod<M>::OP=(Mod<M>&& n)NE{RE Ref(m_n = MO(n.m_n));}TE <uint M> CE Mod<M>& Mod<M>::OP+=(CO Mod<M>& n)NE{RE Ref(Normalise(m_n += n.m_n));}TE <uint M> CE Mod<M>& Mod<M>::OP-=(CO Mod<M>& n)NE{RE Ref(m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n);}TE <uint M> CE Mod<M>& Mod<M>::OP*=(CO Mod<M>& n)NE{RE Ref(m_n = COantsForMod<M>::g_even?RS<M>(ull(m_n)* n.m_n):MN<M>::MU(m_n,n.m_n));}TE <> CE MP& MP::OP*=(CO MP& n)NE{ull m_n_copy = m_n;RE Ref(m_n = MO((m_n_copy *= n.m_n)< P?m_n_copy:RSP(m_n_copy)));}TE <uint M> IN Mod<M>& Mod<M>::OP/=(CO Mod<M>& n){RE OP*=(Mod<M>(n).Invert());}TE <uint M> CE Mod<M>& Mod<M>::OP<<=(int n)NE{WH(n-- > 0){Normalise(m_n <<= 1);}RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP>>=(int n)NE{WH(n-- > 0){((m_n & 1)== 0?m_n:m_n += M)>>= 1;}RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP++()NE{RE Ref(m_n < COantsForMod<M>::g_M_minus?++m_n:m_n = 0);}TE <uint M> CE Mod<M> Mod<M>::OP++(int)NE{Mod<M> n{*TH};OP++();RE n;}TE <uint M> CE Mod<M>& Mod<M>::OP--()NE{RE Ref(m_n == 0?m_n = COantsForMod<M>::g_M_minus:--m_n);}TE <uint M> CE Mod<M> Mod<M>::OP--(int)NE{Mod<M> n{*TH};OP--();RE n;}DF_OF_CM_FOR_MOD(==);DF_OF_CM_FOR_MOD(!=);DF_OF_CM_FOR_MOD(>);DF_OF_CM_FOR_MOD(>=);DF_OF_CM_FOR_MOD(<);DF_OF_CM_FOR_MOD(<=);DF_OF_AR_FOR_MOD(+,Mod<M>(forward<T>(n))+= *TH);DF_OF_AR_FOR_MOD(-,Mod<M>(forward<T>(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MOD(*,Mod<M>(forward<T>(n))*= *TH);DF_OF_AR_FOR_MOD(/,Mod<M>(forward<T>(n)).Invert()*= *TH);TE <uint M> CE Mod<M> Mod<M>::OP<<(int n)CO NE{RE MO(Mod<M>(*TH)<<= n);}TE <uint M> CE Mod<M> Mod<M>::OP>>(int n)CO NE{RE MO(Mod<M>(*TH)>>= n);}TE <uint M> CE Mod<M> Mod<M>::OP-()CO NE{RE MO(Mod<M>(*TH).SignInvert());}TE <uint M> CE Mod<M>& Mod<M>::SignInvert()NE{RE Ref(m_n > 0?m_n = M - m_n:m_n);}TE <uint M> CE Mod<M>& Mod<M>::Double()NE{RE Ref(Normalise(m_n <<= 1));}TE <uint M> CE Mod<M>& Mod<M>::Halve()NE{RE Ref(((m_n & 1)== 0?m_n:m_n += M)>>= 1);}TE <uint M> IN Mod<M>& Mod<M>::Invert(){assert(m_n > 0);uint m_n_neg;RE m_n < COantsForMod<M>::g_memory_LE?Ref(m_n = Inverse(m_n).m_n):((m_n_neg = M - m_n)< COantsForMod<M>::g_memory_LE)?Ref(m_n = M - Inverse(m_n_neg).m_n):PositivePW(uint(COantsForMod<M>::g_M_minus_2));}TE <> IN Mod<2>& Mod<2>::Invert(){assert(m_n > 0);RE *TH;}TE <uint M> TE <TY T> CE Mod<M>& Mod<M>::PositivePW(T&& EX)NE{Mod<M> PW{*TH};EX--;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <> TE <TY T> CE Mod<2>& Mod<2>::PositivePW(T&& EX)NE{RE *TH;}TE <uint M> TE <TY T> CE Mod<M>& Mod<M>::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(m_n = 1):Ref(PositivePW(forward<T>(EX)));}TE <uint M> TE <TY T> CE Mod<M>& Mod<M>::PW(T&& EX){bool neg = EX < 0;assert(!(neg && Mod<M>::m_n == 0));RE neg?PositivePW(forward<T>(EX *= COantsForMod<M>::g_M_minus_2_neg)):NonNegativePW(forward<T>(EX));}TE <uint M> IN CO Mod<M>& Mod<M>::Inverse(CRUI n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr].m_n = M - MN<M>::MU(memory[M % LE_curr].m_n,M / LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::Factorial(CRUI n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>::Factorial(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::FactorialInverse(CRUI n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>::FactorialInverse(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE <uint M> IN Mod<M> Mod<M>::Combination(CRUI n,CRUI i)NE{RE MN<M>::Combination(n,i).Reduce();}TE <uint M> CE VO Mod<M>::swap(Mod<M>& n)NE{std::swap(m_n,n.m_n);}TE <uint M> CE CRUI Mod<M>::RP()CO NE{RE m_n;}TE <uint M> CE Mod<M> Mod<M>::DeRP(CRUI n)NE{Mod<M> n_copy{};n_copy.m_n = n;RE n_copy;}TE <uint M> CE uint& Mod<M>::Normalise(uint& n)NE{RE n < M?n:n -= M;}TE <uint M> IN CO Mod<M>& Mod<M>::zero()NE{ST CE CO Mod<M> z{};RE z;}TE <uint M> IN CO Mod<M>& Mod<M>::one()NE{ST CE CO Mod<M> o{DeRP(1)};RE o;}TE <uint M> TE <TY T> CE Mod<M>& Mod<M>::Ref(T&& n)NE{RE *TH;}TE <uint M> CE Mod<M> Twice(CO Mod<M>& n)NE{RE MO(Mod<M>(n).Double());}TE <uint M> CE Mod<M> Half(CO Mod<M>& n)NE{RE MO(Mod<M>(n).Halve());}TE <uint M> IN Mod<M> Inverse(CO Mod<M>& n){RE MO(Mod<M>(n).Invert());}TE <uint M> CE Mod<M> Inverse_COrexpr(CRUI n)NE{RE MO(Mod<M>::DeRP(RS<M>(n)).NonNegativePW(M - 2));}TE <uint M,TY T> CE Mod<M> PW(Mod<M> n,T EX){RE MO(n.PW(EX));}TE <TY T>CE Mod<2> PW(Mod<2> n,const T& p){RE p == 0?Mod<2>::one():move(n);}TE <uint M> CE VO swap(Mod<M>& n0,Mod<M>& n1)NE{n0.swap(n1);}TE <uint M> IN string to_string(CO Mod<M>& n)NE{RE to_string(n.RP())+ " + MZ";}TE<uint M,CL Traits> IN basic_istream<char,Traits>& OP>>(basic_istream<char,Traits>& is,Mod<M>& n){ll m;is >> m;n = m;RE is;}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO Mod<M>& n){RE os << n.RP();}

// IntervalAddBIT
// c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/IntervalAdd/a.hpp
TE <TY T>CL BIT{PU:int m_SZ;VE<T> m_fenwick;int m_PW;IN BIT(CRI SZ = 0);BIT(CO VE<T>& a);IN BIT<T>& OP=(BIT<T>&& a);IN T Get(CRI i)CO;IN VO Set(CRI i,CO T& n);IN VO Set(CO VE<T>& a);IN VO Initialise(CRI SZ = 0);IN BIT<T>& OP+=(CO VE<T>& a);VO Add(CRI i,CO T& n);IN CO T& LSBSegmentSum(CRI j)CO;T InitialSegmentSum(CRI i_final)CO;IN T IntervalSum(CRI i_start,CRI i_final)CO;int BinarySearch(CO T& n)CO;IN int BinarySearch(CRI i_start,CO T& n)CO;};
TE <TY T> IN BIT<T>::BIT(CRI SZ):m_SZ(SZ),m_fenwick(m_SZ+1),m_PW(1){static_assert(! is_same<T,int>::value);WH(m_PW < m_SZ){m_PW <<= 1;}}TE <TY T>BIT<T>::BIT(CO VE<T>& a):BIT(a.SZ()){for(int j = 1;j <= m_SZ;j++){T& fenwick_j = m_fenwick[j];int i = j - 1;fenwick_j = a[i];int i_lim = j -(j & -j);WH(i > i_lim){fenwick_j += m_fenwick[i];i -=(i & -i);}}}TE <TY T> IN BIT<T>& BIT<T>::OP=(BIT<T>&& a){m_SZ = a.m_SZ;m_fenwick = MO(a.m_fenwick);m_PW = a.m_PW;RE *TH;}TE <TY T> IN T BIT<T>::Get(CRI i)CO{RE IntervalSum(i,i);}TE <TY T> IN VO BIT<T>::Set(CRI i,CO T& n){Add(i,n - IntervalSum(i,i));}TE <TY T> IN VO BIT<T>::Set(CO VE<T>& a){*TH = BIT<T>{a};}TE <TY T> IN VO BIT<T>::Initialise(CRI SZ){*TH = BIT<T>(SZ);}TE <TY T> IN BIT<T>& BIT<T>::OP+=(CO VE<T>&a){ BIT<T> a_copy{ a }; assert(m_SZ == a.m_SZ);for(int i = 1;i <= m_SZ;i++){m_fenwick[i] += a.m_fenwick[i];}RE *TH;}TE <TY T>VO BIT<T>::Add(CRI i,CO T& n){int j = i + 1;WH(j <= m_SZ){m_fenwick[j] += n;j +=(j & -j);}RE;}TE <TY T> IN CO T& BIT<T>::LSBSegmentSum(CRI j)CO{assert(0 < j && j <= m_SZ);RE m_fenwick[j];}TE <TY T>T BIT<T>::InitialSegmentSum(CRI i_final)CO{T sum = 0;int j =(i_final < m_SZ?i_final:m_SZ - 1)+ 1;WH(j > 0){sum += m_fenwick[j];j -= j & -j;}RE sum;}TE <TY T> IN T BIT<T>::IntervalSum(CRI i_start,CRI i_final)CO{RE InitialSegmentSum(i_final)- InitialSegmentSum(i_start - 1);}TE <TY T>int BIT<T>::BinarySearch(CO T& n)CO{int PW = m_PW;int j = 0;T sum{};T sum_next{};WH(PW > 0){int j_next = j | PW;if(j_next < m_SZ){sum_next += m_fenwick[j_next];if(sum_next < n){sum = sum_next;j = j_next;}else{sum_next = sum;}}PW >>= 1;}RE j;}TE <TY T> IN int BIT<T>::BinarySearch(CRI i_start,CO T& n)CO{RE max(i_start,BinarySearch(InitialSegmentSum(i_start)+ n));}
TE <TY T>CL IntervalAddBIT{PU:BIT<T> m_bit_0;BIT<T> m_bit_1;IN IntervalAddBIT(CRI SZ = 0);IN IntervalAddBIT(CO VE<T>& a);IN IntervalAddBIT<T>& OP=(IntervalAddBIT<T>&& a);IN T Get(CRI i)CO;IN VO Set(CRI i,CO T& n);IN VO Set(CO VE<T>& a);IN VO Initialise(CRI SZ = 0);IN IntervalAddBIT<T>& OP+=(CO VE<T>& a);IN VO Add(CRI i,CO T& n);IN VO IntervalAdd(CRI i_start,CRI i_final,CO T& n);IN T InitialSegmentSum(CRI i_final)CO;IN T IntervalSum(CRI i_start,CRI i_final)CO;};
TE <TY T> IN IntervalAddBIT<T>::IntervalAddBIT(CRI SZ):m_bit_0(SZ),m_bit_1(SZ){}TE <TY T> IN IntervalAddBIT<T>::IntervalAddBIT(CO VE<T>& a):m_bit_0(),m_bit_1(){CO int SZ = a.SZ();VE<T> diff(SZ);diff[0]= a[0];for(int i = 1;i < SZ;i++){diff[i] = a[i] - a[i-1];}m_bit_0.Set(diff);for(int i = 1;i < SZ;i++){(diff[i]*= 1 - i)-= a[i];}m_bit_1.Set(diff);}TE <TY T> IN IntervalAddBIT<T>& IntervalAddBIT<T>::OP=(IntervalAddBIT<T>&& a){m_bit_0 = MO(a.m_bit_0);m_bit_1 = MO(a.m_bit_1);}TE <TY T> IN T IntervalAddBIT<T>::Get(CRI i)CO{RE IntervalSum(i,i);}TE <TY T> IN VO IntervalAddBIT<T>::Set(CRI i,CO T& n){Add(i,n - IntervalSum(i,i));}TE <TY T> IN VO IntervalAddBIT<T>::Set(CO VE<T>& a){*TH = IntervalAddBIT<T>(a);}TE <TY T> IN VO IntervalAddBIT<T>::Initialise(CO int& SZ){m_bit_0.Initialise(SZ);m_bit_1.Initialise(SZ);}TE <TY T> IN IntervalAddBIT<T>& IntervalAddBIT<T>::OP+=(CO VE<T>& a){IntervalAddBIT<T> a_copy{a};CO int SZ = a.SZ();for(int i = 1;i < SZ;i++){m_bit_0[i] += a_copy.m_bit_0[i];m_bit_1[i] += a_copy.m_bit_1[i];}RE *TH;}TE <TY T> IN VO IntervalAddBIT<T>::Add(CRI i,CO T& n){IntervalAdd(i,i,n);}TE <TY T> IN VO IntervalAddBIT<T>::IntervalAdd(CRI i_start,CRI i_final,CO T& n){m_bit_0.Add(i_start,-(i_start - 1)* n);m_bit_0.Add(i_final + 1,i_final * n);m_bit_1.Add(i_start,n);m_bit_1.Add(i_final + 1,- n);}TE <TY T> IN T IntervalAddBIT<T>::InitialSegmentSum(CRI i_final)CO{RE m_bit_0.InitialSegmentSum(i_final)+ i_final * m_bit_1.InitialSegmentSum(i_final);}TE <TY T> IN T IntervalAddBIT<T>::IntervalSum(CRI i_start,CRI i_final)CO{RE InitialSegmentSum(i_final)- InitialSegmentSum(i_start - 1);}

// 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

テストケース

ソースコード
