結果
問題 | No.2565 はじめてのおつかい |
ユーザー |
👑 |
提出日時 | 2023-12-02 16:50:15 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 86 ms / 2,000 ms |
コード長 | 63,105 bytes |
コンパイル時間 | 12,395 ms |
コンパイル使用メモリ | 302,028 KB |
最終ジャッジ日時 | 2025-02-18 05:42:27 |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 50 |
コンパイルメッセージ
In file included from main.cpp:263, from main.cpp:616, from main.cpp:946: main.cpp: In function 'void Solve()': main.cpp:79:32: warning: narrowing conversion of 'N' from 'll' {aka 'long long int'} to 'int' [-Wnarrowing] 79 | Dijkstra<E<path>,bound_N> d{ N }; | ^
ソースコード
#ifdef INCLUDE_MAINinline void Solve(){// // 数DEXPR( ll , bound_N , 100000 , 100 ); // 0が5個// // // DEXPR( ll , bound_N , 1000000000 , 100 ); // 0が9個// // // DEXPR( ll , bound_N , 1000000000000000000 , 100 ); // 0が18個// // CEXPR( TYPE_OF( bound_N ) , bound_M , bound_N );// // // DEXPR( ll , bound_M , 100000 , 100 ); // 0が5個// // // DEXPR( ll , bound_M , 1000000000 , 100 ); // 0が9個// // // DEXPR( ll , bound_M , 1000000000000000000 , 100 ); // 0が18個CIN( ll , N , M );// // CIN( ll , M );// // CIN( ll , N , M , K );// // CIN_ASSERT( N , 1 , bound_N ); // ランダムテスト用。上限のデフォルト値は10^5。// // CIN_ASSERT( M , 1 , bound_M ); // ランダムテスト用。上限のデフォルト値は10^5。// ll answer = 0;// // MP answer = 0;// // auto answer = Answer( N , M , K );// // COUT( answer );// RETURN( answer );// // 文字列// CIN( string , S );// // CIN( string , T );// ll answer = 0;// // MP answer = 0;// // auto answer = Answer( N , M , K );// // COUT( answer );// RETURN( answer );// // 配列// CIN_A( ll , A , N );// // CIN_A( ll , B , N );// // vector<ll> A( N );// // vector<ll> B( N );// // ll A[bound_N]; // 関数(コンストラクタ)の引数に使う。長さのデフォルト値は10^5。// // ll B[bound_N]; // 関数(コンストラクタ)の引数に使う。長さのデフォルト値は10^5。// // FOR( i , 0 , N ){// // cin >> A[i] >> B[i];// // }// ll answer = 0;// // MP answer = 0;// // auto answer = Answer( N , M , K );// // COUT( answer );// // COUT_A( A , N );// RETURN( answer );// // 順列// vector<int> A( N );// vector<int> A_inv( N );// FOR( i , 0 , N ){// cin >> A[i];// A_inv[--A[i]] = i;// }// ll answer = 0;// // MP answer = 0;// // auto answer = Answer( N , M , K );// // COUT( answer );// // COUT_A( A , N );// RETURN( answer );// グラフ// e<int>.resize( N );e<path>.resize( N );FOR( j , 0 , M ){CIN_ASSERT( uj , 1 , N );CIN_ASSERT( vj , 1 , N );uj--;vj--;// e<int>[uj].push_back( vj );// e<int>[vj].push_back( uj );// CIN( ll , wj );e<path>[uj].push_back( { vj , 1 } );// e<path>[vj].push_back( { uj , wj } );}Dijkstra<E<path>,bound_N> d{ N };vector<ll> weight;d.Solve( 0 , weight );ll d1 = weight[ N - 2 ];ll d2 = weight[ N - 1 ];d.Solve( N - 2 , weight );ll d3 = weight[ 0 ];ll d4 = weight[ N - 1 ];d.Solve( N - 1 , weight );ll d5 = weight[ 0 ];ll d6 = weight[ N - 2 ];ll answer = d.Infty();if( d1 == d.Infty() ){d1 /= 4;}if( d2 == d.Infty() ){d2 /= 4;}if( d3 == d.Infty() ){d3 /= 4;}if( d4 == d.Infty() ){d4 /= 4;}if( d5 == d.Infty() ){d5 /= 4;}if( d6 == d.Infty() ){d6 /= 4;}ll a[5] = { d1 + d4 + d5 , d2 + d6 + d3 , d1 + d3 + d2 + d5 , d1 + d4 + d6 + d3 , d2 + d6 + d4 + d5 };FOR( i , 0 , 5 ){answer = min( answer , a[i] );}COUT( answer >= d.Infty() / 4 ? -1 : answer );// MP answer = 0;// auto answer = Answer( N , M , K );// COUT( answer );// COUT_A( A , N );// RETURN( answer );// // 座標圧縮や単一クエリタイプなどのための入力格納// vector<T3<ll> > data( M );// FOR( j , 0 , M ){// CIN( ll , x , y , z );// data[j] = { x , y , z };// }// ll answer = 0;// // MP answer = 0;// // auto answer = Answer( N , M , K );// // COUT( answer );// // COUT_A( A , N );// RETURN( answer );// // 一般のクエリ// CIN( int , Q );// // DEXPR( int , bound_Q , 100000 , 100 ); // 基本不要。// // CIN_ASSERT( Q , 1 , bound_Q ); // 基本不要。// // vector<T3<int> > query( Q );// // vector<T2<int> > query( Q );// FOR( q , 0 , Q ){// CIN( int , type );// if( type == 1 ){// CIN( int , x , y );// // query[q] = { type , x , y };// } else if( type == 2 ){// CIN( int , x , y );// // query[q] = { type , x , y };// } else {// CIN( int , x , y );// // query[q] = { type , x , y };// }// // CIN( int , x , y );// // // query[q] = { x , y };// }// // sort( query , query + Q );// // FOR( q , 0 , Q ){// // auto& [x,y] = query[q];// // // auto& [type,x,y] = query[q];// // }// auto answer = Answer( N , M , K );// // COUT( answer );// // COUT_A( A , N );// RETURN( answer );// // グリッド// // DEXPR( int , bound_H , 2000 , 30 );// // // DEXPR( int , bound_H , 100000 , 10 ); // 0が5個// // // CEXPR( int , bound_H , 1000000000 ); // 0が9個// // // CEXPR( int , bound_W , bound_H );// // static_assert( ll( bound_H ) * bound_W < ll( 1 ) << 31 );// // 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// cin >> H >> W;// // SET_ASSERT( H , 1 , bound_H ); // ランダムテスト用。上限のデフォルト値は2*10^3。// // SET_ASSERT( W , 1 , bound_W ); // ランダムテスト用。上限のデフォルト値は2*10^3。// H_minus = H - 1;// W_minus = W - 1;// HW = H * W;// // assert( HW <= bound_HW ); // 基本不要。上限のデフォルト値は4*10^6。// vector<string> S( H );// FOR( i , 0 , H ){// cin >> S[i];// // SetEdgeOnGrid( S[i] , i , e<int> );// // SetWallOnGrid( S[i] , i , non_wall );// }// // {h,w}へデコード: EnumHW( v )// // {h,w}をコード: EnumHW_inv( h , w );// // (i,j)->(k,h)の方向番号を取得: DirectionNumberOnGrid( i , j , k , h );// // v->wの方向番号を取得: DirectionNumberOnGrid( v , w );// // 方向番号の反転U<->D、R<->L: ReverseDirectionNumberOnGrid( n );// ll answer = 0;// // MP answer = 0;// // auto answer = Answer( N , M , K );// // COUT( answer );// // COUT_A( A , N );// RETURN( answer );}REPEAT_MAIN(1);#else // INCLUDE_MAIN#ifdef INCLUDE_SUBtemplate <typename PATH> list<PATH> E( const int& i ){// list<PATH> answer{};list<PATH> answer = e<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;}template <typename T> inline T F( const T& t ){ return f<T>[t]; }template <typename T> inline T G( const int& i ){ return g<T>[i]; }ll Naive( int N , int M , int K ){ll answer = N + M + K;return answer;}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;}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];// }}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.txtCoordinateCompress:c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txtDFSOnTreec:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepthFirstSearch/Tree/a.hppDivisor:c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txtPolynomialc:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txtUnionFindc:/Users/user/Documents/Programming/Utility/VLTree/UnionFindForest/compress.txt*/// VVV 常設でないライブラリは以下に挿入する。#define DIJKSTRA_BODY( SET_FOUND , SET_WEIGHT , UPDATE_FOUND , CHECK_FOUND , INITIALISE_PREV , SET_PREV ) \static const U& unit = Unit(); \assert( unit != m_found && unit < m_infty ); \const int i_start = e_inv( t_start ); \set<pair<U,int> > vertex{}; \SET_FOUND; \SET_WEIGHT; \vertex.insert( pair<U,int>( weight[i_start] = unit , i_start ) ); \INITIALISE_PREV; \\if( i_start != i_final ){ \\while( ! vertex.empty() ){ \\auto itr_vertex = vertex.begin(); \const pair<U,int> v = *itr_vertex; \const int& i = v.second; \\if( i == i_final ){ \\break; \\} \\const U& u = v.first; \UPDATE_FOUND; \vertex.erase( itr_vertex ); \const list<pair<T,U> > edge_i = E( e( i ) ); \list<pair<U,int> > changed_vertex{}; \\for( auto itr_edge_i = edge_i.begin() , end_edge_i = edge_i.end() ; itr_edge_i != end_edge_i ; itr_edge_i++ ){ \\const int& j = e_inv( itr_edge_i->first ); \U& weight_j = weight[j]; \\if( CHECK_FOUND ){ \\const U& edge_ij = itr_edge_i->second; \const U temp = Addition( u , edge_ij ); \assert( edge_ij != m_found && temp != m_found && !( temp < edge_ij ) && temp < m_infty ); \\if( weight_j > temp ){ \\if( weight_j != m_infty ){ \\vertex.erase( pair<U,int>( weight_j , j ) ); \\} \\SET_PREV; \changed_vertex.push_back( pair<U,int>( weight_j = temp , j ) ); \\} \\} \\} \\for( auto itr_changed = changed_vertex.begin() , end_changed = changed_vertex.end() ; itr_changed != end_changed ; itr_changed++ ){ \\vertex.insert( *itr_changed ); \\} \\} \\} \// メモリが不足する場合はEの定義を前計算しないでその都度計算させること。// O((size+|E|)log size)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(size^2)版を検討。template <typename T , typename U , list<pair<T,U> > E(const T&) , int size_max>class DijkstraBody{private:int m_size;U m_infty;U m_found;public:inline DijkstraBody( const int& size , const U& infty , const U& found );// 経路が存在しない場合の返り値はm_inftyU Solve( const T& t_start , const T& t_final );U Solve( const T& t_start , const T& t_final , list<T>& path );void Solve( const T& t_start , vector<U>& weight );void Solve( const T& t_start , vector<U>& weight , list<T> ( &path )[size_max] );const U& Infty() const;private:virtual const U& Unit() const = 0;virtual U Addition( const U& , const U& ) const = 0;virtual T e( const int& i ) = 0;virtual int e_inv( const T& t ) = 0;virtual void Reset() = 0;};// 入力の範囲内で要件// (1) Eの値の各成分の第2成分が0以上である。// (2) 2^{31}-1がEの値の各成分の第2成分size_max個以下の和で表せるいかなる数よりも大きい。// (6) 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((size+|E|)log size)// 単一始点単一終点最短経路探索/経路復元ありO((size+|E|)log size)// 単一始点全終点最短経路探索/経路復元なしO((size+|E|)log size)// 単一始点全終点最短経路探索/経路復元ありO(size^2 + |E| log size)template <list<pair<int,ll> > E(const int&) , int size_max>class Dijkstra :public DijkstraBody<int,ll,E,size_max>{public:inline Dijkstra( const int& size );private:inline const ll& Unit() const;inline ll Addition( const ll& , const ll& ) const;inline int e( const int& i );inline int e_inv( const int& t );inline void Reset();};// 入力の範囲内で要件// (1) Eの値の各成分の第2成分がe_U()以上である。// (2) inftyがEの値の各成分の第2成分size_max個以下の和で表せるいかなる項よりも大きい。// (3) foundがEの値の各成分の第2成分size_max個以下の和で表せず、inftyとも異なる。// (4) (U,m_U:U^2->U,e_U:1->U)がbool operator<(const U&,const U&)に関して全順序モノイドである。// (6) 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((size+|E|)(log size)^2)// 単一始点単一終点最短経路探索/経路復元ありO((size+|E|)(log size)^2)// 単一始点全終点最短経路探索/経路復元なしO((size+|E|)(log size)^2)// 単一始点全終点最短経路探索/経路復元ありO(size^2 log size + |E|(log size)^2)template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max>class MemorisationDijkstra :public DijkstraBody<T,U,E,size_max>{private:int m_length;map<T,int> m_memory;vector<T> m_memory_inv;public:inline MemorisationDijkstra( const int& size , const U& infty = 9223372036854775807 , const U& found = -1 );private:inline const U& Unit() const;inline U Addition( const U& , const U& ) const;inline T e( const int& i );inline int e_inv( const T& t );inline void Reset();};// 入力の範囲内で要件// (1) Eの値の各成分の第2成分がe_U()以上である。// (2) inftyがEの値の各成分の第2成分size_max個以下の和で表せるいかなる項よりも大きい。// (3) foundがEの値の各成分の第2成分size_max個以下の和で表せず、inftyとも異なる。// (4) (U,m_U:U^2->U,e_U:1->U)がbool operator<(const U&,const U&)に関して全順序モノイドである。// (5) (enum_T,enum_T_inv)が互いに逆写像である。// (6) 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((size+|E|)log size)// 単一始点単一終点最短経路探索/経路復元ありO((size+|E|)log size)// 単一始点全終点最短経路探索/経路復元なしO((size+|E|)log size)// 単一始点全終点最短経路探索/経路復元ありO(size^2 + |E| log size)template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max , T enum_T(const int&) ,int enum_T_inv(const T&)>class EnumerationDijkstra :public DijkstraBody<T,U,E,size_max>{public:inline EnumerationDijkstra( const int& size , const U& infty = 9223372036854775807 , const U& found = -1 );private:inline const U& Unit() const;inline U Addition( const U& , const U& ) const;inline T e( const int& i );inline int e_inv( const T& t );inline void Reset();};template <typename T , typename U , list<pair<T,U> > E(const T&) , int size_max> inline DijkstraBody<T,U,E,size_max>::DijkstraBody( const int& size ,const U& infty , const U& found ) : m_size( size ) , m_infty( infty ) , m_found( found ) { static_assert( ! is_same<U,int>::value ); }template <list<pair<int,ll> > E(const int&) , int size_max> inline Dijkstra<E,size_max>::Dijkstra( const int& size ) : DijkstraBody<int,ll,E,size_max>( size , 9223372036854775807 , -1 ) {}template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max> inlineMemorisationDijkstra<T,U,m_U,e_U,E,size_max>::MemorisationDijkstra( const int& size , const U& infty , const U& found ) : DijkstraBody<T,U,E,size_max>( size , infty , found ) , m_length() , m_memory() , m_memory_inv() {}template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max , T enum_T(const int&) ,int enum_T_inv(const T&)> inline EnumerationDijkstra<T,U,m_U,e_U,E,size_max,enum_T,enum_T_inv>::EnumerationDijkstra( const int& size , const U&infty , const U& found ) : DijkstraBody<T,U,E,size_max>( size , infty , found ) {}template <typename T , typename U , list<pair<T,U> > E(const T&) , int size_max>U DijkstraBody<T,U,E,size_max>::Solve( const T& t_start , const T& t_final ){const int i_final = e_inv( t_final ); \DIJKSTRA_BODY( , vector<U> weight( m_size , m_infty ) , weight[i] = m_found , weight_j != m_found , , );Reset();return weight[i_final];}template <typename T , typename U , list<pair<T,U> > E(const T&) , int size_max>U DijkstraBody<T,U,E,size_max>::Solve( const T& t_start , const T& t_final , list<T>& path ){const int i_final = e_inv( t_final ); \DIJKSTRA_BODY( , vector<U> weight( m_size , m_infty ) , weight[i] = m_found , weight_j != m_found , vector<int> prev( m_size ) , prev[j] = i );int i = i_final;while( i != i_start ){path.push_front( e( i ) );i = prev[i];}path.push_front( t_start );Reset();return weight[i_final];}template <typename T , typename U , list<pair<T,U> > E(const T&) , int size_max>void DijkstraBody<T,U,E,size_max>::Solve( const T& t_start , vector<U>& weight ){constexpr const int i_final = -1;DIJKSTRA_BODY( vector<bool> found( m_size ) , weight = vector<U>( m_size , m_infty ) , found[i] = true , !found[j] , , );Reset();return;}template <typename T , typename U , list<pair<T,U> > E(const T&) , int size_max>void DijkstraBody<T,U,E,size_max>::Solve( const T& t_start , vector<U>& weight , list<T> ( &path )[size_max] ){constexpr const int i_final = -1;DIJKSTRA_BODY( vector<bool> found( m_size ) , weight = vector<U>( m_size , m_infty ) , found[i] = true , !found[j] , vector<int> prev( m_size ) ,prev[j] = i );for( int j = 0 ; j < m_size ; j++ ){list<T>& path_j = path[j];int i = j;while( i != i_start ){path_j.push_front( e( i ) );i = prev[i];}path_j.push_front( t_start );}Reset();return;}template <typename T , typename U , list<pair<T,U> > E(const T&) , int size_max> const U& DijkstraBody<T,U,E,size_max>::Infty() const { returnm_infty; }template <list<pair<int,ll> > E(const int&) , int size_max> inline const ll& Dijkstra<E,size_max>::Unit() const { static const ll unit = 0; returnunit; }template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max> inline const U&MemorisationDijkstra<T,U,m_U,e_U,E,size_max>::Unit() const { return e_U(); }template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max , T enum_T(const int&) ,int enum_T_inv(const T&)> inline const U& EnumerationDijkstra<T,U,m_U,e_U,E,size_max,enum_T,enum_T_inv>::Unit() const { return e_U(); }template <list<pair<int,ll> > E(const int&) , int size_max> inline ll Dijkstra<E,size_max>::Addition( const ll& u0 , const ll& u1 ) const { return u0+ u1; }template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max> inline UMemorisationDijkstra<T,U,m_U,e_U,E,size_max>::Addition( const U& u0 , const U& u1 ) const { return m_U( u0 , u1 ); }template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max , T enum_T(const int&) ,int enum_T_inv(const T&)> inline U EnumerationDijkstra<T,U,m_U,e_U,E,size_max,enum_T,enum_T_inv>::Addition( const U& u0 , const U& u1 ) const {return m_U( u0 , u1 ); }template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max> inline TMemorisationDijkstra<T,U,m_U,e_U,E,size_max>::e( const int& i ) { assert( i < m_length ); return m_memory_inv[i]; }template <list<pair<int,ll> > E(const int&) , int size_max> inline int Dijkstra<E,size_max>::e( const int& i ) { return i; }template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max , T enum_T(const int&) ,int enum_T_inv(const T&)> inline T EnumerationDijkstra<T,U,m_U,e_U,E,size_max,enum_T,enum_T_inv>::e( const int& i ) { return enum_T( i ); }template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max> inline intMemorisationDijkstra<T,U,m_U,e_U,E,size_max>::e_inv( const T& t ){using base = DijkstraBody<T,U,E,size_max>;if( m_memory.count( t ) == 0 ){assert( m_length < base::m_size );m_memory_inv.push_back( t );return m_memory[t] = m_length++;}return m_memory[t];}template <list<pair<int,ll> > E(const int&) , int size_max> inline int Dijkstra<E,size_max>::e_inv( const int& t ) { return t; }template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max , T enum_T(const int&) ,int enum_T_inv(const T&)> inline int EnumerationDijkstra<T,U,m_U,e_U,E,size_max,enum_T,enum_T_inv>::e_inv( const T& t ) { return enum_T_inv( t );}template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max> inline voidMemorisationDijkstra<T,U,m_U,e_U,E,size_max>::Reset() { m_length = 0; m_memory.clear(); m_memory_inv.clear(); }template <list<pair<int,ll> > E(const int&) , int size_max> inline void Dijkstra<E,size_max>::Reset() {}template <typename T , typename U , U m_U(const U&,const U&) , const U& e_U() , list<pair<T,U> > E(const T&) , int size_max , T enum_T(const int&) ,int enum_T_inv(const T&)> inline void EnumerationDijkstra<T,U,m_U,e_U,E,size_max,enum_T,enum_T_inv>::Reset() {}// 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// #define REACTIVE// #define USE_GETLINE#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 TYPE_OF( VAR ) decay_t<decltype( VAR )>#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE#define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX )#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )#define 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( 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__ , ":", naive , match ? "==" : "!=" , 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 , constchar& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); }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<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 = ( ( ARGUMENT ) % ( MODULO ) ) % ( MODULO ); \ARGUMENT_FOR_SQUARE_FOR_POWER < 0 ? ARGUMENT_FOR_SQUARE_FOR_POWER += ( MODULO ) : ARGUMENT_FOR_SQUARE_FOR_POWER; \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 ) \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<TYPE_OF( CONST_TARGET ),uint>::value && ! is_same<TYPE_OF( 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 , "<=" , 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 , "<=" , 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> 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 = 0; 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<->Linline 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){constint 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);}}// グラフ用template <typename PATH> vector<list<PATH> > e;template <typename T> map<T,T> f;template <typename T> vector<T> g;// デバッグ用#ifdef DEBUGinline 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_GETLINECEXPR( bool , use_getline , true );#elseCEXPR( bool , use_getline , false );#endif#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。// ConstexprModulo// c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/ConstexprModulo/a.hppCEXPR(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 COull 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);CEMod<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 INMod<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-=(COMN<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 CEuint 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 uintBaseSquareTruncation(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> CET 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_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 uintg_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;STCE 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 uintg_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>>(intn)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 <uintM> 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(CRUIn)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_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> CEMod<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> CEMod<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 && m_n == 0));neg?EX *= COantsForMod<M>::g_M_minus_2_neg:EX;RE m_n == 0?*TH:(EX %= COantsForMod<M>::g_M_minus)== 0?Ref(m_n= 1):PositivePW(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> CEMod<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(CRUIn)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_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.hppTE<int N>CL PWInverse_CE{PU:int m_val;CE PWInverse_CE();};TE<int N>CE PWInverse_CE<N>::PWInverse_CE():m_val(1){WH(m_val < N){m_val <<= 1;}}TE <TY T,int N>CL BIT{PU:T m_fenwick[N + 1];IN BIT();BIT(CO T(&a)[N]);IN T Get(CRI i)CO;IN VO Set(CRI i,CO T& n);IN VO Set(CO T(&a)[N]);IN VOInitialise();IN BIT<T,N>& OP+=(CO T(&a)[N]);VO Add(CRI i,CO T& n);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,int N> IN BIT<T,N>::BIT():m_fenwick(){static_assert(! is_same<T,int>::value);}TE <TY T,int N>BIT<T,N>::BIT(CO T(&a)[N]):m_fenwick(){static_assert(! is_same<T,int>::value);for(int j = 1;j <= N;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,int N> IN T BIT<T,N>::Get(CRI i)CO{RE IntervalSum(i,i);}TE <TY T,int N>IN VO BIT<T,N>::Set(CRI i,CO T& n){Add(i,n - IntervalSum(i,i));}TE <TY T,int N> IN VO BIT<T,N>::Set(CO T(&a)[N]){BIT<T,N> a_copy{a};swap(m_fenwick,a_copy.m_fenwick);}TE <TY T,int N> IN VO BIT<T,N>::Initialise(){for(int j = 1;j <= N;j++){m_fenwick[j] = 0;}}TE <TY T,int N> IN BIT<T,N>& BIT<T,N>::OP+=(CO T(&a)[N]){for(int i = 0;i < N;i++){Add(i,a[i]);}RE *TH;}TE <TY T,int N>VO BIT<T,N>::Add(CRI i,CO T& n){int j = i + 1;WH(j<= N){m_fenwick[j] += n;j +=(j & -j);}RE;}TE <TY T,int N>T BIT<T,N>::InitialSegmentSum(CRI i_final)CO{T sum = 0;int j =(i_final < N?i_final:N - 1)+ 1;WH(j > 0){sum += m_fenwick[j];j -= j & -j;}RE sum;}TE <TY T,int N> IN T BIT<T,N>::IntervalSum(CRI i_start,CRI i_final)CO{REInitialSegmentSum(i_final)- InitialSegmentSum(i_start - 1);}TE <TY T,int N>int BIT<T,N>::BinarySearch(CO T& n)CO{int j = 0;int PW = PWInverse_CE<N>().m_val;T sum{};T sum_next{};WH(PW > 0){int j_next = j | PW;if(j_next < N){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,int N> IN int BIT<T,N>::BinarySearch(CRI i_start,CO T& n)CO{RE max(i_start,BinarySearch(InitialSegmentSum(i_start)+ n));}TE <TY T,int N>CL IntervalAddBIT{PU:BIT<T,N> m_bit_0;BIT<T,N> m_bit_1;IN IntervalAddBIT();IN IntervalAddBIT(CO T(&a)[N]);IN T Get(CRI i)CO;IN VO Set(CRI i,CO T& n);IN VO Set(CO T(&a)[N]);IN VO Initialise();IN IntervalAddBIT<T,N>& OP+=(CO T(&a)[N]);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,int N> IN IntervalAddBIT<T,N>::IntervalAddBIT():m_bit_0(),m_bit_1(){}TE <TY T,int N> IN IntervalAddBIT<T,N>::IntervalAddBIT(CO T(&a)[N]):m_bit_0(),m_bit_1(){OP+=(a);}TE <TY T,int N> IN T IntervalAddBIT<T,N>::Get(CRI i)CO{RE IntervalSum(i,i);}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Set(CRI i,CO T& n){Add(i,n - IntervalSum(i,i));}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Set(CO T(&a)[N]){IntervalAddBIT<T,N> a_copy{a};swap(m_bit_0,a_copy.m_bit_0);swap(m_bit_1,a_copy.m_bit_1);}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Initialise(){m_bit_0.Initialise();m_bit_1.Initialise();}TE <TY T,int N> IN IntervalAddBIT<T,N>& IntervalAddBIT<T,N>::OP+=(CO T(&a)[N]){for(int i = 0;i < N;i++){Add(i,a[i]);}RE *TH;}TE<TY T,int N> IN VO IntervalAddBIT<T,N>::Add(CRI i,CO T& n){IntervalAdd(i,i,n);}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::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,int N> IN T IntervalAddBIT<T,N>::InitialSegmentSum(CRI i_final)CO{RE m_bit_0.InitialSegmentSum(i_final)+ i_final * m_bit_1.InitialSegmentSum(i_final);}TE <TY T,int N> IN T IntervalAddBIT<T,N>::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