#982907 (C++17) No.2759 Take Pictures, Elements?

提出ソース
結果

問題	No.2759 Take Pictures, Elements?
ユーザー	👑 p-adic
提出日時	2024-05-20 09:58:41
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	82 ms / 2,000 ms
コード長	52,206 bytes
コンパイル時間	4,245 ms
コンパイル使用メモリ	272,428 KB
実行使用メモリ	16,216 KB
最終ジャッジ日時	2024-05-20 09:58:47
合計ジャッジ時間	5,746 ms
ジャッジサーバーID （参考情報）	judge3 / judge2
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	47 ms 15,748 KB
testcase_01	AC	82 ms 16,216 KB
testcase_02	AC	1 ms 6,940 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	13 ms 15,244 KB
testcase_10	AC	13 ms 15,260 KB
testcase_11	AC	12 ms 15,460 KB
testcase_12	AC	12 ms 15,324 KB
testcase_13	AC	12 ms 15,400 KB
testcase_14	AC	14 ms 15,344 KB
testcase_15	AC	14 ms 15,248 KB
testcase_16	AC	14 ms 15,248 KB
testcase_17	AC	13 ms 15,280 KB
testcase_18	AC	14 ms 15,280 KB
testcase_19	AC	14 ms 15,272 KB
testcase_20	AC	18 ms 15,456 KB
testcase_21	AC	2 ms 6,940 KB
testcase_22	AC	2 ms 6,944 KB
testcase_23	AC	2 ms 6,940 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

IN VO Solve()
{
  CIN( int , N , Q );
  CIN_A( int , 0 , N , A );
  CIN_A( int , 1 , Q , B );
  SET_HW( Q + 2 , N );
  vector C( H , vector<int>() );
  FOREQ( q , 0 , Q ){
    FOR( i , 0 , N ){
      if( ( q == 0 && i == 0 ) || ( q > 0 && A[i] == B[q] ) ){
	C[q].push_back( i );
      }
    }
  }
  vector L( Q , vector<int>() );
  auto R = L;
  FOR( q , 0 , Q ){
    int size_n = C[q+1].size() , size_m = C[q].size();
    L[q] = R[q] = vector<int>( W , -1 );
    int n = size_n - 1 , m = size_m - 1;
    while( 0 <= n && 0 <= m ){
      if( C[q+1][n] <= C[q][m] ){
	L[q][C[q][m--]] = C[q+1][n];
      } else {
	n--;
      }
    }
    n = 0 , m = 0;
    while( n < size_n && m < size_m ){
      if( C[q+1][n] <= C[q][m] ){
	n++;
      } else {
	R[q][C[q][m++]] = C[q+1][n];
      }
    }
  }
  T2<int> t_final{ H_minus , 0 };
  auto edge = [&]( const T2<int>& v ){
    auto& [q,i] = v;
    vector<pair<T2<int>,int>> answer{};
    if( q < Q ){
      if( L[q][i] != -1 ){
	answer.push_back( { { q + 1 , L[q][i] } , i - L[q][i] } );
      }
      if( R[q][i] != -1 ){
	answer.push_back( { { q + 1 , R[q][i] } , R[q][i] - i } );
      }
    } else {
      answer.push_back( { t_final , 0 } );
    }
    return answer;
  };
  AcyclicGridGraph agg{ edge };
  auto answer = agg.GetDistance( { { 0 , 0 } } , AdditiveMonoid<int>() , int(1e9) , false );
  RETURN( answer[EnumHW_inv(t_final)] );
}
REPEAT_MAIN(1);

#else // INCLUDE_MAIN

#ifdef INCLUDE_SUB

// COMPAREに使用。圧縮時は削除する。
ll Naive( ll N , ll M , ll 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。
IN VO 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。
IN VO SmallTest()
{
  // CEXPR( int , bound , 10 );
  // FOREQ( N , 0 , bound ){
  //   FOREQ( M , 0 , bound ){
  //     FOREQ( K , 0 , bound ){
  //   	COMPARE( N , M , K );
  //     }
  //   }
  // }
}

// 圧縮時は中身だけ削除する。
IN VO RandomTest()
{
  // CEXPR( int , bound_N , 1e5 ); CIN_ASSERT( N , 1 , bound_N );
  // CEXPR( ll , bound_M , 1e18 ); CIN_ASSERT( M , 1 , bound_M );
  // CEXPR( ll , bound_K , 1e9 ); CIN_ASSERT( K , 1 , bound_K );
  // COMPARE( N , M , N );
}

#define INCLUDE_MAIN
#include __FILE__

#else // INCLUDE_SUB

#ifdef INCLUDE_LIBRARY

/*
AdicExhausiveSearch/BFS (11KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/AdicExhausiveSearch/compress.txt

CommutativeDualSqrtDecomposition (6KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/SqrtDecomposition/Dual/Commutative/compress.txt

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

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

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

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

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

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

IntervalMultiplyLazySqrtDecomposition (18KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/SqrtDecomposition/LazyEvaluation/IntervalMultiply/compress.txt

Knapsack (8KB)
c:/Users/user/Documents/Programming/Mathematics/Combinatorial/KnapsackProblem/compress.txt

MinimumCostFlow/PotentialisedDijkstra/Dijkstra (16KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/Dijkstra/Potentialised/MinimumCostFlow/compress.txt

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

TwoByOneMatrix/TwoByTwoMatrix (9KB)
C:/Users/user/Documents/Programming/Mathematics/LinearAlgebra/TwoByOne/compress.txt

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

// VVV 常設でないライブラリは以下に挿入する。

#ifdef DEBUG
  #include "c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/Acyclic/Double/Grid/a_Body.hpp"
#else
CL LinearEdge{PU:int m_SZ;bool m_directed;IN LinearEdge(CRI SZ,CO bool& directed = true);IN VE<int> OP()(CRI t);};CL LinearGraph:PU Graph<LinearEdge>{PU:IN LinearGraph(CRI SZ,CO bool& directed = true);};
IN LinearEdge::LinearEdge(CRI SZ,CO bool& directed):m_SZ(SZ),m_directed(directed){}IN VE<int> LinearEdge::OP()(CRI t){VE<int> AN{};if(!m_directed && t > 0){AN.push_back(t - 1);}if(t + 1 < m_SZ){AN.push_back(t + 1);}RE AN;}IN LinearGraph::LinearGraph(CRI SZ,CO bool& directed):Graph<LinearEdge>(SZ,LinearEdge(SZ,directed)){}

#define DIJKSTRA_PREP(INITIALISE_PREV)CO U& one = m_M.One();AS(one < infty);auto&& i_start = m_G.Enumeration_inv(t_start);AS(0 <= i_start && i_start < SZ);INITIALISE_PREV;
#define DIJKSTRA_BODY_1(SET_PREV)if(walk_LE == -1){walk_LE = SZ - 1;}weight[i_start]= one;int i = i_start;for(int num = 0;num < walk_LE;num++){CO U& weight_i = weight[i];fixed[i]= true;auto&& edge_i = m_G.Edge(m_G.Enumeration(i));for(auto IT = edge_i.BE(),EN = edge_i.EN();IT != EN;IT++){auto&& j = m_G.Enumeration_inv(IT->first);if(!fixed[j]){CO U& edge_ij = get<1>(*IT);U temp = m_M.Product(weight_i,edge_ij);AS(temp < infty);U& weight_j = weight[j];if(temp < weight_j){SET_PREV;weight_j = MO(temp);}}}U temp = infty;for(int j = 0;j < SZ;j++){if(!fixed[j]){U& weight_j = weight[j];if(weight_j < temp){temp = weight_j;i = j;}}}}
#define DIJKSTRA_BODY_2(CHECK_FINAL,SET_PREV)AS(walk_LE == -1);set<pair<U,int>> vertex{};vertex.insert(pair<U,int>(weight[i_start]= one,i_start));WH(! vertex.empty()){auto BE = vertex.BE();auto[weight_i,i]= *BE;CHECK_FINAL;fixed[i]= true;vertex.erase(BE);auto&& edge_i = m_G.Edge(m_G.Enumeration(i));LI<pair<U,int>> changed_vertex{};for(auto IT = edge_i.BE(),EN = edge_i.EN();IT != EN;IT++){auto&& j = m_G.Enumeration_inv(IT->first);if(!fixed[j]){CO U& edge_ij = get<1>(*IT);U temp = m_M.Product(weight_i,edge_ij);AS(temp < infty);U& weight_j = weight[j];if(temp < weight_j){if(weight_j != infty){vertex.erase(pair<U,int>(weight_j,j));}SET_PREV;changed_vertex.push_back(pair<U,int>(weight_j = MO(temp),j));}}}for(auto IT_changed = changed_vertex.BE(),EN_changed = changed_vertex.EN();IT_changed != EN_changed;IT_changed++){vertex.insert(*IT_changed);}}
#define DIJKSTRA_BODY(INITIALISE_PREV,CHECK_FINAL,SET_PREV)DIJKSTRA_PREP(INITIALISE_PREV);if(many_edges){DIJKSTRA_BODY_1(SET_PREV);}else{DIJKSTRA_BODY_2(CHECK_FINAL,SET_PREV);}
TE <TY GRAPH,TY COMM_MONOID,TY U>CL AbstractDijkstra:PU PointedSet<U>{PU:GRAPH& m_G;COMM_MONOID m_M;IN AbstractDijkstra(GRAPH& G,COMM_MONOID M,CO U& infty);U GetDistance(CO inner_t<GRAPH>& t_start,CO inner_t<GRAPH>& t_final,CO bool& many_edges = true,int walk_LE = -1);VE<U> GetDistance(CO inner_t<GRAPH>& t_start,CO bool& many_edges = true,int walk_LE = -1);VO SetDistance(VE<U>& weight,VE<bool>& fixed,CO inner_t<GRAPH>& t_start,CO bool& many_edges = true,int walk_LE = -1);pair<U,LI<inner_t<GRAPH>>> GetPath(CO inner_t<GRAPH>& t_start,CO inner_t<GRAPH>& t_final,CO bool& many_edges = true,int walk_LE = -1);TE <TE <TY...> TY V> pair<VE<U>,VE<LI<inner_t<GRAPH>>>> GetPath(CO inner_t<GRAPH>& t_start,CO V<inner_t<GRAPH>>& t_finals,CO bool& many_edges = true,int walk_LE = -1);pair<VE<U>,VE<LI<inner_t<GRAPH>>>> GetPath(CO inner_t<GRAPH>& t_start,CO bool& many_edges = true,int walk_LE = -1);};TE <TY GRAPH>CL Dijkstra:PU AbstractDijkstra<GRAPH,AdditiveMonoid<>,ll>{PU:IN Dijkstra(GRAPH& G);};
TE <TY GRAPH,TY COMM_MONOID,TY U> IN AbstractDijkstra<GRAPH,COMM_MONOID,U>::AbstractDijkstra(GRAPH& G,COMM_MONOID M,CO U& infty):PointedSet<U>(infty),m_G(G),m_M(MO(M)){}TE <TY GRAPH> IN Dijkstra<GRAPH>::Dijkstra(GRAPH& G):AbstractDijkstra<GRAPH,AdditiveMonoid<>,ll>(G,AdditiveMonoid<>(),4611686018427387904){}TE <TY GRAPH,TY COMM_MONOID,TY U>U AbstractDijkstra<GRAPH,COMM_MONOID,U>::GetDistance(CO inner_t<GRAPH>& t_start,CO inner_t<GRAPH>& t_final,CO bool& many_edges,int walk_LE){CRI SZ = m_G.SZ();CO U& infty = TH->Infty();VE weight(SZ,infty);VE<bool> fixed(SZ);auto&& i_final = m_G.Enumeration_inv(t_final);DIJKSTRA_BODY(,if(i == i_final){break;},);U AN{MO(weight[i_final])};RE AN;}TE <TY GRAPH,TY COMM_MONOID,TY U>VE<U> AbstractDijkstra<GRAPH,COMM_MONOID,U>::GetDistance(CO inner_t<GRAPH>& t_start,CO bool& many_edges,int walk_LE){CRI SZ = m_G.SZ();CO U& infty = TH->Infty();VE weight(SZ,infty);VE<bool> fixed(SZ);DIJKSTRA_BODY(,,);RE weight;}TE <TY GRAPH,TY COMM_MONOID,TY U>VO AbstractDijkstra<GRAPH,COMM_MONOID,U>::SetDistance(VE<U>& weight,VE<bool>& fixed,CO inner_t<GRAPH>& t_start,CO bool& many_edges,int walk_LE){CRI SZ = m_G.SZ();CO U& infty = TH->Infty();AS(int(weight.SZ())== SZ);AS(int(fixed.SZ())== SZ);DIJKSTRA_BODY(,,);RE;}TE <TY GRAPH,TY COMM_MONOID,TY U>pair<U,LI<inner_t<GRAPH>>> AbstractDijkstra<GRAPH,COMM_MONOID,U>::GetPath(CO inner_t<GRAPH>& t_start,CO inner_t<GRAPH>& t_final,CO bool& many_edges,int walk_LE){CRI SZ = m_G.SZ();CO U& infty = TH->Infty();VE weight(SZ,infty);VE<bool> fixed(SZ);auto&& i_final = m_G.Enumeration_inv(t_final);DIJKSTRA_BODY(VE<int> prev(SZ),if(i == i_final){break;},prev[j]= i);int i = i_final;LI<inner_t<GRAPH>> path{};path.push_back(t_final);if(weight[i]!= infty){WH(i != i_start){i = prev[i];path.push_front(m_G.Enumeration(i));}}U AN{MO(weight[i_final])};RE{MO(AN),MO(path)};}TE <TY GRAPH,TY COMM_MONOID,TY U> TE <TE <TY...> TY V>pair<VE<U>,VE<LI<inner_t<GRAPH>>>> AbstractDijkstra<GRAPH,COMM_MONOID,U>::GetPath(CO inner_t<GRAPH>& t_start,CO V<inner_t<GRAPH>>& t_finals,CO bool& many_edges,int walk_LE){CRI SZ = m_G.SZ();CO U& infty = TH->Infty();VE weight(SZ,infty);VE<bool> fixed(SZ);DIJKSTRA_BODY(VE<int> prev(SZ),,prev[j]= i);CO int path_SZ = t_finals.SZ();VE<LI<inner_t<GRAPH>>> path;path.reserve(path_SZ);for(auto IT = t_finals.BE(),EN = t_finals.EN();IT != EN;IT++){LI<inner_t<GRAPH>> path_j{};CO inner_t<GRAPH>& t_final = *IT;path_j.push_back(t_final);int i = m_G.Enumeration_inv(t_final);if(weight[i]!= infty){WH(i != i_start){i = prev[i];path_j.push_front(m_G.Enumeration(i));}}path.push_back(path_j);}RE{MO(weight),MO(path)};}TE <TY GRAPH,TY COMM_MONOID,TY U>pair<VE<U>,VE<LI<inner_t<GRAPH>>>> AbstractDijkstra<GRAPH,COMM_MONOID,U>::GetPath(CO inner_t<GRAPH>& t_start,CO bool& many_edges,int walk_LE){CRI SZ = m_G.SZ();VE<inner_t<GRAPH>> t_finals(SZ);for(int i = 0;i < SZ;i++){t_finals[i]= i;}RE GetPath(t_start,t_finals,many_edges,walk_LE);}

TE <TY ACYCLIC_GRAPH>VE<inner_t<ACYCLIC_GRAPH>> TopologicalSort(ACYCLIC_GRAPH& G){CRI SZ = G.SZ();VE<inner_t<ACYCLIC_GRAPH>> AN(SZ);VE<bool> edged(SZ),fixed(SZ);int num = SZ - 1;for(int i = 0;i < SZ;i++){if(!fixed[i]){VE<VE<int>> dfs ={{i}};WH(!dfs.empty()){auto& e = dfs.back();if(e.empty()){dfs.pop_back();}else{CRI j = e.back();if(fixed[j]){e.pop_back();}else{auto&& t = G.Enumeration(j);if(edged[j]){fixed[j]= true;AN[num--]= t;e.pop_back();}else{edged[j]= true;auto&& edge_t = G.Edge(t);VE<int> edge_j{};for(auto& u:edge_t){auto&& k = G.Enumeration_inv(u);if(!fixed[k]){edge_j.push_back(k);}}dfs.push_back(MO(edge_j));}}}}}}RE AN;}

TE <TY T1,TY ACYCLIC_GRAPH,TY T2,TY U,TY GRAPH,TY VERTEX>CL AcyclicDoubleGraph{PU:ACYCLIC_GRAPH m_G1;GRAPH m_G2;VERTEX m_vertex;VE<T1> m_top_sort;IN AcyclicDoubleGraph(ACYCLIC_GRAPH G1,GRAPH G2,VERTEX vertex);IN AcyclicDoubleGraph(ACYCLIC_GRAPH G1,GRAPH G2,VERTEX vertex,VE<T1> top_sort);IN CO VE<T1>& GetTopologicalSort()CO NE;TE <TY COMM_MONOID> VE<U> GetDistance(CO VE<pair<T1,T2>>& t_starts,COMM_MONOID M,CO U& infty,CO bool& many_edges = true);};TE <TY ACYCLIC_GRAPH,TY GRAPH,TY VERTEX,TY...Args> AcyclicDoubleGraph(ACYCLIC_GRAPH& G1,GRAPH& G2,VERTEX& vertex,Args&&...)-> AcyclicDoubleGraph<inner_t<ACYCLIC_GRAPH>,ACYCLIC_GRAPH,decldecay_t(declval<inner_t<GRAPH>>().second),decldecay_t(declval<GRAPH>().Edge(declval<inner_t<GRAPH>>()).front().second),GRAPH,VERTEX>;
TE <TY T1,TY ACYCLIC_GRAPH,TY T2,TY U,TY GRAPH,TY VERTEX> IN AcyclicDoubleGraph<T1,ACYCLIC_GRAPH,T2,U,GRAPH,VERTEX>::AcyclicDoubleGraph(ACYCLIC_GRAPH G1,GRAPH G2,VERTEX vertex):AcyclicDoubleGraph(MO(G1),MO(G2),MO(vertex),TopologicalSort(G1)){}TE <TY T1,TY ACYCLIC_GRAPH,TY T2,TY U,TY GRAPH,TY VERTEX> IN AcyclicDoubleGraph<T1,ACYCLIC_GRAPH,T2,U,GRAPH,VERTEX>::AcyclicDoubleGraph(ACYCLIC_GRAPH G1,GRAPH G2,VERTEX vertex,VE<T1> top_sort):m_G1(MO(G1)),m_G2(MO(G2)),m_vertex(MO(vertex)),m_top_sort(MO(top_sort)){ST_AS(is_same_v<T1,inner_t<ACYCLIC_GRAPH>> && is_same_v<pair<T1,T2>,inner_t<GRAPH>> && is_same_v<U,decldecay_t(declval<GRAPH>().Edge(declval<inner_t<GRAPH>>()).front().second)> && is_invocable_v<VERTEX,CO T1&>);}TE <TY T1,TY ACYCLIC_GRAPH,TY T2,TY U,TY GRAPH,TY VERTEX> IN CO VE<T1>& AcyclicDoubleGraph<T1,ACYCLIC_GRAPH,T2,U,GRAPH,VERTEX>::GetTopologicalSort()CO NE{RE m_top_sort;}TE <TY T1,TY ACYCLIC_GRAPH,TY T2,TY U,TY GRAPH,TY VERTEX> TE <TY COMM_MONOID> VE<U> AcyclicDoubleGraph<T1,ACYCLIC_GRAPH,T2,U,GRAPH,VERTEX>::GetDistance(CO VE<pair<T1,T2>>& t_starts,COMM_MONOID M,CO U& infty,CO bool& many_edges){VE<U> weight(m_G2.SZ(),infty);if(t_starts.empty()){RE weight;}for(auto& t:t_starts){auto&& i = m_G2.Enumeration_inv(t);weight[i]= M.One();}VE<bool> found(m_G2.SZ());CRI G1_SZ = m_G1.SZ();auto& t_start = t_starts[0];for(int num = 0;num < G1_SZ;num++){CO T1& t1 = m_top_sort[num];auto&& V_t1 = m_vertex(t1);US path_type = pair<pair<T1,T2>,U>;VE<path_type> inits{};for(auto& t2:V_t1){pair<T1,T2> t{t1,t2};auto&& j = m_G2.Enumeration_inv(t);if(weight[j]!= infty){inits.push_back({MO(t),weight[j]});found[j]= false;weight[j]= infty;}}auto edge =[&](CO pair<T1,T2>& t){RE t.first == t1?m_G2.Edge(t):t == t_start?inits:VE<path_type>();};auto graph = m_G2.GetGraph(MO(edge));AbstractDijkstra dijk{graph,M,infty};dijk.SetDistance(weight,found,t_start,many_edges,many_edges?max(int(V_t1.SZ())- 1,0):-1);}RE weight;}

TE <TY E>CL AcyclicGridGraph:PU AcyclicDoubleGraph<int,LinearGraph,int,decldecay_t(declval<E>()({0,0}).front().second),GridGraph<E>,VE<int>(&)(CRI)>{PU:IN AcyclicGridGraph(E e);};
IN VE<int> GridVertex(CRI i){RE id<>(W);}TE <TY E> IN AcyclicGridGraph<E>::AcyclicGridGraph(E e):AcyclicDoubleGraph<int,LinearGraph,int,decldecay_t(declval<E>()({0,0}).front().second),GridGraph<E>,VE<int>(&)(CRI)>(LinearGraph(H),GridGraph(MO(e)),GridVertex){}
#endif

// 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

#ifndef DEBUG
  #pragma GCC optimize ( "O3" )
  #pragma GCC optimize ( "unroll-loops" )
  #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
  #define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if CE( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN
  #define DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE1 )
  #define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) )
  #define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX )
  #define SOLVE_ONLY 
  #define CERR( ... ) 
  #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
  #define CERR_A( A , N ) 
  #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL
  #define CERR_ITR( A ) 
  #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL
#endif
#ifdef REACTIVE
  #define ENDL endl
#else
  #define ENDL "\n"
#endif
#ifdef USE_GETLINE
  #define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); }
  #define GETLINE_SEPARATE( SEPARATOR , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
  #define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#else
  #define SET_LL( A ) cin >> A
  #define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
  #define SET_A( I , N , ... ) SOLVE_ONLY; VariadicResize( N + I , __VA_ARGS__ ); FOR( VARIABLE_FOR_SET_A , 0 , N ){ VariadicSet( cin , VARIABLE_FOR_SET_A + I , __VA_ARGS__ ); }
  #define CIN_A( LL , I , N , ... ) VE<LL> __VA_ARGS__; SET_A( I , N , __VA_ARGS__ )
#endif
#include <bits/stdc++.h>
using namespace std;
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define FINISH_MAIN REPEAT( test_case_num ){ if CE( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } }
#define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now()
#define CURRENT_TIME static_cast<double>( chrono::duration_cast<chrono::microseconds>( chrono::system_clock::now() - watch ).count() / 1000.0 )
#define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 )
#define CEXPR( LL , BOUND , VALUE ) CE LL BOUND = VALUE
#define SET_A_ASSERT( N , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A] , MIN , MAX ); }
#define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define CIN_A_ASSERT( N , A , MIN , MAX ) vector<decldecay_t( MAX )> A( N ); SET_A_ASSERT( N , 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 ITR( ARRAY ) auto begin_ ## ARRAY = ARRAY .BE() , itr_ ## ARRAY = begin_ ## ARRAY , end_ ## ARRAY = ARRAY .EN()
#define FOR_ITR( ARRAY ) for( ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define RUN( VAR , ... ) for( auto&& VAR : __VA_ARGS__ )
#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 RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); RE
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ RE; }

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

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

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

// 単調増加の時にEXPRESSION >= CO_TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , >= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 )
// 単調増加の時にEXPRESSION <= CO_TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , > , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 )
// 単調減少の時にEXPRESSION >= CO_TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , < , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 )
// 単調減少の時にEXPRESSION <= CO_TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , <= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 )

// 尺取り法用
// VAR_TPA_LとVAR_TPA_RをINITで初期化し、VAR_TPA_RがCONTINUE_CONDITIONを満たす限り、
// 閉区間[VAR_TPA_L,VAR_TPA_R]が条件ON_CONDITIONを満たすか否かを判定し、
// trueになるかVAR_TAR_LがVAR_TAR_Rに追い付くまでVAR_TPA_Lの更新操作UPDATE_Lを繰り返し、
// その後VAR_TPA_Rの更新操作UPDATE_Rを行う。
// ON_CONDITIONがtrueとなる極大閉区間とその時点でのINFOをANSWERに格納する。
#define TPA( ANSWER , VAR_TPA , INIT , CONTINUE_CONDITION , UPDATE_L , UPDATE_R , ON_CONDITION , INFO ) \
  VE<tuple<decldecay_t( INIT ),decldecay_t( INIT ),decldecay_t( INFO )>> ANSWER{}; \
  {									\
    auto init_TPA = INIT;						\
    decldecay_t( ANSWER.front() ) ANSWER ## _temp = { init_TPA , init_TPA , INFO }; \
    auto ANSWER ## _prev = ANSWER ## _temp;				\
    auto& VAR_TPA ## _L = get<0>( ANSWER ## _temp );			\
    auto& VAR_TPA ## _R = get<1>( ANSWER ## _temp );			\
    auto& VAR_TPA ## _info = get<2>( ANSWER ## _temp );			\
    bool on_TPA_prev = false;						\
    WH( true ){								\
      bool continuing = CONTINUE_CONDITION;				\
      bool on_TPA = continuing && ( ON_CONDITION );			\
      CERR( continuing ? "尺取り中" : "尺取り終了" , "： [L,R] = [" , VAR_TPA ## _L , "," , VAR_TPA ## _R , "] ," , on_TPA_prev ? "on" : "off" , "->" , on_TPA ? "on" : "off" , ", info =" , VAR_TPA ## _info );	\
      if( on_TPA_prev && ! on_TPA ){					\
	ANSWER.push_back( ANSWER ## _prev );				\
      }									\
      if( continuing ){							\
	if( on_TPA || VAR_TPA ## _L == VAR_TPA ## _R ){			\
	  ANSWER ## _prev = ANSWER ## _temp;				\
	  UPDATE_R;							\
	} else {							\
	  UPDATE_L;							\
	}								\
      } else {								\
	break;								\
      }									\
      on_TPA_prev = on_TPA;						\
    }									\
  }									\

// データ構造用
TE <TY T> IN T Addition(CO T& t0,CO T& t1){RE t0 + t1;}
TE <TY T> IN T Xor(CO T& t0,CO T& t1){RE t0 ^ t1;}
TE <TY T> IN T MU(CO T& t0,CO T& t1){RE t0 * t1;}
TE <TY T> IN CO T& Zero(){ST CO T z{};RE z;}
TE <TY T> IN CO T& One(){ST CO T o = 1;RE o;}TE <TY T> IN T AdditionInv(CO T& t){RE -t;}
TE <TY T> IN T Id(CO T& v){RE v;}
TE <TY T> IN T Min(CO T& a,CO T& b){RE a < b?a:b;}
TE <TY T> IN T Max(CO T& a,CO T& b){RE a < b?b:a;}

// VVV 常設ライブラリは以下に挿入する。
#ifdef DEBUG
  #include "C:/Users/user/Documents/Programming/Contest/Template/include/a_Body.hpp"
#else
// Random（1KB）
ll GetRand(CRI Rand_min,CRI Rand_max){ll AN = time(NULL);RE AN * rand()%(Rand_max + 1 - Rand_min)+ Rand_min;}

// Map (2KB)
#define DC_OF_HASH(...)struct hash<__VA_ARGS__>{IN size_t OP()(CO __VA_ARGS__& n)CO;};
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>US Set = conditional_t<is_COructible_v<unordered_set<T>>,unordered_set<T>,conditional_t<is_ordered::value<T>,set<T>,VO>>;

#define DF_OF_AR_FOR_MAP(MAP,OPR)TE <TY T,TY U> IN MAP<T,U>& OP OPR ## =(MAP<T,U>& a,CO pair<T,U>& v){a[v.first]OPR ## = v.second;RE a;}TE <TY T,TY U> IN MAP<T,U>& OP OPR ## =(MAP<T,U>& a0,CO MAP<T,U>& a1){for(auto&[t,u]:a1){a0[t]OPR ## = u;}RE a0;}TE <TY T,TY U,TY ARG> IN MAP<T,U> OP OPR(MAP<T,U> a,CO ARG& arg){RE MO(a OPR ## = arg);}
#define DF_OF_ARS_FOR_MAP(MAP)DF_OF_AR_FOR_MAP(MAP,+);DF_OF_AR_FOR_MAP(MAP,-);DF_OF_AR_FOR_MAP(MAP,*);DF_OF_AR_FOR_MAP(MAP,/);DF_OF_AR_FOR_MAP(MAP,%);
TE <TY T,TY U>US Map = conditional_t<is_COructible_v<unordered_map<T,int>>,unordered_map<T,U>,conditional_t<is_ordered::value<T>,map<T,U>,VO>>;
DF_OF_ARS_FOR_MAP(map);DF_OF_ARS_FOR_MAP(unordered_map);

// Tuple（3KB）
#define DF_OF_AR_FOR_TUPLE(OPR)TE <TY T,TY U,TE <TY...> TY V> IN auto OP OPR ## =(V<T,U>& t0,CO V<T,U>& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);RE t0;}TE <TY T,TY U,TY V> IN tuple<T,U,V>& OP OPR ## =(tuple<T,U,V>& t0,CO tuple<T,U,V>& t1){get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);RE t0;}TE <TY T,TY U,TY V,TY W> IN tuple<T,U,V,W>& OP OPR ## =(tuple<T,U,V,W>& t0,CO tuple<T,U,V,W>& t1){get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);get<3>(t0)OPR ## = get<3>(t1);RE t0;}TE <TE <TY...> TY V,TY...ARGS> IN auto OP OPR(CO V<ARGS...>& t0,CO V<ARGS...>& t1)-> decldecay_t((get<0>(t0),t0)){auto t = t0;RE MO(t OPR ## = t1);}
#define DF_OF_HASH_FOR_TUPLE(PAIR)TE <TY T,TY U> IN size_t hash<PAIR<T,U>>::OP()(CO PAIR<T,U>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<T> h0;ST CO hash<U> h1;RE(h0(get<0>(n))* seed)^ h1(get<1>(n));}
#define DF_OF_INCREMENT_FOR_TUPLE(INCR)TE <TY T,TY U,TE <TY...> TY V> IN auto OP INCR(V<T,U>& t)-> decldecay_t((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);RE t;}TE <TY T,TY U,TY V> IN tuple<T,U,V>& OP INCR(tuple<T,U,V>& t){INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);RE t;}TE <TY T,TY U,TY V,TY W> IN tuple<T,U,V,W>& OP INCR(tuple<T,U,V,W>& t){INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);INCR get<3>(t);RE t;}
TE <CL Traits,TY T,TY U,TE <TY...> TY V> IN auto OP>>(IS& is,V<T,U>& arg)-> decltype((get<0>(arg),is))&{RE is >> get<0>(arg)>> get<1>(arg);}TE <CL Traits,TY T,TY U,TY V> IN IS& OP>>(IS& is,tuple<T,U,V>& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg);}TE <CL Traits,TY T,TY U,TY V,TY W> IN IS& OP>>(IS& is,tuple<T,U,V,W>& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg)>> get<3>(arg);}TE <CL Traits,TY T,TY U,TE <TY...> TY V> IN auto OP<<(OS& os,CO V<T,U>& arg)-> decltype((get<0>(arg),os))&{RE os << get<0>(arg)<< " " << get<1>(arg);}TE <CL Traits,TY T,TY U,TY V> IN OS& OP<<(OS& os,CO tuple<T,U,V>& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg);}TE <CL Traits,TY T,TY U,TY V,TY W> IN OS& OP<<(OS& os,CO tuple<T,U,V,W>& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg)<< " " << get<3>(arg);}DF_OF_AR_FOR_TUPLE(+);DF_OF_AR_FOR_TUPLE(-);DF_OF_AR_FOR_TUPLE(*);DF_OF_AR_FOR_TUPLE(/);DF_OF_AR_FOR_TUPLE(%);DF_OF_INCREMENT_FOR_TUPLE(++);DF_OF_INCREMENT_FOR_TUPLE(--);
TE <TY T,TY U> DC_OF_HASH(pair<T,U>);TE <TY T,TY U> DC_OF_HASH(tuple<T,U>);TE <TY T,TY U,TY V> DC_OF_HASH(tuple<T,U,V>);TE <TY T,TY U,TY V,TY W> DC_OF_HASH(tuple<T,U,V,W>);
DF_OF_HASH_FOR_TUPLE(pair);DF_OF_HASH_FOR_TUPLE(tuple);TE <TY T,TY U,TY V> IN size_t hash<tuple<T,U,V>>::OP()(CO tuple<T,U,V>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<pair<T,U>> h01;ST CO hash<V> h2;RE(h01({get<0>(n),get<1>(n)})* seed)^ h2(get<2>(n));}TE <TY T,TY U,TY V,TY W> IN size_t hash<tuple<T,U,V,W>>::OP()(CO tuple<T,U,V,W>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<pair<T,U>> h01;ST CO hash<pair<V,W>> h23;RE(h01({get<0>(n),get<1>(n)})* seed)^ h23({get<2>(n),get<3>(n)});}

// Vector（2KB）
#define DF_OF_COUT_FOR_VE(V)TE <CL Traits,TY Arg> IN OS& OP<<(OS& os,CO V<Arg>& arg){auto BE = arg.BE(),EN = arg.EN();auto IT = BE;WH(IT != EN){(IT == BE?os:os << " ")<< *IT;IT++;}RE os;}
#define DF_OF_AR_FOR_VE(V,OPR)TE <TY T> IN V<T>& OP OPR ## =(V<T>& a,CO T& t){for(auto& s:a){s OPR ## = t;}RE a;}TE <TY T> IN V<T>& OP OPR ## =(V<T>& a0,CO V<T>& a1){AS(a0.SZ()<= a1.SZ());auto IT0 = a0.BE(),EN0 = a0.EN();auto IT1 = a1.BE();WH(IT0 != EN0){*(IT0++)OPR ## = *(IT1++);}RE a0;}TE <TY T,TY U> IN V<T> OP OPR(V<T> a,CO U& u){RE MO(a OPR ## = u);}
#define DF_OF_INCREMENT_FOR_VE(V,INCR)TE <TY T> IN V<T>& OP INCR(V<T>& a){for(auto& i:a){INCR i;}RE a;}
#define DF_OF_ARS_FOR_VE(V)DF_OF_AR_FOR_VE(V,+);DF_OF_AR_FOR_VE(V,-);DF_OF_AR_FOR_VE(V,*);DF_OF_AR_FOR_VE(V,/);DF_OF_AR_FOR_VE(V,%);DF_OF_INCREMENT_FOR_VE(V,++);DF_OF_INCREMENT_FOR_VE(V,--)
DF_OF_COUT_FOR_VE(VE);DF_OF_COUT_FOR_VE(LI);DF_OF_COUT_FOR_VE(set);DF_OF_COUT_FOR_VE(unordered_set);DF_OF_ARS_FOR_VE(VE);DF_OF_ARS_FOR_VE(LI);IN VO VariadicResize(CRI SZ){}TE <TY Arg,TY... ARGS> IN VO VariadicResize(CRI SZ,Arg& arg,ARGS&... args){arg.resize(SZ);VariadicResize(SZ,args...);}TE <TY T> VO sort(VE<T>& a,CO bool& reversed = false){if(reversed){ST auto comp =[](CO T& t0,CO T& t1){RE t1 < t0;};sort(a.BE(),a.EN(),comp);}else{sort(a.BE(),a.EN());}}TE <TY V> IN auto Get(V& a){RE[&](CRI i = 0)-> CO decldecay_t(a[0])&{RE a[i];};}TE <TY T = int> IN VE<T> id(CRI SZ){VE<T> AN(SZ);FOR(i,0,SZ){AN[i]= i;}RE AN;}

// StdStream（1KB）
TE <CL Traits> IN IS& VariadicCin(IS& is){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicCin(IS& is,Arg& arg,ARGS&... args){RE VariadicCin(is >> arg,args...);}TE <CL Traits> IN IS& VariadicSet(IS& is,CRI i){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicSet(IS& is,CRI i,Arg& arg,ARGS&... args){RE VariadicSet(is >> arg[i],i,args...);}TE <CL Traits> IN IS& VariadicGetline(IS& is,CO char& separator){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicGetline(IS& is,CO char& separator,Arg& arg,ARGS&... args){RE VariadicGetline(getline(is,arg,separator),separator,args...);}TE <CL Traits,TY Arg> IN OS& VariadicCout(OS& os,CO Arg& arg){RE os << arg;}TE <CL Traits,TY Arg1,TY Arg2,TY... ARGS> IN OS& VariadicCout(OS& os,CO Arg1& arg1,CO Arg2& arg2,CO ARGS&... args){RE VariadicCout(os << arg1 << " ",arg2,args...);}

// Module (6KB)
#define DC_OF_CPOINT(POINT)IN CO U& POINT()CO NE
#define DC_OF_POINT(POINT)IN U& POINT()NE
#define DF_OF_CPOINT(POINT)TE <TY U> IN CO U& VirtualPointedSet<U>::POINT()CO NE{RE Point();}
#define DF_OF_POINT(POINT)TE <TY U> IN U& VirtualPointedSet<U>::POINT()NE{RE Point();}
TE <TY U>CL UnderlyingSet{PU:US type = U;};TE <TY U>CL VirtualPointedSet:VI PU UnderlyingSet<U>{PU:VI CO U& Point()CO NE = 0;VI U& Point()NE = 0;DC_OF_CPOINT(Unit);DC_OF_CPOINT(Zero);DC_OF_CPOINT(One);DC_OF_CPOINT(Infty);DC_OF_POINT(init);DC_OF_POINT(root);};TE <TY U>CL PointedSet:VI PU VirtualPointedSet<U>{PU:U m_b_U;IN PointedSet(U b_u = U());IN CO U& Point()CO NE;IN U& Point()NE;};TE <TY U>CL VirtualNSet:VI PU UnderlyingSet<U>{PU:VI U Transfer(CO U& u)= 0;IN U Inverse(CO U& u);};TE <TY U,TY F_U>CL AbstractNSet:VI PU VirtualNSet<U>{PU:F_U m_f_U;IN AbstractNSet(F_U f_U);IN AbstractNSet<U,F_U>& OP=(CO AbstractNSet&)NE;IN U Transfer(CO U& u);};TE <TY U>CL VirtualMagma:VI PU UnderlyingSet<U>{PU:VI U Product(U u0,CO U& u1)= 0;IN U Sum(U u0,CO U& u1);};TE <TY U = ll>CL AdditiveMagma:VI PU VirtualMagma<U>{PU:IN U Product(U u0,CO U& u1);};TE <TY U = ll>CL MultiplicativeMagma:VI PU VirtualMagma<U>{PU:IN U Product(U u0,CO U& u1);};TE <TY U,TY M_U>CL AbstractMagma:VI PU VirtualMagma<U>{PU:M_U m_m_U;IN AbstractMagma(M_U m_U);IN AbstractMagma<U,M_U>& OP=(CO AbstractMagma<U,M_U>&)NE;IN U Product(U u0,CO U& u1);};
TE <TY U> IN PointedSet<U>::PointedSet(U b_U):m_b_U(MO(b_U)){}TE <TY U> IN CO U& PointedSet<U>::Point()CO NE{RE m_b_U;}TE <TY U> IN U& PointedSet<U>::Point()NE{RE m_b_U;}DF_OF_CPOINT(Unit);DF_OF_CPOINT(Zero);DF_OF_CPOINT(One);DF_OF_CPOINT(Infty);DF_OF_POINT(init);DF_OF_POINT(root);TE <TY U,TY F_U> IN AbstractNSet<U,F_U>::AbstractNSet(F_U f_U):m_f_U(MO(f_U)){ST_AS(is_invocable_r_v<U,F_U,U>);}TE <TY U,TY F_U> IN AbstractNSet<U,F_U>& AbstractNSet<U,F_U>::operator=(CO AbstractNSet<U,F_U>&)NE{RE *TH;}TE <TY U,TY F_U> IN U AbstractNSet<U,F_U>::Transfer(CO U& u){RE m_f_U(u);}TE <TY U> IN U VirtualNSet<U>::Inverse(CO U& u){RE Transfer(u);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>::AbstractMagma(M_U m_U):m_m_U(MO(m_U)){ST_AS(is_invocable_r_v<U,M_U,U,U>);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>& AbstractMagma<U,M_U>::OP=(CO AbstractMagma<U,M_U>&)NE{RE *TH;}TE <TY U> IN U AdditiveMagma<U>::Product(U u0,CO U& u1){RE MO(u0 += u1);}TE <TY U> IN U MultiplicativeMagma<U>::Product(U u0,CO U& u1){RE MO(u0 *= u1);}TE <TY U,TY M_U> IN U AbstractMagma<U,M_U>::Product(U u0,CO U& u1){RE m_m_U(MO(u0),u1);}TE <TY U> IN U VirtualMagma<U>::Sum(U u0,CO U& u1){RE Product(MO(u0),u1);}

TE <TY U>CL VirtualMonoid:VI PU VirtualMagma<U>,VI PU VirtualPointedSet<U>{};TE <TY U = ll>CL AdditiveMonoid:VI PU VirtualMonoid<U>,PU AdditiveMagma<U>,PU PointedSet<U>{};TE <TY U = ll>CL MultiplicativeMonoid:VI PU VirtualMonoid<U>,PU MultiplicativeMagma<U>,PU PointedSet<U>{PU:IN MultiplicativeMonoid(U e_U);};TE <TY U,TY M_U>CL AbstractMonoid:VI PU VirtualMonoid<U>,PU AbstractMagma<U,M_U>,PU PointedSet<U>{PU:IN AbstractMonoid(M_U m_U,U e_U);};
TE <TY U> IN MultiplicativeMonoid<U>::MultiplicativeMonoid(U e_U):PointedSet<U>(MO(e_U)){}TE <TY U,TY M_U> IN AbstractMonoid<U,M_U>::AbstractMonoid(M_U m_U,U e_U):AbstractMagma<U,M_U>(MO(m_U)),PointedSet<U>(MO(e_U)){}

TE <TY U>CL VirtualGroup:VI PU VirtualMonoid<U>,VI PU VirtualPointedSet<U>,VI PU VirtualNSet<U>{};TE <TY U = ll>CL AdditiveGroup:VI PU VirtualGroup<U>,PU AdditiveMonoid<U>{PU:IN U Transfer(CO U& u);};TE <TY U,TY M_U,TY I_U>CL AbstractGroup:VI PU VirtualGroup<U>,PU AbstractMonoid<U,M_U>,PU AbstractNSet<U,I_U>{PU:IN AbstractGroup(M_U m_U,U e_U,I_U i_U);};
TE <TY U,TY M_U,TY I_U> IN AbstractGroup<U,M_U,I_U>::AbstractGroup(M_U m_U,U e_U,I_U i_U):AbstractMonoid<U,M_U>(MO(m_U),MO(e_U)),AbstractNSet<U,I_U>(MO(i_U)){}TE <TY U> IN U AdditiveGroup<U>::Transfer(CO U& u){RE -u;}

TE <TY R,TY U>CL VirtualRSet:VI PU UnderlyingSet<U>{PU:VI U Action(CO R& r,U u)= 0;IN U PW(U u,CO R& r);IN U ScalarProduct(CO R& r,U u);};TE <TY U,TY MAGMA>CL RegularRSet:VI PU VirtualRSet<U,U>,PU MAGMA{PU:IN RegularRSet(MAGMA magma);IN U Action(CO U& r,U u);};TE <TY MAGMA> RegularRSet(MAGMA magma)-> RegularRSet<inner_t<MAGMA>,MAGMA>;TE <TY R,TY U,TY O_U>CL AbstractRSet:VI PU VirtualRSet<R,U>{PU:O_U m_o_U;IN AbstractRSet(CO R& dummy0,CO U& dummy1,O_U o_U);IN AbstractRSet<R,U,O_U>& OP=(CO AbstractRSet<R,U,O_U>&)NE;IN U Action(CO R& r,U u);};TE <TY R,TY U,TY O_U,TY GROUP>CL AbstractModule:PU AbstractRSet<R,U,O_U>,PU GROUP{PU:IN AbstractModule(CO R& dummy,O_U o_U,GROUP M);};TE <TY R,TY O_U,TY GROUP> AbstractModule(CO R& dummy,O_U o_U,GROUP M)-> AbstractModule<R,inner_t<GROUP>,O_U,GROUP>;TE <TY R,TY U>CL Module:VI PU VirtualRSet<R,U>,PU AdditiveGroup<U>{PU:IN U Action(CO R& r,U u);};
TE <TY R,TY MAGMA> IN RegularRSet<R,MAGMA>::RegularRSet(MAGMA magma):MAGMA(MO(magma)){}TE <TY R,TY U,TY O_U> IN AbstractRSet<R,U,O_U>::AbstractRSet(CO R& dummy0,CO U& dummy1,O_U o_U):m_o_U(MO(o_U)){ST_AS(is_invocable_r_v<U,O_U,R,U>);}TE <TY R,TY U,TY O_U,TY GROUP> IN AbstractModule<R,U,O_U,GROUP>::AbstractModule(CO R& dummy,O_U o_U,GROUP M):AbstractRSet<R,U,O_U>(dummy,M.One(),MO(o_U)),GROUP(MO(M)){ST_AS(is_same_v<U,inner_t<GROUP>>);}TE <TY R,TY U,TY O_U> IN AbstractRSet<R,U,O_U>& AbstractRSet<R,U,O_U>::OP=(CO AbstractRSet<R,U,O_U>&)NE{RE *TH;}TE <TY U,TY MAGMA> IN U RegularRSet<U,MAGMA>::Action(CO U& r,U u){RE TH->Product(r,MO(u));}TE <TY R,TY U,TY O_U> IN U AbstractRSet<R,U,O_U>::Action(CO R& r,U u){RE m_o_U(r,MO(u));}TE <TY R,TY U> IN U Module<R,U>::Action(CO R& r,U u){RE MO(u *= r);}TE <TY R,TY U> IN U VirtualRSet<R,U>::PW(U u,CO R& r){RE Action(r,MO(u));}TE <TY R,TY U> IN U VirtualRSet<R,U>::ScalarProduct(CO R& r,U u){RE Action(r,MO(u));}

// Graph (5KB)
TE <TY T,TY R1,TY R2,TY E>CL VirtualGraph:VI PU UnderlyingSet<T>{PU:VI R1 Enumeration(CRI i)= 0;IN R2 Enumeration_inv(CO T& t);TE <TY PATH> IN R2 Enumeration_inv(CO PATH& p);IN VO Reset();VI CRI SZ()CO NE = 0;VI E& edge()NE = 0;VI ret_t<E,T> Edge(CO T& t)= 0;TE <TY PATH> IN ret_t<E,T> Edge(CO PATH& p);ST IN CO T& Vertex(CO T& t)NE;TE <TY PATH> ST IN CO T& Vertex(CO PATH& e)NE;VI R2 Enumeration_inv_Body(CO T& t)= 0;};TE <TY T,TY R1,TY R2,TY E>CL EdgeImplimentation:VI PU VirtualGraph<T,R1,R2,E>{PU:int m_SZ;E m_edge;IN EdgeImplimentation(CRI SZ,E edge);IN CRI SZ()CO NE;IN E& edge()NE;IN ret_t<E,T> Edge(CO T& t);};TE <TY E>CL Graph:PU EdgeImplimentation<int,CRI,CRI,E>{PU:IN Graph(CRI SZ,E edge);IN CRI Enumeration(CRI i);TE <TY F> IN Graph<F> GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CRI t);};TE <TY T,TY Enum_T,TY Enum_T_inv,TY E>CL EnumerationGraph:PU EdgeImplimentation<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>{PU:Enum_T m_enum_T;Enum_T_inv m_enum_T_inv;IN EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge);IN ret_t<Enum_T,int> Enumeration(CRI i);TE <TY F> IN EnumerationGraph<T,Enum_T,Enum_T_inv,F> GetGraph(F edge)CO;IN ret_t<Enum_T_inv,T> Enumeration_inv_Body(CO T& t);};TE <TY Enum_T,TY Enum_T_inv,TY E> EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge)-> EnumerationGraph<decldecay_t(declval<Enum_T>()(0)),Enum_T,Enum_T_inv,E>;TE <TY T,TY E>CL MemorisationGraph:PU EdgeImplimentation<T,T,CRI,E>{PU:int m_LE;VE<T> m_memory;Map<T,int> m_memory_inv;IN MemorisationGraph(CRI SZ,CO T& dummy,E edge);IN T Enumeration(CRI i);IN VO Reset();TE <TY F> IN MemorisationGraph<T,F> GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CO T& t);};
TE <TY T,TY R1,TY R2,TY E> IN EdgeImplimentation<T,R1,R2,E>::EdgeImplimentation(CRI SZ,E edge):m_SZ(SZ),m_edge(MO(edge)){ST_AS(is_COructible_v<T,R1> && is_COructible_v<int,R2> && is_invocable_v<E,T>);}TE <TY E> IN Graph<E>::Graph(CRI SZ,E edge):EdgeImplimentation<int,CRI,CRI,E>(SZ,MO(edge)){}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN EnumerationGraph<T,Enum_T,Enum_T_inv,E>::EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge):EdgeImplimentation<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>(SZ,MO(edge)),m_enum_T(MO(enum_T)),m_enum_T_inv(MO(enum_T_inv)){}TE <TY T,TY E> IN MemorisationGraph<T,E>::MemorisationGraph(CRI SZ,CO T& dummy,E edge):EdgeImplimentation<T,T,CRI,E>(SZ,MO(edge)),m_LE(),m_memory(),m_memory_inv(){ST_AS(is_invocable_v<E,T>);}TE <TY E> IN CRI Graph<E>::Enumeration(CRI i){RE i;}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN ret_t<Enum_T,int> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration(CRI i){RE m_enum_T(i);}TE <TY T,TY E> IN T MemorisationGraph<T,E>::Enumeration(CRI i){AS(0 <= i && i < m_LE);RE m_memory[i];}TE <TY T,TY R1,TY R2,TY E> IN R2 VirtualGraph<T,R1,R2,E>::Enumeration_inv(CO T& t){RE Enumeration_inv_Body(t);}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN R2 VirtualGraph<T,R1,R2,E>::Enumeration_inv(CO PATH& p){RE Enumeration_inv_Body(get<0>(p));}TE <TY E> IN CRI Graph<E>::Enumeration_inv_Body(CRI i){RE i;}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN ret_t<Enum_T_inv,T> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration_inv_Body(CO T& t){RE m_enum_T_inv(t);}TE <TY T,TY E> IN CRI MemorisationGraph<T,E>::Enumeration_inv_Body(CO T& t){if(m_memory_inv.count(t)== 0){AS(m_LE < TH->SZ());m_memory.push_back(t);RE m_memory_inv[t]= m_LE++;}RE m_memory_inv[t];}TE <TY T,TY R1,TY R2,TY E> VO VirtualGraph<T,R1,R2,E>::Reset(){}TE <TY T,TY E> IN VO MemorisationGraph<T,E>::Reset(){m_LE = 0;m_memory.clear();m_memory_inv.clear();}TE <TY T,TY R1,TY R2,TY E> IN CRI EdgeImplimentation<T,R1,R2,E>::SZ()CO NE{RE m_SZ;}TE <TY T,TY R1,TY R2,TY E> IN E& EdgeImplimentation<T,R1,R2,E>::edge()NE{RE m_edge;}TE <TY T,TY R1,TY R2,TY E> IN ret_t<E,T> EdgeImplimentation<T,R1,R2,E>::Edge(CO T& t){RE m_edge(t);}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN ret_t<E,T> VirtualGraph<T,R1,R2,E>::Edge(CO PATH& p){RE Edge(get<0>(p));}TE <TY E> TE <TY F> IN Graph<F> Graph<E>::GetGraph(F edge)CO{RE Graph<F>(TH->SZ(),MO(edge));}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> TE <TY F> IN EnumerationGraph<T,Enum_T,Enum_T_inv,F> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::GetGraph(F edge)CO{RE EnumerationGraph<T,Enum_T,Enum_T_inv,F>(TH->SZ(),m_enum_T,m_enum_T_inv,MO(edge));}TE <TY T,TY E> TE <TY F> IN MemorisationGraph<T,F> MemorisationGraph<T,E>::GetGraph(F edge)CO{RE MemorisationGraph<T,F>(TH->SZ(),MO(edge));}TE <TY T,TY R1,TY R2,TY E> IN CO T& VirtualGraph<T,R1,R2,E>::Vertex(CO T& t)NE{RE t;}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN CO T& VirtualGraph<T,R1,R2,E>::Vertex(CO PATH& e)NE{RE Vertex(get<0>(e));}

// Grid (2KB)
#define SET_GRID H_minus = H - 1;W_minus = W - 1;HW = H * W
#define SET_HW(h,w)H = h;W = w;SET_GRID
#define CIN_HW cin >> H >> W;SET_GRID
TE <TY E>CL GridGraph:PU EnumerationGraph<T2<int>,T2<int>(&)(CRI),int(&)(CO T2<int>&),E>{PU:IN GridGraph(E e);};int H,W,H_minus,W_minus,HW;VE<string> grid;char walkable = '.',unwalkable = '#';
IN T2<int> EnumHW(CRI v){RE{v / W,v % W};}IN int EnumHW_inv(CO T2<int>& ij){auto&[i,j]= ij;RE i * W + j;}TE <TY E> IN GridGraph<E>::GridGraph(E e):EnumerationGraph<T2<int>,T2<int>(&)(CRI),int(&)(CO T2<int>&),E>(HW,EnumHW,EnumHW_inv,MO(e)){AS(H * W == HW);}VE<T2<int>> EdgeOnGrid(CO T2<int>& v){VE<T2<int>> AN{};auto&[i,j]= v;if(i > 0 && grid[i-1][j]== walkable){AN.push_back({i-1,j});}if(i+1 < H && grid[i+1][j]== walkable){AN.push_back({i+1,j});}if(j > 0 && grid[i][j-1]== walkable){AN.push_back({i,j-1});}if(j+1 < W && grid[i][j+1]== walkable){AN.push_back({i,j+1});}RE AN;}VE<pair<T2<int>,ll>> WEdgeOnGrid(CO T2<int>& v){VE<pair<T2<int>,ll>> AN{};auto&[i,j]= v;if(i>0 && grid[i-1][j]== walkable){AN.push_back({{i-1,j},1});}if(i+1 < H && grid[i+1][j]== walkable){AN.push_back({{i+1,j},1});}if(j>0 && grid[i][j-1]== walkable){AN.push_back({{i,j-1},1});}if(j+1 < W && grid[i][j+1]== walkable){AN.push_back({{i,j+1},1});}RE AN;}IN VO SetWallStringOnGrid(CRI i,VE<string>& S){if(S.empty()){S.resize(H);}cin >> S[i];AS(int(S[i].SZ())== W);}CO string direction[4]={"U","R","D","L"};IN int DirectionNumberOnGrid(CRI i,CRI j,CRI k,CRI h){RE i < k?2:i > k?0:j < h?1:(AS(j > h),3);}IN int DirectionNumberOnGrid(CRI v,CRI w){auto[i,j]= EnumHW(v);auto[k,h]= EnumHW(w);RE DirectionNumberOnGrid(i,j,k,h);}IN int ReverseDirectionNumberOnGrid(CRI n){AS(0 <= n && n<4);RE n ^ 2;}

// ConstexprModulo (7KB)
CEXPR(uint,P,998244353);
#define RP Represent
#define DeRP Derepresent

TE <uint M,TY INT> CE INT RS(INT n)NE{RE MO(n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n < INT(M)?n: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 <uint M> CL Mod;TE <uint M>CL COantsForMod{PU:COantsForMod()= delete;ST CE CO uint g_memory_bound = 1e6;ST CE CO uint g_memory_LE = M < g_memory_bound?M:g_memory_bound;ST CE uint g_M_minus = M - 1;ST CE int g_order_minus_1 = M - 2;ST CE int g_order_minus_1_neg = -g_order_minus_1;};
#define DC_OF_CM_FOR_MOD(OPR)CE bool OP OPR(CO Mod<M>& n)CO NE
#define DC_OF_AR_FOR_MOD(OPR,EX)CE Mod<M> OP OPR(Mod<M> n)CO EX;
#define DF_OF_CM_FOR_MOD(OPR)TE <uint M> CE bool Mod<M>::OP OPR(CO Mod<M>& n)CO NE{RE m_n OPR n.m_n;}
#define DF_OF_AR_FOR_MOD(OPR,EX,LEFT,OPR2)TE <uint M> CE Mod<M> Mod<M>::OP OPR(Mod<M> n)CO EX{RE MO(LEFT OPR2 ## = *TH);}TE <uint M,TY T> CE Mod<M> OP OPR(T n0,CO Mod<M>& n1)EX{RE MO(Mod<M>(MO(n0))OPR ## = 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;TE <TY T> CE Mod(T 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/=(Mod<M> n);TE <TY INT> CE Mod<M>& OP<<=(INT n);TE <TY INT> CE Mod<M>& OP>>=(INT n);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(+,NE);DC_OF_AR_FOR_MOD(-,NE);DC_OF_AR_FOR_MOD(*,NE);DC_OF_AR_FOR_MOD(/,);TE <TY INT> CE Mod<M> OP^(INT EX)CO;TE <TY INT> CE Mod<M> OP<<(INT n)CO;TE <TY INT> CE Mod<M> OP>>(INT n)CO;CE Mod<M> OP-()CO NE;CE Mod<M>& SignInvert()NE;IN Mod<M>& Invert();TE <TY INT> CE Mod<M>& PW(INT EX);CE VO swap(Mod<M>& n)NE;CE CRUI RP()CO NE;ST CE Mod<M> DeRP(uint n)NE;ST IN CO Mod<M>& Inverse(CRUI n);ST IN CO Mod<M>& Factorial(CRUI n);ST IN CO Mod<M>& FactorialInverse(CRUI n);ST IN Mod<M> Combination(CRUI n,CRUI i);ST IN CO Mod<M>& zero()NE;ST IN CO Mod<M>& one()NE;TE <TY INT> CE Mod<M>& PositivePW(INT EX)NE;TE <TY INT> CE Mod<M>& NonNegativePW(INT EX)NE;US COants = COantsForMod<M>;};
US MP = Mod<P>;
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(MO(n.m_n)){}TE <uint M> TE <TY T> CE Mod<M>::Mod(T n)NE:m_n(RS<M>(MO(n))){ST_AS(is_COructible_v<uint,decay_t<T> >);}TE <uint M> CE Mod<M>& Mod<M>::OP=(Mod<M> n)NE{m_n = MO(n.m_n);RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP+=(CO Mod<M>& n)NE{(m_n += n.m_n)< M?m_n:m_n -= M;RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP-=(CO Mod<M>& n)NE{m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n;RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP*=(CO Mod<M>& n)NE{m_n = MO(ull(m_n)* n.m_n)% M;RE *TH;}TE <> CE MP& MP::OP*=(CO MP& n)NE{ull m_n_copy = m_n;m_n = MO((m_n_copy *= n.m_n)< P?m_n_copy:RSP(m_n_copy));RE *TH;}TE <uint M> IN Mod<M>& Mod<M>::OP/=(Mod<M> n){RE OP*=(n.Invert());}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::OP<<=(INT n){AS(n >= 0);RE *TH *= Mod<M>(2).NonNegativePW(MO(n));}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::OP>>=(INT n){AS(n >=0);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{m_n < COants::g_M_minus?++m_n:m_n = 0;RE *TH;}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{m_n == 0?m_n = COants::g_M_minus:--m_n;RE *TH;}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(+,NE,n,+);DF_OF_AR_FOR_MOD(-,NE,n.SignInvert(),+);DF_OF_AR_FOR_MOD(*,NE,n,*);DF_OF_AR_FOR_MOD(/,,n.Invert(),*);TE <uint M> TE <TY INT> CE Mod<M> Mod<M>::OP^(INT EX)CO{RE MO(Mod<M>(*TH).PW(MO(EX)));}TE <uint M> TE <TY INT> CE Mod<M> Mod<M>::OP<<(INT n)CO{RE MO(Mod<M>(*TH)<<= MO(n));}TE <uint M> TE <TY INT> CE Mod<M> Mod<M>::OP>>(INT n)CO{RE MO(Mod<M>(*TH)>>= MO(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{m_n > 0?m_n = M - m_n:m_n;RE *TH;}TE <uint M> IN Mod<M>& Mod<M>::Invert(){AS(m_n != 0);uint m_n_neg;RE m_n < COants::g_memory_LE?(m_n = Inverse(m_n).m_n,*TH):((m_n_neg = M - m_n)< COants::g_memory_LE)?(m_n = M - Inverse(m_n_neg).m_n,*TH):NonNegativePW(COants::g_order_minus_1);}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::PositivePW(INT EX)NE{Mod<M> PW{*TH};EX--;WH(EX != 0){(EX & 1)== 1?*TH *= PW:*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::NonNegativePW(INT EX)NE{RE EX == 0?(m_n = 1,*TH):PositivePW(MO(EX));}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::PW(INT EX){bool neg = EX < 0;AS(!(neg && m_n == 0));RE neg?PositivePW(MO(EX *= COants::g_order_minus_1_neg)):NonNegativePW(MO(EX));}TE <uint M> CE VO Mod<M>::swap(Mod<M>& n)NE{std::swap(m_n,n.m_n);}TE <uint M> IN CO Mod<M>& Mod<M>::Inverse(CRUI n){AS(n < COants::g_memory_LE);ST Mod<M> memory[COants::g_memory_LE]={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr].m_n = M - memory[M % LE_curr].m_n * ull(M / LE_curr)% M;LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::Factorial(CRUI n){if(M <= n){RE zero();}AS(n < COants::g_memory_LE);ST Mod<M> memory[COants::g_memory_LE]={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){(memory[LE_curr]= memory[LE_curr - 1])*= LE_curr;LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::FactorialInverse(CRUI n){ST Mod<M> memory[COants::g_memory_LE]={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){(memory[LE_curr]= memory[LE_curr - 1])*= Inverse(LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN Mod<M> Mod<M>::Combination(CRUI n,CRUI i){RE i <= n?Factorial(n)* FactorialInverse(i)* FactorialInverse(n - i):zero();}TE <uint M> CE CRUI Mod<M>::RP()CO NE{RE m_n;}TE <uint M> CE Mod<M> Mod<M>::DeRP(uint n)NE{Mod<M> n_copy{};n_copy.m_n = MO(n);RE n_copy;}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{1};RE o;}TE <uint M> IN Mod<M> Inverse(CO Mod<M>& n){RE MO(Mod<M>(n).Invert());}TE <uint M,TY INT> CE Mod<M> PW(Mod<M> n,INT EX){RE MO(n.PW(MO(EX)));}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())+ " + " + to_string(M)+ "Z";}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();}
#define DF_OF_HASH_FOR_MOD(MOD)IN size_t hash<MOD>::OP()(CO MOD& n)CO{ST CO hash<decldecay_t(n.RP())> h;RE h(n.RP());}
TE <uint M> DC_OF_HASH(Mod<M>); TE <uint M> DF_OF_HASH_FOR_MOD(Mod<M>);
#endif
// 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
