結果

問題 No.2101 [Cherry Alpha N] ずっとこの数列だったらいいのに
ユーザー 👑 p-adic
提出日時 2024-04-28 20:43:53
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,050 ms / 6,000 ms
コード長 46,839 bytes
コンパイル時間 16,996 ms
コンパイル使用メモリ 324,652 KB
最終ジャッジ日時 2025-02-21 09:20:55
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 42
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ソースコード

diff #
プレゼンテーションモードにする

#ifndef INCLUDE_MODE
  #define INCLUDE_MODE
  // #define REACTIVE
  // #define USE_GETLINE
#endif
#ifdef INCLUDE_MAIN
IN VO Solve()
{
  CIN( int , N );
  CIN_A( ll , N , A , T );
  CIN( int , Q );
  CIN_A( T3<ll> , Q , query );
  FOR( q , 0 , Q ){
    auto& [t,l,r] = query[q];
    l--; r--;
  }
  TimeSeriesAddBIT bit{ A };
  FOR( i , 0 , N ){
    bit.Set( T[i] - 1 , i , -1 );
    bit.Set( A[i] + T[i] - 1 , i , 0 );
  }
  auto answer = bit.IntervalSum( query );
  FOR( q , 0 , Q ){
    COUT( answer[q] );
  }
}
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
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/SetTheory/DirectProduct/AffineSpace/BIT/TimeSeriesAdd/a_Body.hpp"
#else
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 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 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));}
TE <TY R,TY ABEL_GROUP,TY U,TY R_SET>CL AbstractIntervalRSet:PU VirtualRSet<pair<R,R>,U>,PU R_SET{PU:ABEL_GROUP m_L;IN AbstractIntervalRSet
    (ABEL_GROUP L,R_SET M);IN U Action(CO pair<R,R>& lr,U u);};TE <TY ABEL_GROUP,TY R_SET> AbstractIntervalRSet(ABEL_GROUP,R_SET)-> 
    AbstractIntervalRSet<inner_t<ABEL_GROUP>,ABEL_GROUP,inner_t<R_SET>,R_SET>;TE <TY R,TY U>CL IntervalModule:PU AbstractIntervalRSet<R,AdditiveGroup
    <R>,U,Module<R,U>>{PU:IN IntervalModule();};
TE <TY R,TY ABEL_GROUP,TY U,TY R_SET> IN AbstractIntervalRSet<R,ABEL_GROUP,U,R_SET>::AbstractIntervalRSet(ABEL_GROUP L,R_SET M):R_SET(MO(M)),m_L(MO(L
    )){ST_AS(is_same_v<R,inner_t<ABEL_GROUP>> && is_same_v<U,inner_t<R_SET>>);}TE <TY R,TY U> IntervalModule<R,U>::IntervalModule
    ():AbstractIntervalRSet<R,AdditiveGroup<R>,U,Module<R,U>>(AdditiveGroup<R>(),Module<R,U>()){}TE <TY R,TY ABEL_GROUP,TY U,TY R_SET> IN U 
    AbstractIntervalRSet<R,ABEL_GROUP,U,R_SET>::Action(CO pair<R,R>& lr,U u){RE R_SET::Action(m_L.Sum(lr.second,m_L.Inverse(lr.first)),MO(u));}
#define SFINAE_FOR_BIT_BS enable_if_t<is_invocable_r_v<bool,F,U,int>>*
TE <TY U,TY ABELIAN_GROUP>CL AbstractBIT{PU:ABELIAN_GROUP m_M;int m_SZ;VE<U> m_fenwick;int m_PW;IN AbstractBIT(ABELIAN_GROUP M,CRI SZ = 0);IN 
    AbstractBIT(ABELIAN_GROUP M,CO VE<U>& a);IN AbstractBIT<U,ABELIAN_GROUP>& OP=(AbstractBIT<U,ABELIAN_GROUP>&& bit);TE <TY...Args> IN VO Initialise
    (CO Args&... args);IN VO Set(CRI i,CO U& u);IN AbstractBIT<U,ABELIAN_GROUP>& OP+=(CO VE<U>& a);VO Add(CRI i,CO U& u);IN CRI SZ()CO NE;IN U OP[]
    (CRI i);IN U Get(CRI i);IN CO U& LSBSegmentSum(CRI j)CO;U InitialSegmentSum(CRI i_final);IN U IntervalSum(CRI i_start,CRI i_final);TE <TY F
    ,SFINAE_FOR_BIT_BS = nullptr> int BinarySearch(CO F& f);TE <TY F,SFINAE_FOR_BIT_BS = nullptr> IN int BinarySearch(CRI i_start,CO F& f);IN int 
    BinarySearch(CO U& u);IN int BinarySearch(CRI i_start,CO U& u);IN VO COruct();};TE <TY ABELIAN_GROUP,TY...Args> AbstractBIT(ABELIAN_GROUP M,CO 
    Args&... args)-> AbstractBIT<inner_t<ABELIAN_GROUP>,ABELIAN_GROUP>;TE <TY U = ll>CL BIT:PU AbstractBIT<U,AdditiveGroup<U>>{PU:TE <TY...Args> IN 
    BIT(CO Args&... args);};TE <TY U> BIT(CO VE<U>& a)-> BIT<U>;
TE <TY U,TY ABELIAN_GROUP> IN AbstractBIT<U,ABELIAN_GROUP>::AbstractBIT(ABELIAN_GROUP M,CRI SZ):m_M(MO(M)),m_SZ(SZ),m_fenwick(m_SZ + 1,m_M.Zero
    ()),m_PW(1){COruct();}TE <TY U,TY ABELIAN_GROUP> IN AbstractBIT<U,ABELIAN_GROUP>::AbstractBIT(ABELIAN_GROUP M,CO VE<U>& a):m_M(MO(M)),m_SZ(a.SZ
    ()),m_fenwick(m_SZ + 1,m_M.Zero()),m_PW(1){COruct();for(int j = 1;j <= m_SZ;j++){U& 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_M.Sum(MO(fenwick_j),m_fenwick[i]);i -=(i & -i);}}}TE <TY U,TY ABELIAN_GROUP> IN VO AbstractBIT<U
    ,ABELIAN_GROUP>::COruct(){ST_AS(is_same_v<U,inner_t<ABELIAN_GROUP>>);WH(m_PW < m_SZ){m_PW <<= 1;}}TE <TY U> TE <TY...Args> IN BIT<U>::BIT(CO 
    Args&... args):AbstractBIT<U,AdditiveGroup<U>>(AdditiveGroup<U>(),args...){ST_AS(!is_same_v<U,int>);}TE <TY U,TY ABELIAN_GROUP> IN AbstractBIT<U
    ,ABELIAN_GROUP>& AbstractBIT<U,ABELIAN_GROUP>::OP=(AbstractBIT<U,ABELIAN_GROUP>&& bit){m_SZ = bit.m_SZ;m_fenwick = MO(bit.m_fenwick);m_PW = bit
    .m_PW;RE *TH;}TE <TY U,TY ABELIAN_GROUP> TE <TY...Args> IN VO AbstractBIT<U,ABELIAN_GROUP>::Initialise(CO Args&... args){*TH = AbstractBIT<U
    ,ABELIAN_GROUP>{m_M,args...};}TE <TY U,TY ABELIAN_GROUP> IN VO AbstractBIT<U,ABELIAN_GROUP>::Set(CRI i,CO U& u){Add(i,m_M.Sum(m_M.Inverse
    (IntervalSum(i,i)),u));}TE <TY U,TY ABELIAN_GROUP> IN AbstractBIT<U,ABELIAN_GROUP>& AbstractBIT<U,ABELIAN_GROUP>::OP+=(CO VE<U>& a){AbstractBIT<U
    ,ABELIAN_GROUP> a_copy{m_M,a};AS(m_SZ == a_copy.m_SZ);for(int j = 1;j <= m_SZ;j++){U& fenwick_j = m_fenwick[j];fenwick_j = m_M.Sum(MO(fenwick_j
    ),a.m_fenwick[j]);}RE *TH;}TE <TY U,TY ABELIAN_GROUP>VO AbstractBIT<U,ABELIAN_GROUP>::Add(CRI i,CO U& u){int j = i + 1;WH(j <= m_SZ){U& fenwick_j 
    = m_fenwick[j];fenwick_j = m_M.Sum(MO(fenwick_j),u);j +=(j & -j);}RE;}TE <TY U,TY ABELIAN_GROUP> IN CRI AbstractBIT<U,ABELIAN_GROUP>::SZ()CO 
    NE{RE m_SZ;}TE <TY U,TY ABELIAN_GROUP> IN U AbstractBIT<U,ABELIAN_GROUP>::OP[](CRI i){AS(i < m_SZ);RE IntervalSum(i,i);}TE <TY U,TY ABELIAN_GROUP
    > IN U AbstractBIT<U,ABELIAN_GROUP>::Get(CRI i){RE OP[](i);}TE <TY U,TY ABELIAN_GROUP> IN CO U& AbstractBIT<U,ABELIAN_GROUP>::LSBSegmentSum(CRI j
    )CO{AS(0 < j && j <= m_SZ);RE m_fenwick[j];}TE <TY U,TY ABELIAN_GROUP>U AbstractBIT<U,ABELIAN_GROUP>::InitialSegmentSum(CRI i_final){U sum = m_M
    .Zero();int j = min(i_final + 1,m_SZ);WH(j > 0){sum = m_M.Sum(MO(sum),m_fenwick[j]);j -= j & -j;}RE sum;}TE <TY U,TY ABELIAN_GROUP> IN U 
    AbstractBIT<U,ABELIAN_GROUP>::IntervalSum(CRI i_start,CRI i_final){RE m_M.Sum(m_M.Inverse(InitialSegmentSum(i_start - 1)),InitialSegmentSum
    (i_final));}TE <TY U,TY ABELIAN_GROUP> TE <TY F,SFINAE_FOR_BIT_BS>int AbstractBIT<U,ABELIAN_GROUP>::BinarySearch(CO F& f){int j = 0;int PW = m_PW
    ;U sum = m_M.Zero();U sum_next = sum;WH(PW > 0){int j_next = j | PW;if(j_next <= m_SZ){sum_next = m_M.Sum(MO(sum_next),m_fenwick[j_next]);if(f
    (sum_next,j_next - 1)){sum_next = sum;}else{sum = sum_next;j = j_next;}}PW >>= 1;}RE j;}TE <TY U,TY ABELIAN_GROUP> TE <TY F,SFINAE_FOR_BIT_BS> IN 
    int AbstractBIT<U,ABELIAN_GROUP>::BinarySearch(CRI i_start,CO F& f){CO U u_inv = m_M.Inverse(InitialSegmentSum(i_start - 1));RE max(i_start
    ,BinarySearch([&](CO U& sum,CRI i){RE i_start <= i && f(m_M.Sum(u_inv,sum),i);}));}TE <TY U,TY ABELIAN_GROUP> IN int AbstractBIT<U,ABELIAN_GROUP
    >::BinarySearch(CO U& u){RE BinarySearch([&](CO U& sum,CRI){RE !(sum < u);});}TE <TY U,TY ABELIAN_GROUP> IN int AbstractBIT<U,ABELIAN_GROUP
    >::BinarySearch(CRI i_start,CO U& u){RE max(i_start,BinarySearch(m_M.Sum(InitialSegmentSum(i_start - 1),u)));}
TE <TY R,TY U,TY C_MODULE>CL AbstractTimeSeriesAddBIT{PU:C_MODULE m_M;R m_init;int m_N;VE<U> m_a;map<pair<R,int>,U> m_event;IN 
    AbstractTimeSeriesAddBIT(C_MODULE M,R init,CRI N = 0);IN AbstractTimeSeriesAddBIT(C_MODULE M,R init,VE<U> a,CO VE<tuple<R,int,U>>& event ={});TE 
    <TY...Args> IN VO Initialise(Args&&... args);IN VO Set(CO R& t,CRI i,CO U& du);TE <TY INT> VE<U> IntervalSum(CO VE<tuple<R,INT,INT>>& query,CO 
    bool& sorted = false);};TE <TY R,TY C_MODULE,TY...Args> AbstractTimeSeriesAddBIT(C_MODULE,R,Args&&...)-> AbstractTimeSeriesAddBIT<R,inner_t
    <C_MODULE>,Args...>;TE <TY U>CL TimeSeriesAddBIT:PU AbstractTimeSeriesAddBIT<ll,U,IntervalModule<ll,U>>{PU:IN TimeSeriesAddBIT(CRI N = 0);TE <TY
    ...Args> IN TimeSeriesAddBIT(VE<U> a,Args&&... args);};
TE <TY R,TY U,TY C_MODULE> IN AbstractTimeSeriesAddBIT<R,U,C_MODULE>::AbstractTimeSeriesAddBIT(C_MODULE M,R init,CRI N):m_M(MO(M)),m_init(MO(init
    )),m_N(N),m_a(N,m_M.Zero()),m_event(){}TE <TY R,TY U,TY C_MODULE> IN AbstractTimeSeriesAddBIT<R,U,C_MODULE>::AbstractTimeSeriesAddBIT(C_MODULE M
    ,R init,VE<U> a,CO VE<tuple<R,int,U>>& event):m_M(MO(M)),m_init(MO(init)),m_N(a.SZ()),m_a(MO(a)),m_event(){for(auto&[t,i,du]:event){Set(t,i,du
    );}}TE <TY U> IN TimeSeriesAddBIT<U>::TimeSeriesAddBIT(CRI N):AbstractTimeSeriesAddBIT<ll,U,IntervalModule<ll,U>>(IntervalModule<ll,U>(),0,N){}TE 
    <TY U> TE <TY...Args> IN TimeSeriesAddBIT<U>::TimeSeriesAddBIT(VE<U> a,Args&&... args):AbstractTimeSeriesAddBIT<ll,U,IntervalModule<ll,U
    >>(IntervalModule<ll,U>(),0,MO(a),forward<Args>(args)...){}TE <TY R,TY U,TY C_MODULE> TE <TY...Args> IN VO AbstractTimeSeriesAddBIT<R,U,C_MODULE
    >::Initialise(Args&&... args){decltype(*TH)temp{m_M,MO(args)...};m_init = MO(temp.m_init);m_N = temp.m_N;m_a = MO(temp.m_a);m_event = MO(temp
    .m_event);}TE <TY R,TY U,TY C_MODULE> IN VO AbstractTimeSeriesAddBIT<R,U,C_MODULE>::Set(CO R& t,CRI i,CO U& du){AS(0 <= i && i < m_N);m_event[{t
    ,i}]= du;}TE <TY R,TY U,TY C_MODULE> TE <TY INT>VE<U> AbstractTimeSeriesAddBIT<R,U,C_MODULE>::IntervalSum(CO VE<tuple<R,INT,INT>>& query,CO bool& 
    sorted){US Query = pair<CO tuple<R,INT,INT>*,int>;CO int Q = query.SZ();VE<Query> query_sorted(Q);for(int q = 0;q < Q;q++){query_sorted[q]={&
    (query[q]),q};}ST auto comp =[](CO Query& q0,CO Query& q1){RE *(q0.first)< *(q1.first)?true:q0.second < q1.second && *(q0.first)== *(q1.first);}
    ;if(!sorted){sort(query_sorted.BE(),query_sorted.EN(),comp);}AbstractBIT a{m_M,m_a};AbstractBIT da{m_M,m_N};auto IT = m_event.BE(),EN = m_event
    .EN();VE<U> AN(Q);for(auto&[p,q]:query_sorted){auto&[t,l,r]= *p;WH(IT != EN && IT->first.first < t){auto&[s,i]= IT->first;auto& du = IT->second
    ;CO U ddu = m_M.Sum(du,m_M.Inverse(da[i]));a.Add(i,m_M.Inverse(m_M.VirtualRSet<pair<R,R>,U>::ScalarProduct({m_init,s},ddu)));da.Add(i,ddu);IT
    ++;}AN[q]= m_M.Sum(a.IntervalSum(l,r),m_M.VirtualRSet<pair<R,R>,U>::ScalarProduct({m_init,t},da.IntervalSum(l,r)));}RE AN;}
#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( N , ... ) SOLVE_ONLY; VariadicResize( N , __VA_ARGS__ ); FOR( VARIABLE_FOR_SET_A , 0 , N ){ VariadicSet( cin , VARIABLE_FOR_SET_A , 
      __VA_ARGS__ ); }
  #define CIN_A( LL , N , ... ) VE<LL> __VA_ARGS__; SET_A( 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 AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .BE() , end_ ## ARRAY = ARRAY .EN()
#define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES )
#define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS )
#define 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>;
// 算術用
TE <TY T> CE T PositiveBaseModulo(T a,CO T& p){RE MO(a < 0?((((++a)*= -1)%= p)*= -1)+= p - 1:a < p?a:a %= p);}
TE <TY T> CE T Modulo(T a,CO T& p){RE PositiveBaseModulo(MO(a),p < 0?-p:p);}
TE <TY T> CE T PositiveBaseQuotient(CO T& a,CO T& p){RE(a - PositiveBaseModulo(a,p))/ p;}
TE <TY T> CE T Quotient(CO T& a,CO T& p){RE p < 0?PositiveBaseQuotient(-a,-p):PositiveBaseQuotient(a,p);}
// 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
#define DF_OF_POINTWISE_SUM(V)TE <TY T> IN auto OP+(CO V<T>& a0,CO V<T>& a1)-> decldecay_t((declval<V<T>>().push_back(declval<T>()),a0)){if(a0.empty
    ()){RE a1;}if(a1.empty()){RE a0;}AS(a0.SZ()== a1.SZ());V<T> AN{};for(auto IT0 = a0.BE(),IT1 = a1.BE(),EN0 = a0.EN();IT0 != EN0;IT0++,IT1++){AN
    .push_back(*IT0 + *IT1);}RE AN;}
DF_OF_POINTWISE_SUM(VE);
DF_OF_POINTWISE_SUM(LI);
DF_OF_POINTWISE_SUM(set);
DF_OF_POINTWISE_SUM(unordered_set);
TE <TY T,TY U> IN pair<T,U> OP+(CO pair<T,U>& t0,CO pair<T,U>& t1){RE{t0.first + t1.first,t0.second + t1.second};}
TE <TY T,TY U,TY V> IN tuple<T,U,V> OP+(CO tuple<T,U,V>& t0,CO tuple<T,U,V>& t1){RE{get<0>(t0)+ get<0>(t1),get<1>(t0)+ get<1>(t1),get<2>(t0)+ get<2
    >(t1)};}
TE <TY T,TY U,TY V,TY W> IN tuple<T,U,V,W> OP+(CO tuple<T,U,V,W>& t0,CO tuple<T,U,V,W>& t1){RE{get<0>(t0)+ get<0>(t1),get<1>(t0)+ get<1>(t1),get<2
    >(t0)+ get<2>(t1),get<3>(t0)+ get<3>(t1)};}
TE <TY T> IN T 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;}
// グラフ用
TE <TY T,TE <TY...> TY V> IN auto Get(CO V<T>& a){RE[&](CRI i = 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;}
// グリッド問題用
int H,W,H_minus,W_minus,HW;
VE<string> wall_str;VE<VE<bool> > non_wall;
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;}
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:j>h?3:(AS(false),-1);}
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)%4;}
IN VE<int> EdgeOnGrid(CRI v){VE<int>AN{};auto[i,j]=EnumHW(v);if(i>0&&wall_str[i-1][j]==walkable){AN.push_back(EnumHW_inv({i-1,j}));}if(i+1
    <H&&wall_str[i+1][j]==walkable){AN.push_back(EnumHW_inv({i+1,j}));}if(j>0&&wall_str[i][j-1]==walkable){AN.push_back(EnumHW_inv({i,j-1}));}if(j+1
    <W&&wall_str[i][j+1]==walkable){AN.push_back(EnumHW_inv({i,j+1}));}RE AN;}
IN VE<path> WeightedEdgeOnGrid(CRI v){VE<path>AN{};auto[i,j]=EnumHW(v);if(i>0&&wall_str[i-1][j]==walkable){AN.push_back({EnumHW_inv({i-1,j}),1});}if
    (i+1<H&&wall_str[i+1][j]==walkable){AN.push_back({EnumHW_inv({i+1,j}),1});}if(j>0&&wall_str[i][j-1]==walkable){AN.push_back({EnumHW_inv({i,j-1}
    ),1});}if(j+1<W&&wall_str[i][j+1]==walkable){AN.push_back({EnumHW_inv({i,j+1}),1});}RE AN;}
IN VO SetWallStringOnGrid(CRI i,VE<string>& S){if(S.empty()){S.reSZ(H);}cin>>S[i];AS(int(S[i].SZ())==W);}
IN VO SetWallOnGrid(CRI i,VE<VE<bool>>& b){if(b.empty()){b.reSZ(H,VE<bool>(W));}auto&S_i=wall_str[i];auto&b_i=b[i];FOR(j,0,W){b_i[j]=S_i[j]==walkable
    ?false:(AS(S_i[j]==unwalkable),true);}}
// 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
// StdStream（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;}
TE <CL Traits,TE <TY...> TY V,TY Arg1,TY Arg2> IN auto OP>>(IS& is,V<Arg1,Arg2>& arg)-> enable_if_t<true,decltype((get<0>(arg),is))&>{RE is >> get<0
    >(arg) >> get<1>(arg);}TE <CL Traits,TY Arg1,TY Arg2,TY Arg3> IN IS& OP>>(IS& is,tuple<Arg1,Arg2,Arg3>& arg){RE is >> get<0>(arg)>> get<1>(arg)>> 
    get<2>(arg);}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...);}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);TE <CL Traits
    ,TY Arg1,TY Arg2> IN OS& OP<<(OS& os,CO pair<Arg1,Arg2>& arg){RE os << arg.first << " " << arg.second;}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...);}
// Vector（1KB）
IN VO VariadicResize(CRI SZ){}TE <TY Arg,TY... ARGS> IN VO VariadicResize(CRI SZ,Arg& arg,ARGS&... args){arg.reSZ(SZ);VariadicResize(SZ,args...);}
// Random（1KB）
ll GetRand(CRI Rand_min,CRI Rand_max){ll AN = time(NULL);RE AN * rand()%(Rand_max + 1 - Rand_min)+ Rand_min;}
// Sort（1KB）
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());}}
// Set (1KB)
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,TE <TY...> TY MOD>struct hash<MOD<T>>{IN size_t OP()(CO MOD<T>& n
    )CO;};TE <TY T1,TY T2,TE <TY...> TY PAIR>struct hash<PAIR<T1,T2>>{IN size_t OP()(CO PAIR<T1,T2>& n)CO;};TE <TY T1,TY T2,TY T3>struct hash<tuple
    <T1,T2,T3>>{IN size_t OP()(CO tuple<T1,T2,T3>& n)CO;};
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>>;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>>;
TE <TY T,TE <TY...> TY MOD> IN size_t hash<MOD<T>>::OP()(CO MOD<T>& n)CO{ST CO hash<T> h;RE h(n.RP());}TE <TY T0,TY T1,TE <TY...> TY PAIR> IN size_t 
    hash<PAIR<T0,T1>>::OP()(CO PAIR<T0,T1>& n)CO{ST CO size_t seed = GetRand(1e3,1e8);ST CO hash<T0> h0;ST CO hash<T1> h1;RE(h0(get<0>(n))+ seed)^ h1
    (get<1>(n));}TE <TY T0,TY T1,TY T2> IN size_t hash<tuple<T0,T1,T2>>::OP()(CO tuple<T0,T1,T2>& n)CO{ST CO size_t seed = GetRand(1e3,1e8);ST CO 
    hash<pair<T0,T1>> h01;ST CO hash<T2> h2;RE(h01({get<0>(n),get<1>(n)})+ seed)^ h2(get<2>(n));}
// Algebra (4KB)
#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 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 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 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> 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;}
// 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));}
// 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();}
#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
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