結果
| 問題 | No.2075 GCD Subsequence |
| ユーザー |
👑  p-adic
|
| 提出日時 | 2024-04-07 23:16:14 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 593 ms / 4,000 ms |
| コード長 | 61,093 bytes |
| コンパイル時間 | 4,240 ms |
| コンパイル使用メモリ | 256,500 KB |
| 実行使用メモリ | 15,080 KB |
| 最終ジャッジ日時 | 2024-10-01 04:48:41 |
| 合計ジャッジ時間 | 14,950 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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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 | 39 ms
14,996 KB |
| testcase_01 | AC | 45 ms
14,900 KB |
| testcase_02 | AC | 40 ms
14,920 KB |
| testcase_03 | AC | 41 ms
15,080 KB |
| testcase_04 | AC | 39 ms
14,976 KB |
| testcase_05 | AC | 38 ms
14,936 KB |
| testcase_06 | AC | 39 ms
14,940 KB |
| testcase_07 | AC | 40 ms
15,052 KB |
| testcase_08 | AC | 188 ms
14,940 KB |
| testcase_09 | AC | 270 ms
14,944 KB |
| testcase_10 | AC | 188 ms
14,940 KB |
| testcase_11 | AC | 235 ms
15,004 KB |
| testcase_12 | AC | 208 ms
14,928 KB |
| testcase_13 | AC | 159 ms
14,940 KB |
| testcase_14 | AC | 235 ms
14,988 KB |
| testcase_15 | AC | 170 ms
15,048 KB |
| testcase_16 | AC | 176 ms
14,992 KB |
| testcase_17 | AC | 266 ms
14,948 KB |
| testcase_18 | AC | 583 ms
14,964 KB |
| testcase_19 | AC | 583 ms
15,044 KB |
| testcase_20 | AC | 554 ms
15,060 KB |
| testcase_21 | AC | 472 ms
15,080 KB |
| testcase_22 | AC | 491 ms
14,944 KB |
| testcase_23 | AC | 585 ms
14,984 KB |
| testcase_24 | AC | 588 ms
15,028 KB |
| testcase_25 | AC | 582 ms
14,956 KB |
| testcase_26 | AC | 585 ms
14,976 KB |
| testcase_27 | AC | 584 ms
14,988 KB |
| testcase_28 | AC | 593 ms
15,020 KB |
| testcase_29 | AC | 39 ms
14,892 KB |
| testcase_30 | AC | 39 ms
14,936 KB |
ソースコード
#ifndef INCLUDE_MODE
#define INCLUDE_MODE
// #define REACTIVE
// #define USE_GETLINE
#endif
#ifdef INCLUDE_MAIN
IN VO Solve()
{
CEXPR( int , bound_Ai , 1e6 );
CEXPR( int , sqrt_bound_Ai , 1e3 );
constexpr PrimeEnumeration<int,sqrt_bound_Ai> pe{};
CIN( int , N );
MultipleZetaTransform zt{ pe , MP(1) , bound_Ai + 1 };
auto least_div = GetLeastDivisor( bound_Ai + 1 );
REPEAT( N ){
CIN_ASSERT( Ai , 1 , bound_Ai );
auto div = EnumerateDivisor( least_div , Ai );
auto range = [&]( const int& ) -> const vector<int>& { return div; };
zt.Add( Ai , 1 + zt.InitialSegmentSum( 1 ) - zt.InverseImageSum( Id<int> , range , 1 ) );
}
RETURN( zt.InitialSegmentSum( 1 ) );
}
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
/*
C-x 3 C-x o C-x C-fによるファイル操作用
BFS (5KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/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/a.hpp
Divisor (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
Polynomial (21KB)
c:/Users/user/Documents/Programming/Mathematics/Polynomial/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/Arithmetic/Prime/Divisor/a_Body.hpp"
#else
// nの素因数分解：SetPrimeFactorisation(CO PE& prime,CO INT& n,VE<INT>& P,VE<INT>& EX)
// nの約数数え上げ：CountDivisor(CO PE& pe,INT n)
// SZ未満の数の最小素因数計算：GetLeastDivisor(CRI SZ)
// nの約数列挙１：EnumerateDivisor(CO PE& pe,INT n)
// nの約数列挙２：EnumerateDivisor(CO VE<INT1>& least_divisor,INT2 n)
// SZ_max未満の数の約数全列挙：TotalEnumerateDivisor(CRI SZ)
// nのメビウス関数MoeviusFunction(CO PE& pe,INT n)
TE <TY INT,INT val_limit,int LE_max = val_limit>CL PrimeEnumeration{PU:bool m_is_composite[val_limit];INT m_val[LE_max];int m_LE;CE PrimeEnumeration();CE CO INT& OP[](CRI n) CO;CE CO INT& Get(CRI n) CO;CE CO bool& IsComposite(CRI i) CO;CE CRI LE() CO NE;};
TE <TY INT,INT val_limit,int LE_max>CE PrimeEnumeration<INT,val_limit,LE_max>::PrimeEnumeration():m_is_composite(),m_val(),m_LE(0){for(INT i = 2;i < val_limit;i++){if(! m_is_composite[i]){for(INT j = i * i;j < val_limit;j +=i){m_is_composite[j] = true;}m_val[m_LE++] = i;if(m_LE >= LE_max){break;}}}}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::OP[](CRI n)CO{assert(n < m_LE);RE m_val[n];}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::Get(CRI n)CO{RE OP[](n);}TE <TY INT,INT val_limit,int LE_max> CE CO bool& PrimeEnumeration<INT,val_limit,LE_max>::IsComposite(CRI i)CO{assert(i < val_limit);RE m_is_composite[i];}TE <TY INT,INT val_limit,int LE_max> CE CRI PrimeEnumeration<INT,val_limit,LE_max>::LE()CO NE{RE m_LE;}
TE <TY INT,INT val_limit,int LE_max,TY INT1,TY INT2,TY INT3>VO SetPrimeFactorisation(CO PrimeEnumeration<INT,val_limit,LE_max>& prime,INT1 n,VE<INT2>& P,VE<INT3>& EX){int i = 0;WH(i < prime.m_LE){CO INT2& p = prime[i];if(p * p > n){break;}if(n % p == 0){P.push_back(p);EX.push_back(1);INT3& EX_back = EX.back();n /= p;WH(n % p == 0){EX_back++;n /= p;}}i++;}if(n != 1){P.push_back(n);EX.push_back(1);}RE;}
TE <TY INT> INT CountDivisorBody(VE<INT>& EX)NE{CO int LE = EX.SZ();INT AN = 1;for(int i = 0;i < LE;i++){AN *= ++EX[i];}RE AN;}TE <TY INT,TY PE> INT CountDivisor(CO PE& pe,INT n)NE{VE<INT> P{},EX{};SetPrimeFactorisation(pe,n,P,EX);RE CountDivisorBody(EX);}TE <TY INT>VE<INT> GetLeastDivisor(CO INT& SZ)NE{VE<INT> AN(SZ,1);for(int d = 1;d < SZ;d++){if(AN[d]== 1){for(int n = d;n < SZ;n += d){INT& AN_n = AN[n];AN_n == 1?AN_n = d:AN_n;}}}RE AN;}TE <TY INT> VE<INT> EnumerateDivisorBody(CO VE<INT>& P,VE<INT>& EX){CO int LE = P.SZ();VE<INT> AN(CountDivisorBody(EX),1);int SZ = 1;for(int i = 0;i < LE;i++){CO INT& P_i = P[i];CRI EX_i = EX[i];INT PW = 1;int j_shift = 0;for(int e = 1;e < EX_i;e++){PW *= P_i;j_shift += SZ;for(int j = 0;j < SZ;j++){AN[j + j_shift]= AN[j]* PW;}}SZ *= EX_i;}RE AN;}TE <TY INT,TY PE>VE<INT> EnumerateDivisor(CO PE& pe,INT n)NE{VE<INT> P{},EX{};SetPrimeFactorisation(pe,MO(n),P,EX);RE EnumerateDivisorBody(P,EX);}TE <TY INT1,TY INT2>VE<INT2> EnumerateDivisor(CO VE<INT1>& least_divisor,INT2 n){VE<INT2> P{},EX{};WH(n > 1){auto& p = least_divisor[n];P.push_back(p);INT2 e = 1;WH((n /= p)% p == 0){e++;}EX.push_back(e);}RE EnumerateDivisorBody(P,EX);}TE <TY INT>VE<VE<INT>> TotalEnumerateDivisor(CO INT& SZ)NE{VE<VE<INT>> AN(SZ);for(int d = 1;d < SZ;d++){for(int n = 0;n < SZ;n += d){AN[n].push_back(d);}}RE AN;}TE <TY INT,TY PE>int MoeviusFunction(CO PE& pe,INT n)NE{CRI LE = pe.LE();int AN = 1;int i = 0;WH(i < LE && n > 1){CRI p = pe[i++];if(n % p == 0){if((n /= p)% p == 0){RE 0;}AN *= -1;}}RE n == 1?AN:AN *= -1;}
#endif
#ifdef DEBUG
#include "c:/Users/user/Documents/Programming/Mathematics/Combinatorial/ZetaTransform/Divisor/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 U,TY MONOID,TY SEMIGROUP>CL VirtualSemirng{PU:VI U Sum(CO U& u0,CO U& u1)= 0;VI CO U& Zero()CO NE = 0;VI U Product(CO U& u0,CO U& u1)= 0;VI MONOID& AdditiveMonoid()NE = 0;VI SEMIGROUP& MultiplicativeSemigroup()NE = 0;US type = U;};TE <TY U,TY MONOID,TY SEMIGROUP>CL AbstractSemirng:VI PU VirtualSemirng<U,MONOID,SEMIGROUP>{PU:MONOID m_R0;SEMIGROUP m_R1;IN AbstractSemirng(MONOID R0,SEMIGROUP R1);IN U Sum(CO U& u0,CO U& u1);IN CO U& Zero()CO NE;IN U Product(CO U& u0,CO U& u1);IN MONOID& AdditiveMonoid()NE;IN SEMIGROUP& MultiplicativeSemigroup()NE;};TE <TY U>CL Semirng:PU AbstractSemirng<U,AdditiveMonoid<U>,MultiplicativeMagma<U>>{PU:IN Semirng();};
TE <TY U,TY MONOID,TY SEMIGROUP> IN AbstractSemirng<U,MONOID,SEMIGROUP>::AbstractSemirng(MONOID R0,SEMIGROUP R1):m_R0(MO(R0)),m_R1(MO(R1)){}TE <TY U> IN Semirng<U>::Semirng():AbstractSemirng<U,AdditiveMonoid<U>,MultiplicativeMagma<U>>(AdditiveMonoid<U>(),MultiplicativeMagma()){}TE <TY U,TY MONOID,TY SEMIGROUP> IN U AbstractSemirng<U,MONOID,SEMIGROUP>::Sum(CO U& u0,CO U& u1){RE m_R0.Sum(u0,u1);}TE <TY U,TY MONOID,TY SEMIGROUP> IN CO U& AbstractSemirng<U,MONOID,SEMIGROUP>::Zero()CO NE{RE m_R0.Zero();}TE <TY U,TY MONOID,TY SEMIGROUP> IN U AbstractSemirng<U,MONOID,SEMIGROUP>::Product(CO U& u0,CO U& u1){RE m_R1.Product(u0,u1);}TE <TY U,TY MONOID,TY SEMIGROUP> IN MONOID& AbstractSemirng<U,MONOID,SEMIGROUP>::AdditiveMonoid()NE{RE m_R0;}TE <TY U,TY MONOID,TY SEMIGROUP> IN SEMIGROUP& AbstractSemirng<U,MONOID,SEMIGROUP>::MultiplicativeSemigroup()NE{RE m_R1;}
TE <TY U,TY GROUP,TY MONOID>CL VirtualRing:VI PU VirtualSemirng<U,GROUP,MONOID>{PU:VI U Inverse(CO U& u)= 0;VI CO U& One()CO NE = 0;IN GROUP& AdditiveGroup()NE;IN MONOID& MultiplicativeMonoid()NE;};TE <TY U,TY GROUP,TY MONOID>CL AbstractRing:VI PU VirtualRing<U,GROUP,MONOID>,PU AbstractSemirng<U,GROUP,MONOID>{PU:IN AbstractRing(GROUP R0,MONOID R1);IN U Inverse(CO U& u);IN CO U& One()CO NE;};TE <TY U = ll>CL Ring:PU AbstractRing<U,AdditiveGroup<U>,MultiplicativeMonoid<U>>{PU:IN Ring(CO U& one_U);};
TE <TY U,TY GROUP,TY MONOID> IN AbstractRing<U,GROUP,MONOID>::AbstractRing(GROUP R0,MONOID R1):AbstractSemirng<U,GROUP,MONOID>(MO(R0),MO(R1)){}TE <TY U> IN Ring<U>::Ring(CO U& one_U):AbstractRing<U,AdditiveGroup<U>,MultiplicativeMonoid<U>>(AdditiveGroup<U>(),MultiplicativeMonoid<U>(one_U)){}TE <TY U,TY GROUP,TY MONOID> IN U AbstractRing<U,GROUP,MONOID>::Inverse(CO U& u){RE TH->m_R0.Inverse(u);}TE <TY U,TY GROUP,TY MONOID> IN CO U& AbstractRing<U,GROUP,MONOID>::One()CO NE{RE TH->m_R1.One();}TE <TY U,TY GROUP,TY MONOID> IN GROUP& VirtualRing<U,GROUP,MONOID>::AdditiveGroup()NE{RE TH->AdditiveMonoid();}TE <TY U,TY GROUP,TY MONOID> IN MONOID& VirtualRing<U,GROUP,MONOID>::MultiplicativeMonoid()NE{RE TH->MultiplicativeSemigroup();}
TE <TY R,TY U>CL Algebra:VI PU VirtualRSet<R,U>,PU Ring<U>{PU:IN Algebra(U one);US Ring<U>::type;IN U Action(CO R& r,U u);IN U PW(U u,CO R& r)= delete;};
TE <TY R,TY U> IN Algebra<R,U>::Algebra(U one):Ring<U>(MO(one)){}TE <TY R,TY U> IN U Algebra<R,U>::Action(CO R& r,U u){RE MO(u *= r);}
TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG>CL VirtualZetaTransform{PU:GRAPH m_G;GRAPH_INV m_G_inv;Z_ALG m_R;VE<U> m_val;IN VirtualZetaTransform(GRAPH G,GRAPH_INV G_inv,Z_ALG R);IN VirtualZetaTransform(GRAPH G,GRAPH_INV G_inv,Z_ALG R,VE<U> a,CO bool& transformed = false);TE <TY...Args> IN VO Initialise(Args&&... args);IN VO Add(CO T& t,CO U& u);IN VO TotalAdd(CO U& u);IN VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>& OP+=(CO VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>& a);IN VO TotalMultiply(CO U& u);IN VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>& OP*=(CO VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>& a);U OP[](CO T& t);IN U Get(CO T& t);IN CO U& InitialSegmentSum(CO T& t);TE <TY S,TY F_INV_MAX,TY RANGE> U InverseImageSum(F_INV_MAX&& f_inv_max,RANGE&& range,CO S& s);TE <TY S,TY F_INV_MAX> IN CO U& InitialSegmentInverseImageSum(F_INV_MAX&& f_inv_max,CO S& s);VI int Moevius(CO T& t0,CO T& t1);};TE <TY GRAPH,TY GRAPH_INV,TY Z_ALG> VirtualZetaTransform(GRAPH&,GRAPH_INV&,Z_ALG)-> VirtualZetaTransform<inner_t<GRAPH>,GRAPH,GRAPH_INV,inner_t<Z_ALG>,Z_ALG>;TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG,TY MU>CL AbstractZetaTransform:PU VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>{PU:MU m_mu;TE <TY...Args> IN AbstractZetaTransform(GRAPH G,GRAPH_INV G_inv,Z_ALG R,MU mu,Args&&... args);IN int Moevius(CO T& t0,CO T& t1);};TE <TY GRAPH,TY GRAPH_INV,TY Z_ALG,TY MU> AbstractZetaTransform(GRAPH&,GRAPH_INV&,Z_ALG,MU)-> AbstractZetaTransform<inner_t<GRAPH>,GRAPH,GRAPH_INV,inner_t<Z_ALG>,Z_ALG,MU>;
TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> IN VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::VirtualZetaTransform(GRAPH G,GRAPH_INV G_inv,Z_ALG R):m_G(MO(G)),m_G_inv(MO(G_inv)),m_R(MO(R)),m_val(m_G.SZ(),m_R.Zero()){ST_AS(is_same_v<T,inner_t<GRAPH>> && is_same_v<T,inner_t<GRAPH_INV>> && is_same_v<U,inner_t<Z_ALG>>);AS(m_G_inv.SZ()== m_G.SZ());}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> IN VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::VirtualZetaTransform(GRAPH G,GRAPH_INV G_inv,Z_ALG R,VE<U> a,CO bool& transformed):m_G(MO(G)),m_G_inv(MO(G_inv)),m_R(MO(R)),m_val(MO(a)){ST_AS(is_same_v<T,inner_t<GRAPH>> && is_same_v<T,inner_t<GRAPH_INV>> && is_same_v<U,inner_t<Z_ALG>>);CRI SZ = m_G.SZ();AS(m_G_inv.SZ()== SZ && int(m_val.SZ())== SZ);if(!transformed){a = m_val;for(int i = 0;i < SZ;i++){U& m_val_i = m_val[i];auto&& sub_i = m_G.Edge(i);for(auto& j:sub_i){j == i?m_val:m_val_i = m_R.Sum(MO(m_val_i),a[j]);}}}}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG,TY MU> TE <TY...Args> IN AbstractZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG,MU>::AbstractZetaTransform(GRAPH G,GRAPH_INV G_inv,Z_ALG R,MU mu,Args&&... args):VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>(MO(G),MO(G_inv),MO(R),forward<Args>(args)...),m_mu(MO(mu)){ST_AS(is_invocable_r_v<int,MU,CO T&,CO T&>);}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG>TE <TY...Args> VO VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::Initialise(Args&&... args){VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG> temp{m_G,m_G_inv,m_R,forward<Args>(args)...};m_val = MO(temp.m_val);}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG>VO VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::Add(CO T& t,CO U& u){auto&& sup = m_G_inv.Edge(t);for(auto& s:sup){U& m_val_i = m_val[m_G.Enumeration_inv(s)];m_val_i = m_R.Sum(MO(m_val_i),u);}}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> IN VO VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::TotalAdd(CO U& u){CRI SZ = m_G.SZ();for(int i = 0;i < SZ;i++){U& m_val_i = m_val[i];m_val_i = m_R.Sum(MO(m_val_i),m_R.ScalarProduct(m_G.Edge(m_G.Enumeration(i)).SZ(),u));}}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> IN VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>& VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::OP+=(CO VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>& a){CRI SZ = m_G.SZ();for(int i = 0;i < SZ;i++){U& m_val_i = m_val[i];m_val_i = Sum(MO(m_val_i),a.m_val[i]);}RE *TH;}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> IN VO VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::TotalMultiply(CO U& u){CRI SZ = m_G.SZ();for(int i = 0;i < SZ;i++){U& m_val_i = m_val[i];m_val_i = m_R.Product(MO(m_val_i),u);}}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> IN VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>& VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::OP*=(CO VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>& a){CRI SZ = m_G.SZ();for(int i = 0;i < SZ;i++){U& m_val_i = m_val[i];m_val_i = m_R.Product(MO(m_val_i),a.m_val[i]);}RE *TH;}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG>U VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::OP[](CO T& t){auto&& sub = m_G.Edge(t);U AN = m_R.Zero();CRI SZ = m_G.SZ();for(auto& s:sub){auto&& i = m_G.Enumeration_inv(s);AS(i < SZ);AN = m_R.Sum(MO(AN),m_R.ScalarProduct(Moevius(s,t),m_val[i]));}RE AN;}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> IN U VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::Get(CO T& t){RE OP[](t);}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> IN CO U& VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::InitialSegmentSum(CO T& t){auto&& i = m_G.Enumeration_inv(t);AS(i < m_G.SZ());RE m_val[i];}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> TE <TY S,TY F_INV_MAX,TY RANGE>U VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::InverseImageSum(F_INV_MAX&& f_inv_max,RANGE&& range,CO S& s){ST_AS(is_invocable_r_v<T,F_INV_MAX,CO S&> && is_invocable_r_v<VE<T>,RANGE,CO S&>);auto&& t = f_inv_max(s);auto&& sub = range(s);U AN = m_R.Zero();CRI SZ = m_G.SZ();for(auto& s_sub:sub){auto&& t_sub = f_inv_max(s_sub);auto&& i = m_G.Enumeration_inv(t_sub);AS(i < SZ);AN = m_R.Sum(MO(AN),m_R.ScalarProduct(Moevius(t_sub,t),m_val[i]));}RE AN;}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG> TE <TY S,TY F_INV_MAX> IN CO U& VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::InitialSegmentInverseImageSum(F_INV_MAX&& f_inv_max,CO S& s){RE m_val[m_G.Enumeration_inv(f_inv_max(s))];}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG>int VirtualZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG>::Moevius(CO T& t0,CO T& t1){ST VE<unordered_map<int,int>> memory(m_G.SZ());auto&& i = m_G.Enumeration_inv(t0);auto&& j = m_G.Enumeration_inv(t1);unordered_map<int,int>& memory_t0 = memory[i];CO bool found = memory_t0.count(j)== 1;int& AN = memory_t0[j];if(! found){if(i == j){AN = 1;}else{AN = 0;auto&& sub = m_G.Edge(t1);for(auto& s:sub){s == t1?AN:AN -= Moevius(t0,s);}}}RE AN;}TE <TY T,TY GRAPH,TY GRAPH_INV,TY U,TY Z_ALG,TY MU> IN int AbstractZetaTransform<T,GRAPH,GRAPH_INV,U,Z_ALG,MU>::Moevius(CO T& t0,CO T& t1){RE m_mu(t0,t1);}
// TE <TY INT,INT val_limit,int LE_max = val_limit>CL PrimeEnumeration{PU:bool m_is_composite[val_limit];INT m_val[LE_max];int m_LE;CE PrimeEnumeration();CE CO INT& OP[](CRI n) CO;CE CO INT& Get(CRI n) CO;CE CO bool& IsComposite(CRI i) CO;CE CRI LE() CO NE;};
// TE <TY INT,INT val_limit,int LE_max>CE PrimeEnumeration<INT,val_limit,LE_max>::PrimeEnumeration():m_is_composite(),m_val(),m_LE(0){for(INT i = 2;i < val_limit;i++){if(! m_is_composite[i]){for(INT j = i * i;j < val_limit;j +=i){m_is_composite[j] = true;}m_val[m_LE++] = i;if(m_LE >= LE_max){break;}}}}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::OP[](CRI n)CO{assert(n < m_LE);RE m_val[n];}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::Get(CRI n)CO{RE OP[](n);}TE <TY INT,INT val_limit,int LE_max> CE CO bool& PrimeEnumeration<INT,val_limit,LE_max>::IsComposite(CRI i)CO{assert(i < val_limit);RE m_is_composite[i];}TE <TY INT,INT val_limit,int LE_max> CE CRI PrimeEnumeration<INT,val_limit,LE_max>::LE()CO NE{RE m_LE;}
// TE <TY INT,INT val_limit,int LE_max,TY INT1,TY INT2,TY INT3>VO SetPrimeFactorisation(CO PrimeEnumeration<INT,val_limit,LE_max>& prime,INT1 n,VE<INT2>& P,VE<INT3>& EX){int i = 0;WH(i < prime.m_LE){CO INT2& p = prime[i];if(p * p > n){break;}if(n % p == 0){P.push_back(p);EX.push_back(1);INT3& EX_back = EX.back();n /= p;WH(n % p == 0){EX_back++;n /= p;}}i++;}if(n != 1){P.push_back(n);EX.push_back(1);}RE;}
// TE <TY INT> VE<INT> EnumerateDivisorBody(CO VE<INT>& P,VE<INT>& EX){CO int LE = P.SZ();VE<INT> AN(CountDivisorBody(EX),1);int SZ = 1;for(int i = 0;i < LE;i++){CO INT& P_i = P[i];CRI EX_i = EX[i];INT PW = 1;int j_shift = 0;for(int e = 1;e < EX_i;e++){PW *= P_i;j_shift += SZ;for(int j = 0;j < SZ;j++){AN[j + j_shift]= AN[j]* PW;}}SZ *= EX_i;}RE AN;}TE <TY INT,TY PE>VE<INT> EnumerateDivisor(CO PE& pe,INT n)NE{VE<INT> P{},EX{};SetPrimeFactorisation(pe,MO(n),P,EX);RE EnumerateDivisorBody(P,EX);}
TE <TY PE>CL TwoAryCLicalMoeviusFunction{PU:int m_SZ;CO PE* m_p_pe;VE<int> m_memory;TwoAryCLicalMoeviusFunction(CRI SZ,CO PE& pe);IN int OP()(CRI t0,CRI t1);};TE <TY PE>CL DivisorMoeviusFunction{PU:TwoAryCLicalMoeviusFunction<PE> m_mu;IN DivisorMoeviusFunction(CRI SZ,CO PE& pe);IN int OP()(CRI t0,CRI t1);};TE <TY PE>CL MultipleMoeviusFunction{PU:TwoAryCLicalMoeviusFunction<PE> m_mu;IN MultipleMoeviusFunction(CRI SZ,CO PE& pe);IN int OP()(CRI t0,CRI t1);};TE <TY PE>CL DivisorEdge{PU:CO PE* m_p_pe;IN DivisorEdge(CO PE& pe);IN VE<int> OP()(CRI t);};CL MultipleEdge{PU:int m_SZ;IN MultipleEdge(CRI SZ);IN VE<int> OP()(CRI t);};TE <TY PE,TY Z_ALG>CL AbstractDivisorZetaTransform:PU AbstractZetaTransform<int,Graph<DivisorEdge<PE>>,Graph<MultipleEdge>,inner_t<Z_ALG>,Z_ALG,DivisorMoeviusFunction<PE>>{PU:IN AbstractDivisorZetaTransform(CO PE& pe,Z_ALG R,CRI SZ = 0);IN AbstractDivisorZetaTransform(CO PE& pe,Z_ALG R,VE<inner_t<Z_ALG>> a,CO bool& transformed = false);};TE <TY PE,TY U>CL DivisorZetaTransform:PU AbstractDivisorZetaTransform<PE,Algebra<int,U>>{PU:TE <TY...Args> IN DivisorZetaTransform(CO PE& pe,CO U& one,Args&&... args);};TE <TY PE,TY Z_ALG>CL AbstractMultipleZetaTransform:PU AbstractZetaTransform<int,Graph<MultipleEdge>,Graph<DivisorEdge<PE>>,inner_t<Z_ALG>,Z_ALG,MultipleMoeviusFunction<PE>>{PU:IN AbstractMultipleZetaTransform(CO PE& pe,Z_ALG R,CRI SZ = 0);IN AbstractMultipleZetaTransform(CO PE& pe,Z_ALG R,VE<inner_t<Z_ALG>> a,CO bool& transformed = false);};TE <TY PE,TY U>CL MultipleZetaTransform:PU AbstractMultipleZetaTransform<PE,Algebra<int,U>>{PU:TE <TY...Args> IN MultipleZetaTransform(CO PE& pe,CO U& one,Args&&... args);};
TE <TY PE>TwoAryCLicalMoeviusFunction<PE>::TwoAryCLicalMoeviusFunction(CRI SZ,CO PE& pe):m_SZ(SZ),m_p_pe(&pe),m_memory(SZ,1){VE<int> rest(m_SZ);for(int n = 0;n < m_SZ;n++){rest[n]= n;}CRI LE = m_p_pe->LE();for(int i = 0;i < LE;i++){auto& p_i =(*m_p_pe)[i];for(int n = 0;n < m_SZ;n += p_i){m_memory[n]*=((rest[n]/= p_i)% p_i == 0?0:-1);}}auto& p_max =(*m_p_pe)[LE - 1];for(int n = p_max + 1;n < m_SZ;n++){if(rest[n]!= 1){m_memory[n]*= -1;}}}TE <TY PE> IN int TwoAryCLicalMoeviusFunction<PE>::OP()(CRI t0,CRI t1){AS(0 < t0 && 0 < t1 && t1 < m_SZ && t1 % t0 == 0);RE m_memory[t1 / t0];}TE <TY PE> IN DivisorMoeviusFunction<PE>::DivisorMoeviusFunction(CRI SZ,CO PE& pe):m_mu(SZ,pe){}TE <TY PE> IN MultipleMoeviusFunction<PE>::MultipleMoeviusFunction(CRI SZ,CO PE& pe):m_mu(SZ,pe){}TE <TY PE> IN int DivisorMoeviusFunction<PE>::OP()(CRI t0,CRI t1){RE m_mu(t0,t1);}TE <TY PE> IN int MultipleMoeviusFunction<PE>::OP()(CRI t0,CRI t1){RE m_mu(t1,t0);}TE <TY PE> IN DivisorEdge<PE>::DivisorEdge(CO PE& pe):m_p_pe(&pe){}IN MultipleEdge::MultipleEdge(CRI SZ):m_SZ(SZ){}TE <TY PE> IN VE<int> DivisorEdge<PE>::OP()(CRI t){AS(0 <= t);VE<int> AN{};RE t == 0?VE<int>(1):EnumerateDivisor(*m_p_pe,t);}IN VE<int> MultipleEdge::OP()(CRI t){AS(0 <= t && t < m_SZ);CO int SZ = t == 0?0:(m_SZ - 1)/ t;VE<int> AN(SZ);for(int i = 0;i < SZ;i++){AN[i]= t *(i + 1);}RE AN;}TE <TY PE,TY Z_ALG> IN AbstractDivisorZetaTransform<PE,Z_ALG>::AbstractDivisorZetaTransform(CO PE& pe,Z_ALG R,CRI SZ):AbstractZetaTransform<int,Graph<DivisorEdge<PE>>,Graph<MultipleEdge>,inner_t<Z_ALG>,Z_ALG,DivisorMoeviusFunction<PE>>(Graph(SZ,DivisorEdge(pe)),Graph(SZ,MultipleEdge(SZ)),MO(R),DivisorMoeviusFunction(SZ,pe)){}TE <TY PE,TY Z_ALG> IN AbstractDivisorZetaTransform<PE,Z_ALG>::AbstractDivisorZetaTransform(CO PE& pe,Z_ALG R,VE<inner_t<Z_ALG>> a,CO bool& transformed):AbstractZetaTransform<int,Graph<DivisorEdge<PE>>,Graph<MultipleEdge>,inner_t<Z_ALG>,Z_ALG,DivisorMoeviusFunction<PE>>(Graph(a.SZ(),DivisorEdge(pe)),Graph(a.SZ(),MultipleEdge(a.SZ())),MO(R),DivisorMoeviusFunction(a.SZ(),pe),MO(a),transformed){}TE <TY PE,TY U> TE <TY...Args> IN DivisorZetaTransform<PE,U>::DivisorZetaTransform(CO PE& pe,CO U& one,Args&&... args):AbstractDivisorZetaTransform<PE,Algebra<int,U>>(pe,Algebra<int,U>(one),forward<Args>(args)...){}TE <TY PE,TY Z_ALG> IN AbstractMultipleZetaTransform<PE,Z_ALG>::AbstractMultipleZetaTransform(CO PE& pe,Z_ALG R,CRI SZ):AbstractZetaTransform<int,Graph<MultipleEdge>,Graph<DivisorEdge<PE>>,inner_t<Z_ALG>,Z_ALG,MultipleMoeviusFunction<PE>>(Graph(SZ,MultipleEdge(SZ)),Graph(SZ,DivisorEdge(pe)),MO(R),MultipleMoeviusFunction(SZ,pe)){}TE <TY PE,TY Z_ALG> IN AbstractMultipleZetaTransform<PE,Z_ALG>::AbstractMultipleZetaTransform(CO PE& pe,Z_ALG R,VE<inner_t<Z_ALG>> a,CO bool& transformed):AbstractZetaTransform<int,Graph<MultipleEdge>,Graph<DivisorEdge<PE>>,inner_t<Z_ALG>,Z_ALG,MultipleMoeviusFunction<PE>>(Graph(a.SZ(),MultipleEdge(a.SZ())),Graph(a.SZ(),DivisorEdge(pe)),MO(R),MultipleMoeviusFunction(a.SZ(),pe),MO(a),transformed){}TE <TY PE,TY U> TE <TY...Args> IN MultipleZetaTransform<PE,U>::MultipleZetaTransform(CO PE& pe,CO U& one,Args&&... args):AbstractMultipleZetaTransform<PE,Algebra<int,U>>(pe,Algebra<int,U>(one),forward<Args>(args)...){}
#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
#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define REPEAT_MAIN( BOUND ) START_MAIN; signal( SIGABRT , &AlertAbort ); AutoCheck( exec_mode , use_getline ); CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if( exec_mode == solve_mode ){ if CE( bound_test_case_num > 1 ){ CERR( "テストケースの個数を入力してください。" ); SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } } else { if( exec_mode == experiment_mode ){ Experiment(); } else if( exec_mode == small_test_mode ){ SmallTest(); } else if( exec_mode == random_test_mode ){ CERR( "ランダムテストを行う回数を指定してください。" ); SET_LL( test_case_num ); REPEAT( test_case_num ){ RandomTest(); } } RE 0; } FINISH_MAIN
#define DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE2 )
#define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); AS( ( MIN ) <= A && A <= ( MAX ) )
#define SET_ASSERT( A , MIN , MAX ) if( exec_mode == solve_mode ){ SET_LL( A ); ASSERT( A , MIN , MAX ); } else if( exec_mode == random_test_mode ){ CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ); } else { AS( false ); }
#define SOLVE_ONLY ST_AS( __FUNCTION__[0] == 'S' )
#define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl
#define COUT( ... ) VariadicCout( cout << "出力： " , __VA_ARGS__ ) << endl
#define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl
#define COUT_A( A , N ) cout << "出力： "; OUTPUT_ARRAY( cout , A , N ) << endl
#define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl
#define COUT_ITR( A ) cout << "出力： "; OUTPUT_ITR( cout , A ) << endl
#else
#pragma GCC optimize ( "O3" )
#pragma GCC optimize ( "unroll-loops" )
#pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
#define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if 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( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_SET_A , 0 , N ){ cin >> A[VARIABLE_FOR_SET_A]; }
#define CIN_A( LL , A , N ) VE<LL> A( N ); SET_A( A , N );
#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( A , N , 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( A , N , MIN , MAX ) vector<decldecay_t( MAX )> A( N ); SET_A_ASSERT( A , N , 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 OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS
#define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.BE() , EN_FOR_OUTPUT_ITR = A.EN(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; WH( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS
#define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); 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 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>;
// 入出力用
#ifndef DEBUG
#define DF_OF_COUT_FOR_VE(V)TE <CL Traits,TY Arg> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& 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> IN basic_istream<char,Traits>& VariadicCin(basic_istream<char,Traits>& is){RE is;}
TE <CL Traits,TY Arg,TY... ARGS> IN basic_istream<char,Traits>& VariadicCin(basic_istream<char,Traits>& is,Arg& arg,ARGS&... args){RE VariadicCin(is >> arg,args...);}
TE <CL Traits> IN basic_istream<char,Traits>& VariadicGetline(basic_istream<char,Traits>& is,CO char& separator){RE is;}
TE <CL Traits,TY Arg,TY... ARGS> IN basic_istream<char,Traits>& VariadicGetline(basic_istream<char,Traits>& 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 basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO pair<Arg1,Arg2>& arg){RE os << arg.first << " " << arg.second;}
TE <CL Traits,TY Arg> IN basic_ostream<char,Traits>& VariadicCout(basic_ostream<char,Traits>& os,CO Arg& arg){RE os << arg;}
TE <CL Traits,TY Arg1,TY Arg2,TY... ARGS> IN basic_ostream<char,Traits>& VariadicCout(basic_ostream<char,Traits>& os,CO Arg1& arg1,CO Arg2& arg2,CO ARGS&... args){RE VariadicCout(os << arg1 << " ",arg2,args...);}
#endif
// 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 PositiveBaseRS(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);}
#ifdef DEBUG
#include "c:/Users/user/Documents/Programming/Utility/BinarySearch/a_Body.hpp"
#include "c:/Users/user/Documents/Programming/Utility/TwoPointerapproach/a_Body.hpp"
#else
// 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 )
// t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。
TE <TY T> IN TY set<T>::iterator MaximumLeq(set<T>& S,CO T& t){CO auto EN = S.EN();if(S.empty()){RE EN;}auto IT = S.upper_bound(t);RE IT == EN?S.find(*(S.rBE())):IT == S.BE()?EN:--IT;}
// t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。
TE <TY T> IN TY set<T>::iterator MaximumLt(set<T>& S,CO T& t){CO auto EN = S.EN();if(S.empty()){RE EN;}auto IT = S.lower_bound(t);RE IT == EN?S.find(*(S.rBE())):IT == S.BE()?EN:--IT;}
// t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。
TE <TY T> IN TY set<T>::iterator MinimumGeq(set<T>& S,CO T& t){RE S.lower_bound(t);}
// tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。
TE <TY T> IN TY set<T>::iterator MinimumGt(set<T>& S,CO T& t){RE S.upper_bound(t);}
// 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; \
} \
} \
#endif
// データ構造用
TE <TY T,TE <TY...> TY V> 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;}
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);}}
// デバッグ用
#ifdef DEBUG
IN VO AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); }
VO AutoCheck( int& exec_mode , CO bool& use_getline );
IN VO Solve();
IN VO Experiment();
IN VO SmallTest();
IN VO RandomTest();
ll GetRand( CRL Rand_min , CRL Rand_max );
IN VO BreakPoint( CRI LINE ) {}
int exec_mode;
CEXPR( int , solve_mode , 0 );
CEXPR( int , sample_debug_mode , 1 );
CEXPR( int , submission_debug_mode , 2 );
CEXPR( int , library_search_mode , 3 );
CEXPR( int , experiment_mode , 4 );
CEXPR( int , small_test_mode , 5 );
CEXPR( int , random_test_mode , 6 );
#ifdef USE_GETLINE
CEXPR( bool , use_getline , true );
#else
CEXPR( bool , use_getline , false );
#endif
#else
ll GetRand( CRL Rand_min , CRL Rand_max ) { ll answer = time( NULL ); RE answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; }
#endif
// VVV 常設ライブラリは以下に挿入する。
#ifdef DEBUG
#include "c:/Users/user/Documents/Programming/Utility/Set/a_Body.hpp"
#include "c:/Users/user/Documents/Programming/Mathematics/Algebra/Monoid/Group/a_Body.hpp"
#include "c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/a_Body.hpp"
#include "c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/ConstexprModulo/Debug/a_Body.hpp"
CEXPR(uint,P,998244353);US MP = Mod<P>;
#else
// 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;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,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 E> MemorisationGraph(CRI SZ,E edge)-> MemorisationGraph<decldecay_t(declval<E>()().back()),E>;TE <TY E> MemorisationGraph(CRI SZ,E edge)-> MemorisationGraph<decldecay_t(get<0>(declval<E>()().back())),E>;
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,E edge):EdgeImplimentation<T,T,CRI,E>(SZ,MO(edge)),m_LE(),m_memory(),m_memory_inv(){ST_AS(is_invocable_v<E> && 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 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));}
// 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