結果
| 問題 | No.2230 Good Omen of White Lotus |
| ユーザー |
👑  p-adic
|
| 提出日時 | 2024-05-18 17:57:53 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 74 ms / 2,000 ms |
| コード長 | 47,988 bytes |
| コンパイル時間 | 3,804 ms |
| コンパイル使用メモリ | 241,480 KB |
| 実行使用メモリ | 7,296 KB |
| 最終ジャッジ日時 | 2024-05-18 17:58:01 |
| 合計ジャッジ時間 | 7,620 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
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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 | 1 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 2 ms
5,376 KB |
| testcase_04 | AC | 2 ms
5,376 KB |
| testcase_05 | AC | 2 ms
5,376 KB |
| testcase_06 | AC | 1 ms
5,376 KB |
| testcase_07 | AC | 2 ms
5,376 KB |
| testcase_08 | AC | 2 ms
5,376 KB |
| testcase_09 | AC | 2 ms
5,376 KB |
| testcase_10 | AC | 1 ms
5,376 KB |
| testcase_11 | AC | 1 ms
5,376 KB |
| testcase_12 | AC | 2 ms
5,376 KB |
| testcase_13 | AC | 2 ms
5,376 KB |
| testcase_14 | AC | 25 ms
5,376 KB |
| testcase_15 | AC | 2 ms
5,376 KB |
| testcase_16 | AC | 36 ms
5,376 KB |
| testcase_17 | AC | 36 ms
5,376 KB |
| testcase_18 | AC | 37 ms
5,376 KB |
| testcase_19 | AC | 37 ms
5,376 KB |
| testcase_20 | AC | 4 ms
5,376 KB |
| testcase_21 | AC | 2 ms
5,376 KB |
| testcase_22 | AC | 5 ms
5,376 KB |
| testcase_23 | AC | 6 ms
5,376 KB |
| testcase_24 | AC | 3 ms
5,632 KB |
| testcase_25 | AC | 3 ms
5,632 KB |
| testcase_26 | AC | 3 ms
5,632 KB |
| testcase_27 | AC | 43 ms
7,296 KB |
| testcase_28 | AC | 48 ms
7,168 KB |
| testcase_29 | AC | 46 ms
7,168 KB |
| testcase_30 | AC | 54 ms
7,168 KB |
| testcase_31 | AC | 53 ms
7,168 KB |
| testcase_32 | AC | 49 ms
7,168 KB |
| testcase_33 | AC | 69 ms
7,168 KB |
| testcase_34 | AC | 68 ms
7,168 KB |
| testcase_35 | AC | 69 ms
7,168 KB |
| testcase_36 | AC | 69 ms
7,168 KB |
| testcase_37 | AC | 71 ms
7,168 KB |
| testcase_38 | AC | 74 ms
7,040 KB |
| testcase_39 | AC | 72 ms
7,168 KB |
| testcase_40 | AC | 21 ms
5,888 KB |
| testcase_41 | AC | 21 ms
5,376 KB |
| testcase_42 | AC | 46 ms
5,376 KB |
| testcase_43 | AC | 5 ms
5,504 KB |
| testcase_44 | AC | 57 ms
5,760 KB |
| testcase_45 | AC | 23 ms
5,376 KB |
| testcase_46 | AC | 37 ms
5,888 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()
{
cin >> H >> W;
CIN( int , N , p );
CIN_A( T2<int> , N , xy ); --xy;
sort( xy.begin() , xy.end() );
IntervalMaxBIT<int> bit{ 0 , W };
FOR( i , 0 , N ){
auto& [x,y] = xy[i];
bit.SetMax( y , bit.IntervalMax( 0 , y ) + 1 );
}
int count = bit.IntervalMax( 0 , W - 1 );
MP a = Power( MP( p - 1 ) , H + W - 3 - count );
MP b = Power( MP( p - 2 ) , count );
MP c = Power( MP( p ) , P - 1 - ( H + W - 3 ) );
RETURN( - a * b * c + 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
/*
AdicExhausiveSearch/BFS (11KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/AdicExhausiveSearch/compress.txt
CommutativeDualSqrtDecomposition (6KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/SqrtDecomposition/Dual/Commutative/compress.txt
CoordinateCompress (3KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txt
DFSOnTree (11KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepthFirstSearch/Tree/compress.txt
DifferenceSequence (9KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/DifferenceSequence/compress.txt
Divisor/Prime (4KB)
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt
IntervalAddBIT (9KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/IntervalAdd/compress.txt
IntervalMaxBIT (9KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/IntervalMax/compress.txt
IntervalMultiplyLazySqrtDecomposition (18KB)
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/SqrtDecomposition/LazyEvaluation/IntervalMultiply/compress.txt
Knapsack (8KB)
c:/Users/user/Documents/Programming/Mathematics/Combinatorial/KnapsackProblem/compress.txt
MinimumCostFlow/PotentialisedDijkstra/Dijkstra (16KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/Dijkstra/Potentialised/MinimumCostFlow/compress.txt
Polynomial (21KB)
c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt
TwoByOneMatrix/TwoByTwoMatrix (9KB)
C:/Users/user/Documents/Programming/Mathematics/LinearAlgebra/TwoByOne/compress.txt
UnionFind (3KB)
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/UnionFindForest/compress.txt
*/
// VVV 常設でないライブラリは以下に挿入する。
#ifdef DEBUG
#include "c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/IntervalMax/a_Body.hpp"
#else
TE <TY U>CL VirtualMeetSemilattice:VI PU VirtualMonoid<U>{PU:IN U Meet(U u0,CO U& u1);};TE <TY U>CL MinSemilattice:VI PU VirtualMeetSemilattice<U>,PU PointedSet<U>{PU:IN MinSemilattice(U infty_U);IN U Product(U u0,CO U& u1);};TE <TY U>CL MaxSemilattice:VI PU VirtualMeetSemilattice<U>,PU PointedSet<U>{PU:IN MaxSemilattice(U zero_U);IN U Product(U u0,CO U& u1);};
TE <TY U> IN U VirtualMeetSemilattice<U>::Meet(U u0,CO U& u1){RE TH->Product(MO(u0),u1);}TE <TY U> IN MinSemilattice<U>::MinSemilattice(U infty_U):PointedSet<U>(MO(infty_U)){}TE <TY U> IN MaxSemilattice<U>::MaxSemilattice(U zero_U):PointedSet<U>(MO(zero_U)){}TE <TY U> IN U MinSemilattice<U>::Product(U u0,CO U& u1){RE u0 < u1?MO(u0):u1;}TE <TY U> IN U MaxSemilattice<U>::Product(U u0,CO U& u1){RE u1 < u0?MO(u0):u1;}
#define SFINAE_FOR_BIT_BS enable_if_t<is_invocable_r_v<bool,F,U,int>>*
TE <TY U,TY COMM_IDEM_MONOID>CL IdempotentMonoidBIT{PU:COMM_IDEM_MONOID m_M;int m_SZ;VE<U> m_a;VE<U> m_fenwick_0;VE<U> m_fenwick_1;int m_PW;IN IdempotentMonoidBIT(COMM_IDEM_MONOID M,CRI SZ = 0);IN IdempotentMonoidBIT(COMM_IDEM_MONOID M,VE<U> a);IN IdempotentMonoidBIT(CO IdempotentMonoidBIT<U,COMM_IDEM_MONOID>& bit);TE <TY...Args> IN VO Initialise(Args&&... args);VO Set(CRI i,CO U& u);IN IdempotentMonoidBIT<U,COMM_IDEM_MONOID>& OP+=(VE<U>&& a);VO Multiply(CRI i,CO U& u);VO IntervalMultiply(CRI i_start,CRI i_final,CO U& u);IN CRI SZ()CO NE;IN CO U& OP[](CRI i)CO;IN CO U& Get(CRI i)CO;IN CO U& LSBSegmentProduct(CRI j,CO bool& left = true)CO;U IntervalProduct(CRI i_start,CRI i_final);TE <TY F,SFINAE_FOR_BIT_BS = nullptr> int BinarySearch(CO F& f);int BinarySearch(CO U& u);IN VO COruct();};TE <TY COMM_IDEM_MONOID> IdempotentMonoidBIT(COMM_IDEM_MONOID M)-> IdempotentMonoidBIT<inner_t<COMM_IDEM_MONOID>,COMM_IDEM_MONOID>;TE <TY U>CL IntervalMaxBIT:PU IdempotentMonoidBIT<U,MaxSemilattice<U>>{PU:TE <TY...Args> IN IntervalMaxBIT(CO U& zero_U,Args&&... args);IN VO SetMax(CRI i,CO U& u);IN VO IntervalSetMax(CRI i_start,CRI i_final,CO U& u);IN CO U& LSBSegmentMax(CRI j,CO bool& left = true)CO;IN U IntervalMax(CRI i_start,CRI i_final);};TE <TY U>CL IntervalMinBIT:PU IdempotentMonoidBIT<U,MinSemilattice<U>>{PU:TE <TY...Args> IN IntervalMinBIT(CO U& infty_U,Args&&... args);IN VO SetMin(CRI i,CO U& u);IN VO IntervalSetMin(CRI i_start,CRI i_final,CO U& u);IN CO U& LSBSegmentMin(CRI j,CO bool& left = true)CO;IN U IntervalMin(CRI i_start,CRI i_final);};
TE <TY U,TY COMM_IDEM_MONOID> IN IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::IdempotentMonoidBIT(COMM_IDEM_MONOID M,CRI SZ):m_M(MO(M)),m_SZ(SZ),m_a(SZ,m_M.One()),m_fenwick_0(m_SZ + 1,m_M.One()),m_fenwick_1(m_SZ + 1,m_M.One()),m_PW(1){COruct();}TE <TY U,TY COMM_IDEM_MONOID> IN IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::IdempotentMonoidBIT(COMM_IDEM_MONOID M,VE<U> a):m_M(MO(M)),m_SZ(a.SZ()),m_a(MO(a)),m_fenwick_0(m_SZ + 1),m_fenwick_1(m_SZ + 1),m_PW(1){COruct();for(int i = 0;i < m_SZ;i++){int j = i + 1;U& fenwick_0i = m_fenwick_0[j];fenwick_0i = m_a[i];CO int j_llim = j -(j & -j);j--;WH(j > j_llim){fenwick_0i = m_M.Product(m_fenwick_0[j],fenwick_0i);j -=(j & -j);}}for(int i = m_SZ - 1;i >= 0;i--){int j = i + 1;U& fenwick_1i = m_fenwick_1[j];fenwick_1i = m_a[i];CO int j_ulim = min(j +(j & -j),m_SZ + 1);j++;WH(j < j_ulim){fenwick_1i = m_M.Product(MO(fenwick_1i),m_fenwick_1[j]);j +=(j & -j);}}}TE <TY U> TE <TY...Args> IN IntervalMaxBIT<U>::IntervalMaxBIT(CO U& zero_U,Args&&... args):IdempotentMonoidBIT<U,MaxSemilattice<U>>(MaxSemilattice<U>(zero_U),forward<Args>(args)...){}TE <TY U> TE <TY...Args> IN IntervalMinBIT<U>::IntervalMinBIT(CO U& infty_U,Args&&... args):IdempotentMonoidBIT<U,MinSemilattice<U>>(MinSemilattice<U>(infty_U),forward<Args>(args)...){}TE <TY U,TY COMM_IDEM_MONOID> IN VO IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::COruct(){ST_AS(is_same_v<U,inner_t<COMM_IDEM_MONOID>>);WH(m_PW < m_SZ){m_PW <<= 1;}}TE <TY U,TY COMM_IDEM_MONOID> IN IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::IdempotentMonoidBIT(CO IdempotentMonoidBIT<U,COMM_IDEM_MONOID>& bit):m_SZ(bit.m_SZ),m_a(bit.m_a),m_fenwick_0(bit.m_fenwick_0),m_fenwick_1(bit.m_fenwick_1),m_PW(bit.m_PW){}TE <TY U,TY COMM_IDEM_MONOID> TE <TY...Args> IN VO IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::Initialise(Args&&... args){IdempotentMonoidBIT<U,COMM_IDEM_MONOID> temp{m_M,forward<Args>(args)...};m_SZ = temp.m_SZ;m_a = MO(temp.m_a);m_fenwick_0 = MO(temp.m_fenwick_0);m_fenwick_1 = MO(temp.m_fenwick_1);m_PW = temp.m_PW;}TE <TY U,TY COMM_IDEM_MONOID>VO IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::Set(CRI i,CO U& u){U& ai = m_a[i];if(u == m_M.Product(ai,u)){Multiply(i,u);}else{ai = u;int j = i + 1;int j_minus = j -(j & -j);U temp_left = m_M.Product(IntervalProduct(j_minus,i - 1),ai);U temp_right = m_M.One();WH(j <= m_SZ){m_fenwick_0[j]= m_M.Product(temp_left,temp_right);int j_next = j +(j & -j);int j_minus_next = j_next -(j_next & -j_next);if(j_minus_next != j_minus - 1){temp_left = m_M.Product(IntervalProduct(j_minus_next,j_minus - 1),temp_left);j_minus = j_minus_next;}temp_right = m_M.Product(MO(temp_right),IntervalProduct(j,j_next - 1));j = j_next;}j = i + 1;int j_plus = j +(j & -j)- 1;temp_left = m_M.One();temp_right = m_M.Product(ai,IntervalProduct(j,j_plus - 1));WH(j > 0){m_fenwick_1[j]= m_M.Product(temp_left,temp_right);int j_next = j -(j & -j);int j_plus_next = j_next +(j_next & -j_next)- 1;temp_left = m_M.Product(IntervalProduct(j_next - 1,j - 2),temp_left);j = j_next;if(j_plus != j_plus_next - 1){temp_right = m_M.Product(MO(temp_right),IntervalProduct(j_plus,j_plus_next - 1));j_plus = j_plus_next;}}}RE;}TE <TY U,TY COMM_IDEM_MONOID> IN IdempotentMonoidBIT<U,COMM_IDEM_MONOID>& IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::OP+=(VE<U>&& a){IdempotentMonoidBIT<U,COMM_IDEM_MONOID> a_copy{m_M,MO(a)};AS(m_SZ == a_copy.m_SZ);for(int j = 1;j <= m_SZ;j++){U& t0j = m_fenwick_0[j];t0j = m_M.Product(MO(t0j),a_copy.m_fenwick_0[j]);U& t1j = m_fenwick_1[j];t1j = m_M.Product(MO(t1j),a_copy.m_fenwick_1[j]);}}TE <TY U,TY COMM_IDEM_MONOID>VO IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::Multiply(CRI i,CO U& u){U& ai = m_a[i];ai = m_M.Product(MO(ai),u);int j = i + 1;WH(j <= m_SZ){U& tj = m_fenwick_0[j];tj = m_M.Product(MO(tj),u);j +=(j & -j);}j = i + 1;WH(j > 0){U& tj = m_fenwick_1[j];tj = m_M.Product(MO(tj),u);j -=(j & -j);}RE;}TE <TY U> VO IntervalMaxBIT<U>::SetMax(CRI i,CO U& u){TH->Multiply(i,u);}TE <TY U> VO IntervalMinBIT<U>::SetMin(CRI i,CO U& u){TH->Multiply(i,u);}TE <TY U,TY COMM_IDEM_MONOID>VO IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::IntervalMultiply(CRI i_start,CRI i_final,CO U& u){CO int j_min = max(i_start + 1,1);CO int j_max = min(i_final + 1,m_SZ);for(int i = j_min - 1;i < j_max;i++){U& ai = m_a[i];ai = m_M.Product(MO(ai),u);}CO int j_llim = j_min -(j_min & -j_min);CO int j_ulim = min(j_max +(j_max & j_max),m_SZ + 1);if(j_min <= j_max){int j = j_min;WH(j < j_ulim){if(j -(j & -j)< j_max){U& tj = m_fenwick_0[j];tj = m_M.Product(MO(tj),u);}j++;}j = j_max;WH(j > j_llim){if(j +(j & -j)> j_min){U& tj = m_fenwick_0[j];tj = m_M.Product(MO(tj),u);}j--;}}RE;}TE <TY U> VO IntervalMaxBIT<U>::IntervalSetMax(CRI i_start,CRI i_final,CO U& u){TH->IntervalMultiply(i_start,i_final,u);}TE <TY U> VO IntervalMinBIT<U>::IntervalSetMin(CRI i_start,CRI i_final,CO U& u){TH->IntervalMultiply(i_start,i_final,u);}TE <TY U,TY COMM_IDEM_MONOID> IN CRI IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::SZ()CO NE{RE m_SZ;}TE <TY U,TY COMM_IDEM_MONOID> IN CO U& IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::OP[](CRI i)CO{AS(0 <= i && i < m_SZ);RE m_a[i];}TE <TY U,TY COMM_IDEM_MONOID> IN CO U& IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::Get(CRI i)CO{RE OP[](i);}TE <TY U,TY COMM_IDEM_MONOID> IN CO U& IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::LSBSegmentProduct(CRI j,CO bool& left)CO{AS(0 < j && j <= m_SZ);RE(left?m_fenwick_0:m_fenwick_1)[j];}TE <TY U> CO U& IntervalMaxBIT<U>::LSBSegmentMax(CRI j,CO bool& left)CO{RE TH->LSBSegmentProduct(j,left);}TE <TY U> CO U& IntervalMinBIT<U>::LSBSegmentMin(CRI j,CO bool& left)CO{RE TH->LSBSegmentProduct(j,left);}TE <TY U,TY COMM_IDEM_MONOID>U IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::IntervalProduct(CRI i_start,CRI i_final){CO int j_min = max(i_start + 1,1);CO int j_max = min(i_final + 1,m_SZ);if(j_min > j_max){RE m_M.One();}U AN1 = m_M.One();int j = j_min;int j_next = j +(j & -j);WH(j_next <= j_max){AN1 = m_M.Product(MO(AN1),m_fenwick_1[j]);j = j_next;j_next +=(j & -j);}AN1 = m_M.Product(MO(AN1),m_a[j-1]);U AN0 = m_M.One();j = j_max;j_next = j -(j & -j);WH(j_next >= j_min){AN0 = m_M.Product(MO(AN0),m_fenwick_0[j]);j = j_next;j_next -=(j & -j);}RE m_M.Product(MO(AN1),AN0);}TE <TY U> U IntervalMaxBIT<U>::IntervalMax(CRI i_start,CRI i_final){RE TH->IntervalProduct(i_start,i_final);}TE <TY U> U IntervalMinBIT<U>::IntervalMin(CRI i_start,CRI i_final){RE TH->IntervalProduct(i_start,i_final);}TE <TY U,TY COMM_IDEM_MONOID> TE <TY F,SFINAE_FOR_BIT_BS> IN int IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::BinarySearch(CO F& f){int j = 0;int PW = m_PW;U product = m_M.One();U product_next = product;WH(PW > 0){int j_next = j | PW;if(j_next <= m_SZ){product_next = m_M.Product(product_next,m_fenwick_0[j_next]);if(f(product_next,j_next - 1)){product_next = product;}else{product = product_next;j = j_next;}}PW >>= 1;}RE j;}TE <TY U,TY COMM_IDEM_MONOID> IN int IdempotentMonoidBIT<U,COMM_IDEM_MONOID>::BinarySearch(CO U& u){RE BinarySearch([&](CO U& prod,CRI){RE prod == m_M.Product(prod,u);});}
#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 ITR( ARRAY ) auto begin_ ## ARRAY = ARRAY .BE() , itr_ ## ARRAY = begin_ ## ARRAY , end_ ## ARRAY = ARRAY .EN()
#define FOR_ITR( ARRAY ) for( ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define RUN( VAR , ... ) for( auto&& VAR : __VA_ARGS__ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES )
#define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS )
#define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); RE
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ RE; }
// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#define AS assert
#define IN inline
#define CL class
#define PU public
#define OP operator
#define CE constexpr
#define CO const
#define NE noexcept
#define RE return
#define WH while
#define VO void
#define VE vector
#define LI list
#define BE begin
#define EN end
#define SZ size
#define LE length
#define PW Power
#define MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&
#define VI virtual
#define IS basic_istream<char,Traits>
#define OS basic_ostream<char,Traits>
#define ST_AS static_assert
#define reMO_CO remove_const
#define is_COructible_v is_constructible_v
#define rBE rbegin
#define reSZ resize
// 型のエイリアス
#define decldecay_t(VAR)decay_t<decltype(VAR)>
TE <TY F,TY...Args> US ret_t = decltype(declval<F>()(declval<Args>()...));
TE <TY T> US inner_t = TY T::type;
US uint = unsigned int;
US ll = long long;
US ull = unsigned long long;
US ld = long double;
US lld = __float128;
TE <TY INT> US T2 = pair<INT,INT>;
TE <TY INT> US T3 = tuple<INT,INT,INT>;
TE <TY INT> US T4 = tuple<INT,INT,INT,INT>;
US path = pair<int,ll>;
// 二分探索用
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CO_TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , CO_TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
ST_AS( ! is_same<decldecay_t( CO_TARGET ),uint>::value && ! is_same<decldecay_t( CO_TARGET ),ull>::value ); \
ll ANSWER = MINIMUM; \
{ \
ll L_BS = MINIMUM; \
ll U_BS = MAXIMUM; \
ANSWER = UPDATE_ANSWER; \
ll EXPRESSION_BS; \
CO ll CO_TARGET_BS = ( CO_TARGET ); \
ll DIFFERENCE_BS; \
WH( L_BS < U_BS ){ \
DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CO_TARGET_BS; \
CERR( "二分探索中：" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS : (" , #EXPRESSION , ") =" , EXPRESSION_BS , DIFFERENCE_BS > 0 ? ">" : DIFFERENCE_BS < 0 ? "<" : "=" , CO_TARGET_BS , "= (" , #CO_TARGET , ")" ); \
if( DIFFERENCE_BS INEQUALITY_FOR_CHECK 0 ){ \
U_BS = UPDATE_U; \
} else { \
L_BS = UPDATE_L; \
} \
ANSWER = UPDATE_ANSWER; \
} \
if( L_BS > U_BS ){ \
CERR( "二分探索失敗：" , "L_BS =" , L_BS , ">" , U_BS , "= U_BS :" , #ANSWER , ":= (" , #MAXIMUM , ") + 1 =" , MAXIMUM + 1 ); \
CERR( "二分探索マクロにミスがある可能性があります。変更前の版に戻してください。" ); \
ANSWER = MAXIMUM + 1; \
} else { \
CERR( "二分探索終了：" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS" ); \
CERR( "二分探索が成功したかを確認するために" , #EXPRESSION , "を計算します。" ); \
CERR( "成功判定が不要な場合はこの計算を削除しても構いません。" ); \
EXPRESSION_BS = ( EXPRESSION ); \
CERR( "二分探索結果： (" , #EXPRESSION , ") =" , EXPRESSION_BS , ( EXPRESSION_BS > CO_TARGET_BS ? ">" : EXPRESSION_BS < CO_TARGET_BS ? "<" : "=" ) , CO_TARGET_BS ); \
if( EXPRESSION_BS DESIRED_INEQUALITY CO_TARGET_BS ){ \
CERR( "二分探索成功：" , #ANSWER , ":=" , ANSWER ); \
} else { \
CERR( "二分探索失敗：" , #ANSWER , ":= (" , #MAXIMUM , ") + 1 =" , MAXIMUM + 1 ); \
CERR( "単調でないか、単調増加性と単調減少性を逆にしてしまったか、探索範囲内に解が存在しません。" ); \
ANSWER = MAXIMUM + 1; \
} \
} \
} \
// 単調増加の時にEXPRESSION >= CO_TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , >= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 )
// 単調増加の時にEXPRESSION <= CO_TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , > , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 )
// 単調減少の時にEXPRESSION >= CO_TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , < , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 )
// 単調減少の時にEXPRESSION <= CO_TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , <= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 )
// 尺取り法用
// VAR_TPA_LとVAR_TPA_RをINITで初期化し、VAR_TPA_RがCONTINUE_CONDITIONを満たす限り、
// 閉区間[VAR_TPA_L,VAR_TPA_R]が条件ON_CONDITIONを満たすか否かを判定し、
// trueになるかVAR_TAR_LがVAR_TAR_Rに追い付くまでVAR_TPA_Lの更新操作UPDATE_Lを繰り返し、
// その後VAR_TPA_Rの更新操作UPDATE_Rを行う。
// ON_CONDITIONがtrueとなる極大閉区間とその時点でのINFOをANSWERに格納する。
#define TPA( ANSWER , VAR_TPA , INIT , CONTINUE_CONDITION , UPDATE_L , UPDATE_R , ON_CONDITION , INFO ) \
VE<tuple<decldecay_t( INIT ),decldecay_t( INIT ),decldecay_t( INFO )>> ANSWER{}; \
{ \
auto init_TPA = INIT; \
decldecay_t( ANSWER.front() ) ANSWER ## _temp = { init_TPA , init_TPA , INFO }; \
auto ANSWER ## _prev = ANSWER ## _temp; \
auto& VAR_TPA ## _L = get<0>( ANSWER ## _temp ); \
auto& VAR_TPA ## _R = get<1>( ANSWER ## _temp ); \
auto& VAR_TPA ## _info = get<2>( ANSWER ## _temp ); \
bool on_TPA_prev = false; \
WH( true ){ \
bool continuing = CONTINUE_CONDITION; \
bool on_TPA = continuing && ( ON_CONDITION ); \
CERR( continuing ? "尺取り中" : "尺取り終了" , "： [L,R] = [" , VAR_TPA ## _L , "," , VAR_TPA ## _R , "] ," , on_TPA_prev ? "on" : "off" , "->" , on_TPA ? "on" : "off" , ", info =" , VAR_TPA ## _info ); \
if( on_TPA_prev && ! on_TPA ){ \
ANSWER.push_back( ANSWER ## _prev ); \
} \
if( continuing ){ \
if( on_TPA || VAR_TPA ## _L == VAR_TPA ## _R ){ \
ANSWER ## _prev = ANSWER ## _temp; \
UPDATE_R; \
} else { \
UPDATE_L; \
} \
} else { \
break; \
} \
on_TPA_prev = on_TPA; \
} \
} \
// データ構造用
TE <TY T> IN T Addition(CO T& t0,CO T& t1){RE t0 + t1;}
TE <TY T> IN T Xor(CO T& t0,CO T& t1){RE t0 ^ t1;}
TE <TY T> IN T MU(CO T& t0,CO T& t1){RE t0 * t1;}
TE <TY T> IN CO T& Zero(){ST CO T z{};RE z;}
TE <TY T> IN CO T& One(){ST CO T o = 1;RE o;}TE <TY T> IN T AdditionInv(CO T& t){RE -t;}
TE <TY T> IN T Id(CO T& v){RE v;}
TE <TY T> IN T Min(CO T& a,CO T& b){RE a < b?a:b;}
TE <TY T> IN T Max(CO T& a,CO T& b){RE a < b?b:a;}
// グラフ用
TE <TY V> IN auto Get(V& a){RE[&](CRI i = 0)->CO decldecay_t(a[0])&{RE a[i];};}
TE <TY T = int> IN VE<T> id(CRI SZ){VE<T> AN(SZ);FOR(i,0,SZ){AN[i]= i;}RE AN;}
// グリッド問題用
int H,W,H_minus,W_minus,HW;
VE<string> grid;
char walkable = '.',unwalkable = '#';
IN T2<int> EnumHW(CRI v){RE{v / W,v % W};}
IN int EnumHW_inv(CO T2<int>& ij){auto&[i,j]= ij;RE i * W + j;}
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<T2<int>> EdgeOnGrid(CO T2<int>& v){VE<T2<int>>AN{};auto[i,j]=v;if(i>0&&grid[i-1][j]==walkable){AN.push_back({i-1,j});}if(i+1<H&&grid[i+1][j]==walkable){AN.push_back({i+1,j});}if(j>0&&grid[i][j-1]==walkable){AN.push_back({i,j-1});}if(j+1<W&&grid[i][j+1]==walkable){AN.push_back({i,j+1});}RE AN;}
IN VE<pair<T2<int>,ll>> WEdgeOnGrid(CO T2<int>& v){VE<pair<T2<int>,ll>>AN{};auto[i,j]=v;if(i>0&&grid[i-1][j]==walkable){AN.push_back({{i-1,j},1});}if(i+1<H&&grid[i+1][j]==walkable){AN.push_back({{i+1,j},1});}if(j>0&&grid[i][j-1]==walkable){AN.push_back({{i,j-1},1});}if(j+1<W&&grid[i][j+1]==walkable){AN.push_back({{i,j+1},1});}RE AN;}
IN VO SetWallStringOnGrid(CRI i,VE<string>& S){if(S.empty()){S.reSZ(H);}cin>>S[i];AS(int(S[i].SZ())==W);}
// VVV 常設ライブラリは以下に挿入する。
#ifdef DEBUG
#include "C:/Users/user/Documents/Programming/Contest/Template/include/a_Body.hpp"
#else
// Random（1KB）
ll GetRand(CRI Rand_min,CRI Rand_max){ll AN = time(NULL);RE AN * rand()%(Rand_max + 1 - Rand_min)+ Rand_min;}
// Map (2KB)
#define DC_OF_HASH(...)struct hash<__VA_ARGS__>{IN size_t OP()(CO __VA_ARGS__& n)CO;};
CL is_ordered{PU:is_ordered()= delete;TE <TY T> ST CE auto Check(CO T& t)-> decltype(t < t,true_type());ST CE false_type Check(...);TE <TY T> ST CE CO bool value = is_same_v< decltype(Check(declval<T>())),true_type >;};
TE <TY T>US Set = conditional_t<is_COructible_v<unordered_set<T>>,unordered_set<T>,conditional_t<is_ordered::value<T>,set<T>,VO>>;
#define DF_OF_AR_FOR_MAP(MAP,OPR)TE <TY T,TY U> IN MAP<T,U>& OP OPR ## =(MAP<T,U>& a,CO pair<T,U>& v){a[v.first]OPR ## = v.second;RE a;}TE <TY T,TY U> IN MAP<T,U>& OP OPR ## =(MAP<T,U>& a0,CO MAP<T,U>& a1){for(auto&[t,u]:a1){a0[t]OPR ## = u;}RE a0;}TE <TY T,TY U,TY ARG> IN MAP<T,U> OP OPR(MAP<T,U> a,CO ARG& arg){RE MO(a OPR ## = arg);}
#define DF_OF_ARS_FOR_MAP(MAP)DF_OF_AR_FOR_MAP(MAP,+);DF_OF_AR_FOR_MAP(MAP,-);DF_OF_AR_FOR_MAP(MAP,*);DF_OF_AR_FOR_MAP(MAP,/);DF_OF_AR_FOR_MAP(MAP,%);
TE <TY T,TY U>US Map = conditional_t<is_COructible_v<unordered_map<T,int>>,unordered_map<T,U>,conditional_t<is_ordered::value<T>,map<T,U>,VO>>;
DF_OF_ARS_FOR_MAP(map);DF_OF_ARS_FOR_MAP(unordered_map);
// Tuple（3KB）
#define DF_OF_AR_FOR_TUPLE(OPR)TE <TY T,TY U,TE <TY...> TY V> IN auto OP OPR ## =(V<T,U>& t0,CO V<T,U>& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);RE t0;}TE <TY T,TY U,TY V> IN tuple<T,U,V>& OP OPR ## =(tuple<T,U,V>& t0,CO tuple<T,U,V>& t1){get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);RE t0;}TE <TY T,TY U,TY V,TY W> IN tuple<T,U,V,W>& OP OPR ## =(tuple<T,U,V,W>& t0,CO tuple<T,U,V,W>& t1){get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);get<3>(t0)OPR ## = get<3>(t1);RE t0;}TE <TE <TY...> TY V,TY...ARGS> IN auto OP OPR(CO V<ARGS...>& t0,CO V<ARGS...>& t1)-> decldecay_t((get<0>(t0),t0)){auto t = t0;RE MO(t OPR ## = t1);}
#define DF_OF_HASH_FOR_TUPLE(PAIR)TE <TY T,TY U> IN size_t hash<PAIR<T,U>>::OP()(CO PAIR<T,U>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<T> h0;ST CO hash<U> h1;RE(h0(get<0>(n))* seed)^ h1(get<1>(n));}
#define DF_OF_INCREMENT_FOR_TUPLE(INCR)TE <TY T,TY U,TE <TY...> TY V> IN auto OP INCR(V<T,U>& t)-> decldecay_t((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);RE t;}TE <TY T,TY U,TY V> IN tuple<T,U,V>& OP INCR(tuple<T,U,V>& t){INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);RE t;}TE <TY T,TY U,TY V,TY W> IN tuple<T,U,V,W>& OP INCR(tuple<T,U,V,W>& t){INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);INCR get<3>(t);RE t;}
TE <CL Traits,TY T,TY U,TE <TY...> TY V> IN auto OP>>(IS& is,V<T,U>& arg)-> decltype((get<0>(arg),is))&{RE is >> get<0>(arg)>> get<1>(arg);}TE <CL Traits,TY T,TY U,TY V> IN IS& OP>>(IS& is,tuple<T,U,V>& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg);}TE <CL Traits,TY T,TY U,TY V,TY W> IN IS& OP>>(IS& is,tuple<T,U,V,W>& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg)>> get<3>(arg);}TE <CL Traits,TY T,TY U,TE <TY...> TY V> IN auto OP<<(OS& os,CO V<T,U>& arg)-> decltype((get<0>(arg),os))&{RE os << get<0>(arg)<< " " << get<1>(arg);}TE <CL Traits,TY T,TY U,TY V> IN OS& OP<<(OS& os,CO tuple<T,U,V>& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg);}TE <CL Traits,TY T,TY U,TY V,TY W> IN OS& OP<<(OS& os,CO tuple<T,U,V,W>& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg)<< " " << get<3>(arg);}DF_OF_AR_FOR_TUPLE(+);DF_OF_AR_FOR_TUPLE(-);DF_OF_AR_FOR_TUPLE(*);DF_OF_AR_FOR_TUPLE(/);DF_OF_AR_FOR_TUPLE(%);DF_OF_INCREMENT_FOR_TUPLE(++);DF_OF_INCREMENT_FOR_TUPLE(--);
TE <TY T,TY U> DC_OF_HASH(pair<T,U>);TE <TY T,TY U> DC_OF_HASH(tuple<T,U>);TE <TY T,TY U,TY V> DC_OF_HASH(tuple<T,U,V>);TE <TY T,TY U,TY V,TY W> DC_OF_HASH(tuple<T,U,V,W>);
DF_OF_HASH_FOR_TUPLE(pair);DF_OF_HASH_FOR_TUPLE(tuple);TE <TY T,TY U,TY V> IN size_t hash<tuple<T,U,V>>::OP()(CO tuple<T,U,V>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<pair<T,U>> h01;ST CO hash<V> h2;RE(h01({get<0>(n),get<1>(n)})* seed)^ h2(get<2>(n));}TE <TY T,TY U,TY V,TY W> IN size_t hash<tuple<T,U,V,W>>::OP()(CO tuple<T,U,V,W>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<pair<T,U>> h01;ST CO hash<pair<V,W>> h23;RE(h01({get<0>(n),get<1>(n)})* seed)^ h23({get<2>(n),get<3>(n)});}
// Vector（2KB）
#define DF_OF_COUT_FOR_VE(V)TE <CL Traits,TY Arg> IN OS& OP<<(OS& os,CO V<Arg>& arg){auto BE = arg.BE(),EN = arg.EN();auto IT = BE;WH(IT != EN){(IT == BE?os:os << " ")<< *IT;IT++;}RE os;}
#define DF_OF_AR_FOR_VE(V,OPR)TE <TY T> IN V<T>& OP OPR ## =(V<T>& a,CO T& t){for(auto& s:a){s OPR ## = t;}RE a;}TE <TY T> IN V<T>& OP OPR ## =(V<T>& a0,CO V<T>& a1){AS(a0.SZ()<= a1.SZ());auto IT0 = a0.BE(),EN0 = a0.EN();auto IT1 = a1.BE();WH(IT0 != EN0){*(IT0++)OPR ## = *(IT1++);}RE a0;}TE <TY T,TY U> IN V<T> OP OPR(V<T> a,CO U& u){RE MO(a OPR ## = u);}
#define DF_OF_INCREMENT_FOR_VE(V,INCR)TE <TY T> IN V<T>& OP INCR(V<T>& a){for(auto& i:a){INCR i;}RE a;}
#define DF_OF_ARS_FOR_VE(V)DF_OF_AR_FOR_VE(V,+);DF_OF_AR_FOR_VE(V,-);DF_OF_AR_FOR_VE(V,*);DF_OF_AR_FOR_VE(V,/);DF_OF_AR_FOR_VE(V,%);DF_OF_INCREMENT_FOR_VE(V,++);DF_OF_INCREMENT_FOR_VE(V,--)
DF_OF_COUT_FOR_VE(VE);DF_OF_COUT_FOR_VE(LI);DF_OF_COUT_FOR_VE(set);DF_OF_COUT_FOR_VE(unordered_set);DF_OF_ARS_FOR_VE(VE);DF_OF_ARS_FOR_VE(LI);IN VO VariadicResize(CRI SZ){}TE <TY Arg,TY... ARGS> IN VO VariadicResize(CRI SZ,Arg& arg,ARGS&... args){arg.resize(SZ);VariadicResize(SZ,args...);}TE <TY T> VO sort(VE<T>& a,CO bool& reversed = false){if(reversed){ST auto comp =[](CO T& t0,CO T& t1){RE t1 < t0;};sort(a.BE(),a.EN(),comp);}else{sort(a.BE(),a.EN());}}
// StdStream（1KB）
TE <CL Traits> IN IS& VariadicCin(IS& is){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicCin(IS& is,Arg& arg,ARGS&... args){RE VariadicCin(is >> arg,args...);}TE <CL Traits> IN IS& VariadicSet(IS& is,CRI i){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicSet(IS& is,CRI i,Arg& arg,ARGS&... args){RE VariadicSet(is >> arg[i],i,args...);}TE <CL Traits> IN IS& VariadicGetline(IS& is,CO char& separator){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicGetline(IS& is,CO char& separator,Arg& arg,ARGS&... args){RE VariadicGetline(getline(is,arg,separator),separator,args...);}TE <CL Traits,TY Arg> IN OS& VariadicCout(OS& os,CO Arg& arg){RE os << arg;}TE <CL Traits,TY Arg1,TY Arg2,TY... ARGS> IN OS& VariadicCout(OS& os,CO Arg1& arg1,CO Arg2& arg2,CO ARGS&... args){RE VariadicCout(os << arg1 << " ",arg2,args...);}
// 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();}
#define DF_OF_HASH_FOR_MOD(MOD)IN size_t hash<MOD>::OP()(CO MOD& n)CO{ST CO hash<decldecay_t(n.RP())> h;RE h(n.RP());}
TE <uint M> DC_OF_HASH(Mod<M>); TE <uint M> DF_OF_HASH_FOR_MOD(Mod<M>);
#endif
// AAA 常設ライブラリは以上に挿入する。
#define INCLUDE_LIBRARY
#include __FILE__
#endif // INCLUDE_LIBRARY
#endif // INCLUDE_SUB
#endif // INCLUDE_MAIN