結果
| 問題 | No.2888 Mamehinata |
| ユーザー |
👑  p-adic
|
| 提出日時 | 2024-09-13 22:53:22 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 168 ms / 2,000 ms |
| コード長 | 52,888 bytes |
| コンパイル時間 | 5,409 ms |
| コンパイル使用メモリ | 246,060 KB |
| 実行使用メモリ | 21,880 KB |
| 最終ジャッジ日時 | 2024-09-13 22:53:34 |
| 合計ジャッジ時間 | 10,688 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / 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 | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,812 KB |
| testcase_02 | AC | 2 ms
6,940 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 2 ms
6,944 KB |
| testcase_05 | AC | 2 ms
6,940 KB |
| testcase_06 | AC | 2 ms
6,940 KB |
| testcase_07 | AC | 2 ms
6,944 KB |
| testcase_08 | AC | 2 ms
6,940 KB |
| testcase_09 | AC | 2 ms
6,940 KB |
| testcase_10 | AC | 2 ms
6,940 KB |
| testcase_11 | AC | 2 ms
6,944 KB |
| testcase_12 | AC | 2 ms
6,940 KB |
| testcase_13 | AC | 22 ms
6,944 KB |
| testcase_14 | AC | 21 ms
7,680 KB |
| testcase_15 | AC | 80 ms
10,880 KB |
| testcase_16 | AC | 120 ms
14,352 KB |
| testcase_17 | AC | 22 ms
9,208 KB |
| testcase_18 | AC | 43 ms
6,940 KB |
| testcase_19 | AC | 132 ms
14,464 KB |
| testcase_20 | AC | 106 ms
12,672 KB |
| testcase_21 | AC | 109 ms
12,416 KB |
| testcase_22 | AC | 39 ms
11,212 KB |
| testcase_23 | AC | 69 ms
13,680 KB |
| testcase_24 | AC | 107 ms
15,328 KB |
| testcase_25 | AC | 72 ms
14,584 KB |
| testcase_26 | AC | 81 ms
14,620 KB |
| testcase_27 | AC | 37 ms
12,492 KB |
| testcase_28 | AC | 17 ms
6,940 KB |
| testcase_29 | AC | 40 ms
7,936 KB |
| testcase_30 | AC | 133 ms
14,948 KB |
| testcase_31 | AC | 103 ms
13,036 KB |
| testcase_32 | AC | 64 ms
10,240 KB |
| testcase_33 | AC | 102 ms
12,172 KB |
| testcase_34 | AC | 83 ms
10,996 KB |
| testcase_35 | AC | 67 ms
9,856 KB |
| testcase_36 | AC | 164 ms
15,972 KB |
| testcase_37 | AC | 168 ms
16,404 KB |
| testcase_38 | AC | 33 ms
7,040 KB |
| testcase_39 | AC | 127 ms
13,776 KB |
| testcase_40 | AC | 162 ms
15,924 KB |
| testcase_41 | AC | 20 ms
6,944 KB |
| testcase_42 | AC | 141 ms
14,088 KB |
| testcase_43 | AC | 99 ms
18,116 KB |
| testcase_44 | AC | 104 ms
19,824 KB |
| testcase_45 | AC | 125 ms
21,880 KB |
| testcase_46 | AC | 14 ms
6,940 KB |
| testcase_47 | AC | 110 ms
19,336 KB |
| testcase_48 | AC | 99 ms
13,276 KB |
| testcase_49 | AC | 10 ms
6,940 KB |
| testcase_50 | AC | 30 ms
6,944 KB |
| testcase_51 | AC | 3 ms
6,944 KB |
| testcase_52 | AC | 2 ms
6,944 KB |
| testcase_53 | AC | 6 ms
6,944 KB |
| testcase_54 | AC | 2 ms
6,944 KB |
ソースコード
#ifndef INCLUDE_MODE
#define INCLUDE_MODE
// #define REACTIVE
// #define USE_GETLINE
// #define SUBMIT_ONLY
#define SAMPLE_CHECK C
#endif
#ifdef INCLUDE_MAIN
IN VO Solve()
{
CIN( int , N , M );
vector<vector<int>> e( N );
REPEAT( M ){
CIN( int , u , v ); --u; --v;
e[u].push_back( v );
e[v].push_back( u );
}
Graph graph{ N , Get( e ) };
BreadthFirstSearch bfs{ graph , -1 , 0 }; vector<int> d = bfs.GetDistance();
vector<int> hind( N + 1 );
FOR( i , 0 , N ){
d[i] < 0 ? 0 : hind[d[i]]++;
}
CERR( hind );
int even = 1 , odd = 0;
if( e[0].empty() ){
FOREQ( i , 1 , N ){
COUT( 0 );
}
} else {
FOREQ( i , 1 , N ){
COUT( ( ( i & 1 ) == 0 ? even : odd ) += hind[i] );
}
}
}
REPEAT_MAIN(1);
#else // INCLUDE_MAIN
#ifdef INCLUDE_SUB
// COMPAREに使用。圧縮時は削除する。
int Naive( int N , int M , int K , const bool& experiment = false )
{
int 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()
{
// // 1変数
// int N_min = 1 , N_max = bound;
// vector<decldecay_t(Naive(0))> naive1( N_max - N_min + 1 );
// FOREQ( N , N_min , N_max ){
// naive1[N-N_min] = Naive( N , true );
// }
// CERRNS( "N∈[",N_min,"--",N_max,"]: " , naive3[N] , "\n" };
// // 2変数
// int N_min = 1 , N_max = bound;
// vector<vector<decldecay_t(Naive(0,0))>> naive2( N_max - N_min + 1 );
// FOREQ( N , N_min , N_max ){
// int M_min = 1 , M_max = bound;
// naive2[N-N_min].resize( M_max - M_min + 1 );
// FOREQ( M , M_min , M_max ){
// naive2[N-N_min][M-M_min] = Naive( N , M , true );
// }
// CERRNS( "N=",N,",M∈[",M_min,"--",M_max,"]: " , naive2[N-N_min] , "\n" );
// }
// CERRNS( "Inline: " , naive2 , "\n" );
// // 3変数
// int N_min = 1 , N_max = bound;
// vector<vector<vector<decldecay_t(Naive(0,0,0))>>> naive3( N_max - N_min + 1 );
// FOREQ( N , N_min , N_max ){
// int M_min = 1 , M_max = bound;
// naive3[N-N_min].resize( M_max - M_min + 1 );
// FOREQ( M , M_min , M_max ){
// int K_min = 1 , K_max = bound;
// naive3[N-N_min][M-M_min].resize( K_max - K_min + 1 );
// FOREQ( K , K_min , K_max ){
// naive3[N-N_min][M-M_min][K-K_min] = Naive( N , M , K , true );
// }
// CERRNS( "(N,M)=(",N,",",M,"),K∈[",K_min,"--",K_max,"]: " , naive3[N-N_min][M-M_min] , "\n" );
// }
// }
// CERRNS( "Inline: " ); FOREQ( N , N_min , N_max ){ CERRNS( naive3[N-N_min] , " \n"[N==N_max] ) };
}
// 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( CRI test_case_num )
{
// REPEAT( test_case_num ){
// 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 , K );
// }
}
#define INCLUDE_MAIN
#include __FILE__
#else // INCLUDE_SUB
#ifdef INCLUDE_LIBRARY
/*
- BFS (6KB)
Geometry/Graph/Algorithm/BreadthFirstSearch/
- AdicExhausiveSearch (11KB)
Geometry/Graph/Algorithm/BreadthFirstSearch/AdicExhausiveSearch/
- BitExhausiveSearch (10KB)
Geometry/Graph/Algorithm/BreadthFirstSearch/BitExhausiveSearch/
- ZeroOneBreadthFirstSearch (4KB)
Geometry/Graph/Algorithm/BreadthFirstSearch/01/
- BIT (5KB)
SetTheory/DirectProduct/AffineSpace/BIT/
- IntervalAdd (9KB)
SetTheory/DirectProduct/AffineSpace/BIT/IntervalAdd/
- IntervalMax (9KB)
SetTheory/DirectProduct/AffineSpace/BIT/IntervalMax/
- CoordinateCompress (3KB)
SetTheory/DirectProduct/CoordinateCompress/
- DFS (6KB)
Geometry/Graph/Algorithm/DepthFirstSearch/
- Tree (11KB)
Geometry/Graph/Algorithm/DepthFirstSearch/Tree/
- DifferenceSequence (9KB)
SetTheory/DirectProduct/AffineSpace/DifferenceSequence/
- TwoDimensional (5KB)
SetTheory/DirectProduct/AffineSpace/DifferenceSequence/TwoDimensional/
- Dijkstra (6KB)
Geometry/Graph/Algorithm/Dijkstra/
- MinimumCostFlow (16KB)
Geometry/Graph/Algorithm/Dijkstra/Potentialised/MinimumCostFlow/
- Divisor/Prime/Factorisation (4KB)
Arithmetic/Divisor/
- Knapsack (8KB)
Combinatorial/KnapsackProblem/
- SqrtDecomposition
- Monoid (5KB)
SetTheory/DirectProduct/AffineSpace/SqrtDecomposition/Monoid/
- CommutativeDual (6KB)
SetTheory/DirectProduct/AffineSpace/SqrtDecomposition/Dual/Commutative/
- IntervalMultiplyLazy (18KB)
SetTheory/DirectProduct/AffineSpace/SqrtDecomposition/LazyEvaluation/IntervalMultiply/
- TruncatedPolynomial (31KB)
Polynomial/Truncate/
- NonProth (34KB)
Polynomial/Truncate/NonProth/
- TwoByTwoMatrix (6KB)
LinearAlgebra/
- TwoByOneMatrix (9KB)
LinearAlgebra/TwoByOne/
- UnionFind (3KB)
Geometry/Graph/Algorithm/UnionFindForest/
*/
// VVV 常設でないライブラリは以下に挿入する。
// #ifdef DEBUG
// #include "c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/Algorithm/BreadthFirstSearch/Debug/a_Body.hpp"
// #else
TE <TY T,TY GRAPH>CL VirtualBreadthFirstSearch{PU:GRAPH& m_G;T m_not_found;bool m_initialised;LI<T> m_next;VE<bool> m_found;VE<T> m_prev;IN VirtualBreadthFirstSearch(GRAPH& G,CO T& not_found);TE <TY Arg> IN VirtualBreadthFirstSearch(GRAPH& G,CO T& not_found,Arg&& init);IN VO Initialise();IN VO Initialise(CO T& init);IN VO Initialise(LI<T> inits);IN VO Shift(CO T& init);IN VO Shift(LI<T> inits);IN CRI SZ()CO NE;IN VE<bool>::reference found(CO T& t);IN CO T& prev(CO T& t);IN T Next();TE <TY U = T> auto GetDistance()-> enable_if_t<is_same_v<GRAPH,MemorisationGraph<U,decldecay_t(declval<GRAPH>().edge())>>,Map<T,int>>;TE <TY U = T> auto GetDistance()-> enable_if_t<!is_same_v<GRAPH,MemorisationGraph<U,decldecay_t(declval<GRAPH>().edge())>>,VE<int>>;pair<VE<int>,int> GetConnectedComponent();VE<T> GetNodeEnumeration();VE<T> GetReversedNodeEnumeration();VI VO Push(LI<T>& next,CO T& t)= 0;TE <TY PATH> IN VO Push(LI<T>& next,CO PATH& p);};
TE <TY T,TY GRAPH> IN VirtualBreadthFirstSearch<T,GRAPH>::VirtualBreadthFirstSearch(GRAPH& G,CO T& not_found):m_G(G),m_not_found(not_found),m_initialised(false),m_next(),m_found(),m_prev(){ST_AS(is_same_v<inner_t<GRAPH>,T>);}TE <TY T,TY GRAPH> TE <TY Arg> IN VirtualBreadthFirstSearch<T,GRAPH>::VirtualBreadthFirstSearch(GRAPH& G,CO T& not_found,Arg&& init):VirtualBreadthFirstSearch<T,GRAPH>(G,not_found){Initialise(forward<Arg>(init));}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Initialise(){m_initialised = true;CRI V = SZ();m_next.clear();m_found = VE<bool>(V);m_prev = VE<T>(V,m_not_found);}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Initialise(CO T& init){auto&& i = m_G.Enumeration_inv(init);AS(0 <= i && i < SZ());Initialise();m_next.push_back(init);m_found[i]= true;}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Initialise(LI<T> inits){Initialise();m_next = MO(inits);CRI V = SZ();for(auto& u:m_next){auto&& i = m_G.Enumeration_inv(u);AS(0 <= i && i < V);m_found[i]= true;}}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Shift(CO T& init){if(m_initialised){CRI V = SZ();auto&& i = m_G.Enumeration_inv(init);AS(0 <= i && i < V);m_next.clear();if(! m_found[i]){m_next.push_back(init);m_found[i]= true;}}else{Initialise(init);}}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Shift(LI<T> inits){if(m_initialised){m_next.clear();CRI V = SZ();for(auto& u:m_next){auto&& i = m_G.Enumeration_inv(u);AS(0 <= i && i < V);if(! m_found[i]){m_next.push_back(u);m_found[i]= true;}}}else{Initialise(MO(inits));}}TE <TY T,TY GRAPH> IN CRI VirtualBreadthFirstSearch<T,GRAPH>::SZ()CO NE{RE m_G.SZ();}TE <TY T,TY GRAPH> IN VE<bool>::reference VirtualBreadthFirstSearch<T,GRAPH>::found(CO T& t){auto&& i = m_G.Enumeration_inv(t);AS(0 <= i && i < SZ());if(!m_initialised){Initialise();}RE m_found[i];}TE <TY T,TY GRAPH> IN CO T& VirtualBreadthFirstSearch<T,GRAPH>::prev(CO T& t){auto&& i = m_G.Enumeration_inv(t);AS(0 <= i && i < SZ());if(!m_initialised){Initialise();}RE m_prev[i];}TE <TY T,TY GRAPH> IN T VirtualBreadthFirstSearch<T,GRAPH>::Next(){if(m_next.empty()){RE m_not_found;}CO T t_curr = m_next.front();m_next.pop_front();for(auto& t:m_G.Edge(t_curr)){auto&& i = m_G.Enumeration_inv(t);auto&& found_i = m_found[i];if(! found_i){Push(m_next,t);m_prev[i]= t_curr;found_i = true;}}RE t_curr;}TE <TY T,TY GRAPH> TE <TY U>auto VirtualBreadthFirstSearch<T,GRAPH>::GetDistance()-> enable_if_t<is_same_v<GRAPH,MemorisationGraph<U,decldecay_t(declval<GRAPH>().edge())>>,Map<T,int>>{Map<T,int> AN{};for(auto IT = m_next.BE(),EN = m_next.EN();IT != EN;IT++){AN[*IT]= 0;}T t;WH((t = Next())!= m_not_found){if(AN.count(t)== 0){AN[t]= AN[m_prev[m_G.Enumeration_inv(t)]]+ 1;}}RE AN;}TE <TY T,TY GRAPH> TE <TY U>auto VirtualBreadthFirstSearch<T,GRAPH>::GetDistance()-> enable_if_t<!is_same_v<GRAPH,MemorisationGraph<U,decldecay_t(declval<GRAPH>().edge())>>,VE<int>>{VE AN(SZ(),-1);for(auto IT = m_next.BE(),EN = m_next.EN();IT != EN;IT++){AN[m_G.Enumeration_inv(*IT)]= 0;}T t;WH((t = Next())!= m_not_found){auto&& i = m_G.Enumeration_inv(t);int& AN_i = AN[i];AN_i == -1?AN_i = AN[m_G.Enumeration_inv(m_prev[i])]+ 1:AN_i;}RE AN;}TE <TY T,TY GRAPH>pair<VE<int>,int> VirtualBreadthFirstSearch<T,GRAPH>::GetConnectedComponent(){ST_AS(!is_same_v<GRAPH,MemorisationGraph<T,decldecay_t(m_G.edge())>>);CRI V = SZ();VE cc_num(V,-1);int count = 0;for(int i = 0;i < V;i++){if(cc_num[i]== -1){Shift(m_G.Enumeration(i));T t = Next();if(t != m_not_found){WH(t != m_not_found){cc_num[m_G.Enumeration_inv(t)]= count;t = Next();}count++;}}}RE{MO(cc_num),MO(count)};}TE <TY T,TY GRAPH>VE<T> VirtualBreadthFirstSearch<T,GRAPH>::GetNodeEnumeration(){VE<T> AN{};T t = Next();WH(t != m_not_found){AN.push_back(t);t = Next();}RE AN;}TE <TY T,TY GRAPH>VE<T> VirtualBreadthFirstSearch<T,GRAPH>::GetReversedNodeEnumeration(){VE<T> AN{};VE<T> next{};T t;bool searched;WH(!(searched =(t = Next())== m_not_found)|| !next.empty()){WH(!next.empty()&&(searched || next.back()!= m_prev[m_G.Enumeration_inv(t)])){AN.push_back(next.back());next.pop_back();}if(!searched){next.push_back(t);}}RE AN;}TE <TY T,TY GRAPH> TE <TY PATH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Push(LI<T>& next,CO PATH& p){Push(next,get<0>(p));}
TE <TY T,TY GRAPH>CL BreadthFirstSearch:PU VirtualBreadthFirstSearch<T,GRAPH>{PU:TE <TY...Args> IN BreadthFirstSearch(GRAPH& G,CO T& not_found,Args&&... args);IN VO Push(LI<T>& next,CO T& t);};
TE <TY T,TY GRAPH> TE <TY...Args> IN BreadthFirstSearch<T,GRAPH>::BreadthFirstSearch(GRAPH& G,CO T& not_found,Args&&... args):VirtualBreadthFirstSearch<T,GRAPH>(G,not_found,forward<Args>(args)...){}TE <TY T,TY GRAPH> IN VO BreadthFirstSearch<T,GRAPH>::Push(LI<T>& next,CO T& t){next.push_back(t);}
// #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
#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 FINISH_MAIN REPEAT( test_case_num ){ if CE( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } }
#define DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE1 )
#define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) )
#ifdef USE_GETLINE
#define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
#define GETLINE( ... ) GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); }
#else
#define CIN( LL , ... ) LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
#define SET_A( I , N , ... ) VariadicResize( N + I , __VA_ARGS__ ); FOR( VARIABLE_FOR_SET_A , 0 , N ){ VariadicSet( cin , VARIABLE_FOR_SET_A + I , __VA_ARGS__ ); }
#define CIN_A( LL , I , N , ... ) VE<LL> __VA_ARGS__; SET_A( I , N , __VA_ARGS__ )
#define CIN_AA( LL , I0 , N0 , I1 , N1 , VAR ) VE<VE<LL>> VAR( N0 + I0 ); FOR( VARIABLE_FOR_CIN_AA , 0 , N0 ){ SET_A( I1 , N1 , VAR[VARIABLE_FOR_CIN_AA + I0] ); }
#define SET_LL( A ) cin >> A
#endif
#define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX )
#define SOLVE_ONLY
#define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
#define COUTNS( ... ) VariadicCoutNonSep( cout , __VA_ARGS__ )
#define CERR( ... )
#define CERRNS( ... )
#define COUT_A( I , N , A ) CoutArray( cout , I , N , A ) << ENDL
#define CERR_A( I , N , A )
#endif
#ifdef REACTIVE
#ifdef DEBUG
#define RSET( A , ... ) A = __VA_ARGS__
#else
#define RSET( A , ... ) cin >> A
#endif
#define RCIN( LL , A , ... ) LL A; RSET( A , __VA_ARGS__ )
#define ENDL endl
#else
#define ENDL "\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 START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now(); double loop_average_time = 0.0 , loop_start_time = 0.0 , current_time = 0.0; int loop_count = 0
#define CURRENT_TIME ( 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 , loop_count == 0 ? loop_start_time = current_time : loop_average_time = ( current_time - loop_start_time ) / loop_count , ++loop_count , current_time < TL_MS - loop_average_time * 2 - 100.0 )
#define CEXPR( LL , BOUND , VALUE ) CE LL BOUND = VALUE
#define SET_A_ASSERT( I , N , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A + I] , MIN , MAX ); }
#define SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_AA0 , 0 , N0 ){ FOR( VARIABLE_FOR_SET_AA1 , 0 , N1 ){ SET_ASSERT( A[VARIABLE_FOR_SET_AA0 + I0][VARIABLE_FOR_SET_AA1 + I1] , MIN , MAX ); } }
#define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define CIN_A_ASSERT( I , N , A , MIN , MAX ) vector<decldecay_t( MAX )> A( N + I ); SET_A_ASSERT( I , N , A , MIN , MAX )
#define CIN_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) vector A( N0 + I0 , vector<decldecay_t( MAX )>( N1 + I1 ) ); SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX )
#define OUTPUT_ARRAY( C , I , N , A ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , I , N ){ C << A[VARIABLE_FOR_OUTPUT_ARRAY] << " \n"[VARIABLE_FOR_OUTPUT_ARRAY==(N)-1]; }
#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( ARRAY , ... ) for( auto&& __VA_ARGS__ : ARRAY )
#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 ); cerr << fixed << setprecision( DECIMAL_DIGITS )
#define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); RE
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ , true ); 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 >= CONST_TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , CONST_TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
static_assert( ! is_same<decldecay_t( CONST_TARGET ),uint>::value && ! is_same<decldecay_t( CONST_TARGET ),ull>::value ); \
ll ANSWER = MINIMUM; \
{ \
ll ANSWER ## _L = MINIMUM; \
ll ANSWER ## _R = MAXIMUM; \
ANSWER = UPDATE_ANSWER; \
ll EXPRESSION_BS; \
const ll CONST_TARGET_BS = ( CONST_TARGET ); \
ll DIFFERENCE_BS; \
while( ANSWER ## _L < ANSWER ## _R ){ \
DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CONST_TARGET_BS; \
CERR( "二分探索中：" , string{ #ANSWER } + "_L" , "=" , ANSWER ## _L , "<=" , #ANSWER , "=" , ANSWER , "<=" , ANSWER ## _R , "=" , string{ #ANSWER } + "_R" , ":" , #EXPRESSION , "=" , EXPRESSION_BS , DIFFERENCE_BS > 0 ? ">" : DIFFERENCE_BS < 0 ? "<" : "=" , CONST_TARGET_BS , "=" , #CONST_TARGET ); \
if( DIFFERENCE_BS INEQUALITY_FOR_CHECK 0 ){ \
ANSWER ## _R = UPDATE_U; \
} else { \
ANSWER ## _L = UPDATE_L; \
} \
ANSWER = UPDATE_ANSWER; \
} \
if( ANSWER ## _L > ANSWER ## _R ){ \
CERR( "二分探索失敗：" , string{ #ANSWER } + "_L" , "=" , ANSWER ## _L , ">" , ANSWER ## _R , "=" , string{ #ANSWER } + "_R" , ":" , #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：" , string{ #ANSWER } + "_L" , "=" , ANSWER ## _L , "<=" , #ANSWER , "=" , ANSWER , "<=" , ANSWER ## _R , "=" , string{ #ANSWER } + "_R" ); \
CERR( "二分探索が成功したかを確認するために" , #EXPRESSION , "を計算します。" ); \
CERR( "成功判定が不要な場合はこの計算を削除しても構いません。" ); \
EXPRESSION_BS = ( EXPRESSION ); \
CERR( "二分探索結果：" , #EXPRESSION , "=" , EXPRESSION_BS , ( EXPRESSION_BS > CONST_TARGET_BS ? ">" : EXPRESSION_BS < CONST_TARGET_BS ? "<" : "=" ) , CONST_TARGET_BS ); \
if( EXPRESSION_BS DESIRED_INEQUALITY CONST_TARGET_BS ){ \
CERR( "二分探索成功：" , #ANSWER , ":=" , ANSWER ); \
} else { \
CERR( "二分探索失敗：" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \
CERR( "単調でないか、単調増加性と単調減少性を逆にしてしまったか、探索範囲内に解が存在しません。" ); \
ANSWER = MAXIMUM + 1; \
} \
} \
} \
// 単調増加の時にEXPRESSION >= CONST_TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CONST_TARGET , >= , ANSWER , ANSWER + 1 , ( ANSWER ## _L + ANSWER ## _R ) / 2 )
// 単調増加の時にEXPRESSION <= CONST_TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CONST_TARGET , > , ANSWER - 1 , ANSWER , ( ANSWER ## _L + 1 + ANSWER ## _R ) / 2 )
// 単調減少の時にEXPRESSION >= CONST_TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CONST_TARGET , < , ANSWER - 1 , ANSWER , ( ANSWER ## _L + 1 + ANSWER ## _R ) / 2 )
// 単調減少の時にEXPRESSION <= CONST_TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CONST_TARGET , <= , ANSWER , ANSWER + 1 , ( ANSWER ## _L + ANSWER ## _R ) / 2 )
// 尺取り法用
// VAR_TPAは尺取り法用の変数名の接頭辞で、実際の変数名ではなく、_Lと_Rと_infoがつく。
// ANSWER ## _temp = {VAR_TPA ## _L,VAR_TPA ## _R,VPA_TPA ## _info}を{INIT,INIT,INFO_init}で初期化する。VPA_TPA ## _infoは区間和など。
// ANSWER ## _tempがCONTINUE_CONDITIONを満たす限り、ANSWER ## _tempが条件ON_CONDITIONを満たすか否かを判定し、
// それがtrueになるかVAR_TAR ## _LがVAR_TAR ## _Rに追い付くまでVAR_TPA ## _LとVPA_TPA ## _infoの更新操作UPDATE_Lを繰り返し、
// その後VAR_TPA ## _RとVPA_TPA ## _infoの更新操作UPDATE_Rを行う。（マクロとコンマの制約上、関数オブジェクトを用いる）
// 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。
// 例えば長さNの非負整数値配列Aで極大な正値区間とそこでの総和を取得したい場合
// auto update_L = [&]( int& i_L , ll& i_info ){
// i_info -= A[i_L++];
// };
// auto update_R = [&]( int& i_R , ll& i_info ){
// ++i_R < N ? i_info += A[i_R] : i_info;
// };
// TPA( interval , i , 0 , i_R < N , update_L( i_L , i_info ) , update_R( i_R , i_info ) , A[i_L] > 0 && A[i_R] > 0 , ll( A[0] ) );
// とすればtuple<int,int,ll>値配列intervalに{左端,右端,総和}の列が格納される。
#define TPA( ANSWER , VAR_TPA , INIT , CONTINUE_CONDITION , UPDATE_L , UPDATE_R , ON_CONDITION , INFO_init ) \
vector<tuple<decldecay_t( INIT ),decldecay_t( INIT ),decldecay_t( INFO_init )>> ANSWER{}; \
{ \
auto init_TPA = INIT; \
decldecay_t( ANSWER.front() ) ANSWER ## _temp = { init_TPA , init_TPA , INFO_init }; \
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; \
while( 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 ); \
CERR( #ANSWER , "に" , ANSWER ## _prev , "を格納します。" ); \
} \
if( continuing ){ \
if( on_TPA || VAR_TPA ## _L == VAR_TPA ## _R ){ \
ANSWER ## _prev = ANSWER ## _temp; \
UPDATE_R; \
} else { \
UPDATE_L; \
} \
} else { \
break; \
} \
on_TPA_prev = on_TPA; \
} \
} \
// データ構造用
TE <TY T> IN T Addition(CO T& t0,CO T& t1){RE t0 + t1;}
TE <TY T> IN T Xor(CO T& t0,CO T& t1){RE t0 ^ t1;}
TE <TY T> IN T MU(CO T& t0,CO T& t1){RE t0 * t1;}
TE <TY T> IN CO T& Zero(){ST CO T z{};RE z;}
TE <TY T> IN CO T& One(){ST CO T o = 1;RE o;}TE <TY T> IN T AdditionInv(CO T& t){RE -t;}
TE <TY T> IN T Id(CO T& v){RE v;}
TE <TY T> IN T Min(CO T& a,CO T& b){RE a < b?a:b;}
TE <TY T> IN T Max(CO T& a,CO T& b){RE a < b?b:a;}
// VVV 常設ライブラリは以下に挿入する。
#ifdef DEBUG
#include "C:/Users/user/Documents/Programming/Contest/Template/include/a_Body.hpp"
#else
// Random（1KB）
ll GetRand(CRI Rand_min,CRI Rand_max){AS(Rand_min <= Rand_max);ll AN = time(NULL);RE AN * rand()%(Rand_max + 1 - Rand_min)+ Rand_min;}
// Set (1KB)
#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>>;
// Tuple（4KB）
#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 <TY ARG,TY T,TY U,TE <TY...> TY V> IN auto OP OPR ## =(V<T,U>& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;RE t0;}TE <TY ARG,TY T,TY U,TY V> IN tuple<T,U,V>& OP OPR ## =(tuple<T,U,V>& t0,CO ARG& t1){get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;RE t0;}TE <TY ARG,TY T,TY U,TY V,TY W> IN tuple<T,U,V,W>& OP OPR ## =(tuple<T,U,V,W>& t0,CO ARG& t1){get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;get<3>(t0)OPR ## = t1;RE t0;}TE <TE <TY...> TY V,TY...ARGS,TY ARG> IN auto OP OPR(CO V<ARGS...>& t0,CO ARG& t1)-> decldecay_t((get<0>(t0),t0)){auto t = t0;RE MO(t OPR ## = t1);}
#define DF_OF_INCREMENT_FOR_TUPLE(INCR)TE <TY T,TY U,TE <TY...> TY V> IN auto OP INCR(V<T,U>& t)-> decltype((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> IN IS& OP>>(IS& is,tuple<T>& arg){RE is >> get<0>(arg);}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> IN OS& OP<<(OS& os,CO tuple<T>& arg){RE os << get<0>(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(--);
#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));}
TE <TY T> DC_OF_HASH(tuple<T>);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>);
TE <TY T> IN size_t hash<tuple<T>>::OP()(CO tuple<T>& n)CO{ST CO hash<T> h;RE h(get<0>(n));}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,--);TE <TY T> IN V<T> OP*(CO T& scalar,V<T> v){for(auto& t:v){v *= t;}RE MO(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 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;}TE <TY T> VO Sort(VE<T>& a,CO bool& reversed = false){if(reversed){ST auto comp =[](CO T& t0,CO T& t1){RE t1 < t0;};sort(a.BE(),a.EN(),comp);}else{sort(a.BE(),a.EN());}}TE <TY T> IN VE<int> IndexSort(CO VE<T>& a,CO bool& reversed = false){auto index = id<int>(a.SZ());if(reversed){sort(index.BE(),index.EN(),[&](CRI i,CRI j){RE a[j]< a[i];});}else{sort(index.BE(),index.EN(),[&](CRI i,CRI j){RE a[i]< a[j];});}RE index;}
// Map (1KB)
#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);
// StdStream（2KB）
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,Arg&& arg){RE os << forward<Arg>(arg);}TE <CL Traits,TY Arg1,TY Arg2,TY... ARGS> IN OS& VariadicCout(OS& os,Arg1&& arg1,Arg2&& arg2,ARGS&&... args){RE VariadicCout(os << forward<Arg1>(arg1)<< " ",forward<Arg2>(arg2),forward<ARGS>(args)...);}TE <CL Traits,TY Arg> IN OS& VariadicCoutNonSep(OS& os,Arg&& arg){RE os << forward<Arg>(arg);}TE <CL Traits,TY Arg1,TY Arg2,TY... ARGS> IN OS& VariadicCoutNonSep(OS& os,Arg1&& arg1,Arg2&& arg2,ARGS&&... args){RE VariadicCoutNonSep(os << forward<Arg1>(arg1),forward<Arg2>(arg2),forward<ARGS>(args)...);}TE <CL Traits,TY ARRAY> IN OS& CoutArray(OS& os,CRI i_start,CRI i_ulim,ARRAY&& a){for(int i = i_start;i < i_ulim;i++){(i == i_start?os:(os << " "))<< a[i];}RE os;}
// Module (6KB)
#define DC_OF_CPOINT(POINT)IN CO U& POINT()CO NE
#define DC_OF_POINT(POINT)IN U& POINT()NE
#define DF_OF_CPOINT(POINT)TE <TY U> IN CO U& VirtualPointedSet<U>::POINT()CO NE{RE Point();}
#define DF_OF_POINT(POINT)TE <TY U> IN U& VirtualPointedSet<U>::POINT()NE{RE Point();}
TE <TY U>CL UnderlyingSet{PU:US type = U;};TE <TY U>CL VirtualPointedSet:VI PU UnderlyingSet<U>{PU:VI CO U& Point()CO NE = 0;VI U& Point()NE = 0;DC_OF_CPOINT(Unit);DC_OF_CPOINT(Zero);DC_OF_CPOINT(One);DC_OF_CPOINT(Infty);DC_OF_POINT(init);DC_OF_POINT(root);};TE <TY U>CL PointedSet:VI PU VirtualPointedSet<U>{PU:U m_b_U;IN PointedSet(U b_u = U());IN CO U& Point()CO NE;IN U& Point()NE;};TE <TY U>CL VirtualNSet:VI PU UnderlyingSet<U>{PU:VI U Transfer(CO U& u)= 0;IN U Inverse(CO U& u);};TE <TY U,TY F_U>CL AbstractNSet:VI PU VirtualNSet<U>{PU:F_U m_f_U;IN AbstractNSet(F_U f_U);IN AbstractNSet<U,F_U>& OP=(CO AbstractNSet&)NE;IN U Transfer(CO U& u);};TE <TY U>CL VirtualMagma:VI PU UnderlyingSet<U>{PU:VI U Product(U u0,CO U& u1)= 0;IN U Sum(U u0,CO U& u1);};TE <TY U = ll>CL AdditiveMagma:VI PU VirtualMagma<U>{PU:IN U Product(U u0,CO U& u1);};TE <TY U = ll>CL MultiplicativeMagma:VI PU VirtualMagma<U>{PU:IN U Product(U u0,CO U& u1);};TE <TY U,TY M_U>CL AbstractMagma:VI PU VirtualMagma<U>{PU:M_U m_m_U;IN AbstractMagma(M_U m_U);IN AbstractMagma<U,M_U>& OP=(CO AbstractMagma<U,M_U>&)NE;IN U Product(U u0,CO U& u1);};
TE <TY U> IN PointedSet<U>::PointedSet(U b_U):m_b_U(MO(b_U)){}TE <TY U> IN CO U& PointedSet<U>::Point()CO NE{RE m_b_U;}TE <TY U> IN U& PointedSet<U>::Point()NE{RE m_b_U;}DF_OF_CPOINT(Unit);DF_OF_CPOINT(Zero);DF_OF_CPOINT(One);DF_OF_CPOINT(Infty);DF_OF_POINT(init);DF_OF_POINT(root);TE <TY U,TY F_U> IN AbstractNSet<U,F_U>::AbstractNSet(F_U f_U):m_f_U(MO(f_U)){ST_AS(is_invocable_r_v<U,F_U,U>);}TE <TY U,TY F_U> IN AbstractNSet<U,F_U>& AbstractNSet<U,F_U>::operator=(CO AbstractNSet<U,F_U>&)NE{RE *TH;}TE <TY U,TY F_U> IN U AbstractNSet<U,F_U>::Transfer(CO U& u){RE m_f_U(u);}TE <TY U> IN U VirtualNSet<U>::Inverse(CO U& u){RE Transfer(u);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>::AbstractMagma(M_U m_U):m_m_U(MO(m_U)){ST_AS(is_invocable_r_v<U,M_U,U,U>);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>& AbstractMagma<U,M_U>::OP=(CO AbstractMagma<U,M_U>&)NE{RE *TH;}TE <TY U> IN U AdditiveMagma<U>::Product(U u0,CO U& u1){RE MO(u0 += u1);}TE <TY U> IN U MultiplicativeMagma<U>::Product(U u0,CO U& u1){RE MO(u0 *= u1);}TE <TY U,TY M_U> IN U AbstractMagma<U,M_U>::Product(U u0,CO U& u1){RE m_m_U(MO(u0),u1);}TE <TY U> IN U VirtualMagma<U>::Sum(U u0,CO U& u1){RE Product(MO(u0),u1);}
TE <TY U>CL VirtualMonoid:VI PU VirtualMagma<U>,VI PU VirtualPointedSet<U>{};TE <TY U = ll>CL AdditiveMonoid:VI PU VirtualMonoid<U>,PU AdditiveMagma<U>,PU PointedSet<U>{};TE <TY U = ll>CL MultiplicativeMonoid:VI PU VirtualMonoid<U>,PU MultiplicativeMagma<U>,PU PointedSet<U>{PU:IN MultiplicativeMonoid(U e_U);};TE <TY U,TY M_U>CL AbstractMonoid:VI PU VirtualMonoid<U>,PU AbstractMagma<U,M_U>,PU PointedSet<U>{PU:IN AbstractMonoid(M_U m_U,U e_U);};
TE <TY U> IN MultiplicativeMonoid<U>::MultiplicativeMonoid(U e_U):PointedSet<U>(MO(e_U)){}TE <TY U,TY M_U> IN AbstractMonoid<U,M_U>::AbstractMonoid(M_U m_U,U e_U):AbstractMagma<U,M_U>(MO(m_U)),PointedSet<U>(MO(e_U)){}
TE <TY U>CL VirtualGroup:VI PU VirtualMonoid<U>,VI PU VirtualPointedSet<U>,VI PU VirtualNSet<U>{};TE <TY U = ll>CL AdditiveGroup:VI PU VirtualGroup<U>,PU AdditiveMonoid<U>{PU:IN U Transfer(CO U& u);};TE <TY U,TY M_U,TY I_U>CL AbstractGroup:VI PU VirtualGroup<U>,PU AbstractMonoid<U,M_U>,PU AbstractNSet<U,I_U>{PU:IN AbstractGroup(M_U m_U,U e_U,I_U i_U);};
TE <TY U,TY M_U,TY I_U> IN AbstractGroup<U,M_U,I_U>::AbstractGroup(M_U m_U,U e_U,I_U i_U):AbstractMonoid<U,M_U>(MO(m_U),MO(e_U)),AbstractNSet<U,I_U>(MO(i_U)){}TE <TY U> IN U AdditiveGroup<U>::Transfer(CO U& u){RE -u;}
TE <TY R,TY U>CL VirtualRSet:VI PU UnderlyingSet<U>{PU:VI U Action(CO R& r,U u)= 0;IN U PW(U u,CO R& r);IN U ScalarProduct(CO R& r,U u);};TE <TY U,TY MAGMA>CL RegularRSet:VI PU VirtualRSet<U,U>,PU MAGMA{PU:IN RegularRSet(MAGMA magma);IN U Action(CO U& r,U u);};TE <TY MAGMA> RegularRSet(MAGMA magma)-> RegularRSet<inner_t<MAGMA>,MAGMA>;TE <TY R,TY U,TY O_U>CL AbstractRSet:VI PU VirtualRSet<R,U>{PU:O_U m_o_U;IN AbstractRSet(CO R& dummy0,CO U& dummy1,O_U o_U);IN AbstractRSet<R,U,O_U>& OP=(CO AbstractRSet<R,U,O_U>&)NE;IN U Action(CO R& r,U u);};TE <TY R,TY U,TY O_U,TY GROUP>CL AbstractModule:PU AbstractRSet<R,U,O_U>,PU GROUP{PU:IN AbstractModule(CO R& dummy,O_U o_U,GROUP M);};TE <TY R,TY O_U,TY GROUP> AbstractModule(CO R& dummy,O_U o_U,GROUP M)-> AbstractModule<R,inner_t<GROUP>,O_U,GROUP>;TE <TY R,TY U>CL Module:VI PU VirtualRSet<R,U>,PU AdditiveGroup<U>{PU:IN U Action(CO R& r,U u);};
TE <TY R,TY MAGMA> IN RegularRSet<R,MAGMA>::RegularRSet(MAGMA magma):MAGMA(MO(magma)){}TE <TY R,TY U,TY O_U> IN AbstractRSet<R,U,O_U>::AbstractRSet(CO R& dummy0,CO U& dummy1,O_U o_U):m_o_U(MO(o_U)){ST_AS(is_invocable_r_v<U,O_U,R,U>);}TE <TY R,TY U,TY O_U,TY GROUP> IN AbstractModule<R,U,O_U,GROUP>::AbstractModule(CO R& dummy,O_U o_U,GROUP M):AbstractRSet<R,U,O_U>(dummy,M.One(),MO(o_U)),GROUP(MO(M)){ST_AS(is_same_v<U,inner_t<GROUP>>);}TE <TY R,TY U,TY O_U> IN AbstractRSet<R,U,O_U>& AbstractRSet<R,U,O_U>::OP=(CO AbstractRSet<R,U,O_U>&)NE{RE *TH;}TE <TY U,TY MAGMA> IN U RegularRSet<U,MAGMA>::Action(CO U& r,U u){RE TH->Product(r,MO(u));}TE <TY R,TY U,TY O_U> IN U AbstractRSet<R,U,O_U>::Action(CO R& r,U u){RE m_o_U(r,MO(u));}TE <TY R,TY U> IN U Module<R,U>::Action(CO R& r,U u){RE MO(u *= r);}TE <TY R,TY U> IN U VirtualRSet<R,U>::PW(U u,CO R& r){RE Action(r,MO(u));}TE <TY R,TY U> IN U VirtualRSet<R,U>::ScalarProduct(CO R& r,U u){RE Action(r,MO(u));}
// Graph (5KB)
TE <TY T,TY R1,TY R2,TY E>CL VirtualGraph:VI PU UnderlyingSet<T>{PU:VI R1 Enumeration(CRI i)= 0;IN R2 Enumeration_inv(CO T& t);TE <TY PATH> IN R2 Enumeration_inv(CO PATH& p);IN VO Reset();VI CRI SZ()CO NE = 0;VI E& edge()NE = 0;VI ret_t<E,T> Edge(CO T& t)= 0;TE <TY PATH> IN ret_t<E,T> Edge(CO PATH& p);ST IN CO T& Vertex(CO T& t)NE;TE <TY PATH> ST IN CO T& Vertex(CO PATH& e)NE;VI R2 Enumeration_inv_Body(CO T& t)= 0;};TE <TY T,TY R1,TY R2,TY E>CL EdgeImplimentation:VI PU VirtualGraph<T,R1,R2,E>{PU:int m_SZ;E m_edge;IN EdgeImplimentation(CRI SZ,E edge);IN CRI SZ()CO NE;IN E& edge()NE;IN ret_t<E,T> Edge(CO T& t);};TE <TY E>CL Graph:PU EdgeImplimentation<int,CRI,CRI,E>{PU:IN Graph(CRI SZ,E edge);IN CRI Enumeration(CRI i);TE <TY F> IN Graph<F> GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CRI t);};TE <TY T,TY Enum_T,TY Enum_T_inv,TY E>CL EnumerationGraph:PU EdgeImplimentation<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>{PU:Enum_T m_enum_T;Enum_T_inv m_enum_T_inv;IN EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge);IN ret_t<Enum_T,int> Enumeration(CRI i);TE <TY F> IN EnumerationGraph<T,Enum_T,Enum_T_inv,F> GetGraph(F edge)CO;IN ret_t<Enum_T_inv,T> Enumeration_inv_Body(CO T& t);};TE <TY Enum_T,TY Enum_T_inv,TY E> EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge)-> EnumerationGraph<decldecay_t(declval<Enum_T>()(0)),Enum_T,Enum_T_inv,E>;TE <TY T,TY E>CL MemorisationGraph:PU EdgeImplimentation<T,T,CRI,E>{PU:int m_LE;VE<T> m_memory;Map<T,int> m_memory_inv;IN MemorisationGraph(CRI SZ,CO T& dummy,E edge);IN T Enumeration(CRI i);IN VO Reset();TE <TY F> IN MemorisationGraph<T,F> GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CO T& t);};
TE <TY T,TY R1,TY R2,TY E> IN EdgeImplimentation<T,R1,R2,E>::EdgeImplimentation(CRI SZ,E edge):m_SZ(SZ),m_edge(MO(edge)){ST_AS(is_COructible_v<T,R1> && is_COructible_v<int,R2> && is_invocable_v<E,T>);}TE <TY E> IN Graph<E>::Graph(CRI SZ,E edge):EdgeImplimentation<int,CRI,CRI,E>(SZ,MO(edge)){}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN EnumerationGraph<T,Enum_T,Enum_T_inv,E>::EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge):EdgeImplimentation<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>(SZ,MO(edge)),m_enum_T(MO(enum_T)),m_enum_T_inv(MO(enum_T_inv)){}TE <TY T,TY E> IN MemorisationGraph<T,E>::MemorisationGraph(CRI SZ,CO T& dummy,E edge):EdgeImplimentation<T,T,CRI,E>(SZ,MO(edge)),m_LE(),m_memory(),m_memory_inv(){ST_AS(is_invocable_v<E,T>);}TE <TY E> IN CRI Graph<E>::Enumeration(CRI i){RE i;}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN ret_t<Enum_T,int> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration(CRI i){RE m_enum_T(i);}TE <TY T,TY E> IN T MemorisationGraph<T,E>::Enumeration(CRI i){AS(0 <= i && i < m_LE);RE m_memory[i];}TE <TY T,TY R1,TY R2,TY E> IN R2 VirtualGraph<T,R1,R2,E>::Enumeration_inv(CO T& t){RE Enumeration_inv_Body(t);}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN R2 VirtualGraph<T,R1,R2,E>::Enumeration_inv(CO PATH& p){RE Enumeration_inv_Body(get<0>(p));}TE <TY E> IN CRI Graph<E>::Enumeration_inv_Body(CRI i){RE i;}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN ret_t<Enum_T_inv,T> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration_inv_Body(CO T& t){RE m_enum_T_inv(t);}TE <TY T,TY E> IN CRI MemorisationGraph<T,E>::Enumeration_inv_Body(CO T& t){if(m_memory_inv.count(t)== 0){AS(m_LE < TH->SZ());m_memory.push_back(t);RE m_memory_inv[t]= m_LE++;}RE m_memory_inv[t];}TE <TY T,TY R1,TY R2,TY E> VO VirtualGraph<T,R1,R2,E>::Reset(){}TE <TY T,TY E> IN VO MemorisationGraph<T,E>::Reset(){m_LE = 0;m_memory.clear();m_memory_inv.clear();}TE <TY T,TY R1,TY R2,TY E> IN CRI EdgeImplimentation<T,R1,R2,E>::SZ()CO NE{RE m_SZ;}TE <TY T,TY R1,TY R2,TY E> IN E& EdgeImplimentation<T,R1,R2,E>::edge()NE{RE m_edge;}TE <TY T,TY R1,TY R2,TY E> IN ret_t<E,T> EdgeImplimentation<T,R1,R2,E>::Edge(CO T& t){RE m_edge(t);}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN ret_t<E,T> VirtualGraph<T,R1,R2,E>::Edge(CO PATH& p){RE Edge(get<0>(p));}TE <TY E> TE <TY F> IN Graph<F> Graph<E>::GetGraph(F edge)CO{RE Graph<F>(TH->SZ(),MO(edge));}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> TE <TY F> IN EnumerationGraph<T,Enum_T,Enum_T_inv,F> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::GetGraph(F edge)CO{RE EnumerationGraph<T,Enum_T,Enum_T_inv,F>(TH->SZ(),m_enum_T,m_enum_T_inv,MO(edge));}TE <TY T,TY E> TE <TY F> IN MemorisationGraph<T,F> MemorisationGraph<T,E>::GetGraph(F edge)CO{RE MemorisationGraph<T,F>(TH->SZ(),MO(edge));}TE <TY T,TY R1,TY R2,TY E> IN CO T& VirtualGraph<T,R1,R2,E>::Vertex(CO T& t)NE{RE t;}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN CO T& VirtualGraph<T,R1,R2,E>::Vertex(CO PATH& e)NE{RE Vertex(get<0>(e));}
// Grid (2KB)
#define SET_GRID H_minus = H - 1;W_minus = W - 1;HW = ll(H)* W
#define SET_HW(h,w)H = h;W = w;SET_GRID
#define CIN_HW cin >> H >> W;SET_GRID
TE <TY E>CL GridGraph:PU EnumerationGraph<T2<int>,T2<int>(&)(CRI),int(&)(CO T2<int>&),E>{PU:IN GridGraph(E e);};int H,W,H_minus,W_minus;ll HW;VE<string> grid;char walkable = '.',unwalkable = '#';
IN T2<int> EnumHW(CRI v){RE{v / W,v % W};}IN int EnumHW_inv(CO T2<int>& ij){auto&[i,j]= ij;RE i * W + j;}TE <TY E> IN GridGraph<E>::GridGraph(E e):EnumerationGraph<T2<int>,T2<int>(&)(CRI),int(&)(CO T2<int>&),E>(HW,EnumHW,EnumHW_inv,MO(e)){AS(HW >> 31 == 0 && H * W == HW);}VE<T2<int>> EdgeOnGrid(CO T2<int>& v){VE<T2<int>> AN{};auto&[i,j]= v;if(grid[i][j]== walkable){if(i > 0 && grid[i-1][j]== walkable){AN.push_back({i-1,j});}if(i+1 < H && grid[i+1][j]== walkable){AN.push_back({i+1,j});}if(j > 0 && grid[i][j-1]== walkable){AN.push_back({i,j-1});}if(j+1 < W && grid[i][j+1]== walkable){AN.push_back({i,j+1});}}RE AN;}VE<pair<T2<int>,ll>> WEdgeOnGrid(CO T2<int>& v){VE<pair<T2<int>,ll>> AN{};auto&[i,j]= v;if(grid[i][j]== walkable){if(i>0 && grid[i-1][j]== walkable){AN.push_back({{i-1,j},1});}if(i+1 < H && grid[i+1][j]== walkable){AN.push_back({{i+1,j},1});}if(j>0 && grid[i][j-1]== walkable){AN.push_back({{i,j-1},1});}if(j+1 < W && grid[i][j+1]== walkable){AN.push_back({{i,j+1},1});}}RE AN;}IN VO SetWallStringOnGrid(CRI i,VE<string>& S){if(S.empty()){S.resize(H);}cin >> S[i];AS(int(S[i].SZ())== W);}CO string direction="URDL";IN int DirectionNumberOnGrid(CRI i,CRI j,CRI k,CRI h){RE i < k?2:i > k?0:j < h?1:(AS(j > h),3);}IN int DirectionNumberOnGrid(CO T2<int>& v,CO T2<int>& w){auto&[i,j]= v;auto&[k,h]= w;RE DirectionNumberOnGrid(i,j,k,h);}IN int DirectionNumberOnGrid(CRI v,CRI w){RE DirectionNumberOnGrid(EnumHW(v),EnumHW(w));}IN int ReverseDirectionNumberOnGrid(CRI n){AS(0 <= n && n<4);RE n ^ 2;}
// ConstexprModulo (7KB)
CEXPR(uint,P,998244353);
#define RP Represent
#define DeRP Derepresent
TE <uint M,TY INT> CE INT RS(INT n)NE{RE MO(n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n < INT(M)?n:n %= M);}TE <TY INT> CE INT& RSP(INT& n)NE{CE CO uint trunc =(1 << 23)- 1;INT n_u = n >> 23;n &= trunc;INT n_uq =(n_u / 7)/ 17;n_u -= n_uq * 119;n += n_u << 23;RE n < n_uq?n += P - n_uq:n -= n_uq;}
TE <uint M> CL Mod;TE <uint M>CL COantsForMod{PU:COantsForMod()= delete;ST CE CO uint g_memory_bound = 1e6;ST CE CO uint g_memory_LE = M < g_memory_bound?M:g_memory_bound;ST CE uint g_M_minus = M - 1;ST CE int g_order_minus_1 = M - 2;ST CE int g_order_minus_1_neg = -g_order_minus_1;};
#define SFINAE_FOR_MOD enable_if_t<is_COructible_v<uint,decay_t<T>>>*
#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,SFINAE_FOR_MOD = nullptr> 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,SFINAE_FOR_MOD = nullptr> 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,SFINAE_FOR_MOD> CE Mod<M>::Mod(T n)NE:m_n(RS<M>(MO(n))){}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(ll(MO(EX %= COants::g_M_minus))* COants::g_order_minus_1_neg %COants::g_M_minus):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 IS& OP>>(IS& is,Mod<M>& n){ll m;is >> m;n = m;RE is;}TE <uint M,CL Traits> IN OS& OP<<(OS& 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