結果

問題 No.2487 Multiple of M
ユーザー 👑 p-adicp-adic
提出日時 2023-09-30 11:25:11
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 5 ms / 2,000 ms
コード長 50,097 bytes
コンパイル時間 3,914 ms
コンパイル使用メモリ 243,768 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-09-30 12:53:19
合計ジャッジ時間 5,886 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge11
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,376 KB
testcase_01 AC 1 ms
4,376 KB
testcase_02 AC 2 ms
4,380 KB
testcase_03 AC 4 ms
4,376 KB
testcase_04 AC 1 ms
4,376 KB
testcase_05 AC 4 ms
4,380 KB
testcase_06 AC 4 ms
4,376 KB
testcase_07 AC 2 ms
4,380 KB
testcase_08 AC 1 ms
4,376 KB
testcase_09 AC 4 ms
4,380 KB
testcase_10 AC 1 ms
4,376 KB
testcase_11 AC 3 ms
4,380 KB
testcase_12 AC 3 ms
4,376 KB
testcase_13 AC 3 ms
4,376 KB
testcase_14 AC 3 ms
4,380 KB
testcase_15 AC 4 ms
4,376 KB
testcase_16 AC 4 ms
4,376 KB
testcase_17 AC 4 ms
4,380 KB
testcase_18 AC 3 ms
4,380 KB
testcase_19 AC 4 ms
4,376 KB
testcase_20 AC 3 ms
4,376 KB
testcase_21 AC 4 ms
4,376 KB
testcase_22 AC 4 ms
4,380 KB
testcase_23 AC 4 ms
4,376 KB
testcase_24 AC 4 ms
4,380 KB
testcase_25 AC 4 ms
4,380 KB
testcase_26 AC 4 ms
4,380 KB
testcase_27 AC 4 ms
4,376 KB
testcase_28 AC 4 ms
4,380 KB
testcase_29 AC 4 ms
4,380 KB
testcase_30 AC 5 ms
4,376 KB
testcase_31 AC 4 ms
4,380 KB
testcase_32 AC 4 ms
4,380 KB
testcase_33 AC 4 ms
4,380 KB
testcase_34 AC 3 ms
4,380 KB
testcase_35 AC 3 ms
4,376 KB
testcase_36 AC 4 ms
4,376 KB
testcase_37 AC 4 ms
4,376 KB
testcase_38 AC 3 ms
4,376 KB
testcase_39 AC 3 ms
4,376 KB
testcase_40 AC 4 ms
4,376 KB
testcase_41 AC 4 ms
4,376 KB
testcase_42 AC 3 ms
4,380 KB
testcase_43 AC 3 ms
4,376 KB
testcase_44 AC 3 ms
4,380 KB
testcase_45 AC 3 ms
4,376 KB
testcase_46 AC 4 ms
4,376 KB
testcase_47 AC 3 ms
4,380 KB
testcase_48 AC 3 ms
4,380 KB
testcase_49 AC 3 ms
4,380 KB
testcase_50 AC 4 ms
4,376 KB
testcase_51 AC 2 ms
4,376 KB
testcase_52 AC 3 ms
4,380 KB
testcase_53 AC 2 ms
4,376 KB
testcase_54 AC 3 ms
4,376 KB
testcase_55 AC 3 ms
4,380 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#ifdef DEBUG
  #define _GLIBCXX_DEBUG
  #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ); signal( SIGABRT , &AlertAbort )
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE )
  #define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl
  #define COUT( ... ) VariadicCout( cout << "出力： " , __VA_ARGS__ ) << endl
  #define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl
  #define COUT_A( A , N ) cout << "出力： "; OUTPUT_ARRAY( cout , A , N ) << endl
  #define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl
  #define COUT_ITR( A ) cout << "出力： "; OUTPUT_ITR( cout , A ) << endl
  #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
  #define AUTO_CHECK int auto_checked; AutoCheck( auto_checked ); if( auto_checked == 3 ){ Jikken(); return 0; } else if( auto_checked == 4 ){ Debug(); return 0; } else if( auto_checked != 0 ){ return 0; };
#else
  #pragma GCC optimize ( "O3" )
  #pragma GCC optimize ( "unroll-loops" )
  #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
  #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr )
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE )
  #define CERR( ... ) 
  #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << "\n"
  #define CERR_A( A , N ) 
  #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << "\n"
  #define CERR_ITR( A ) 
  #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << "\n"
  #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
  #define AUTO_CHECK
#endif
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using lld = __float128;
template <typename INT> using T2 = pair<INT,INT>;
template <typename INT> using T3 = tuple<INT,INT,INT>;
template <typename INT> using T4 = tuple<INT,INT,INT,INT>;
using path = pair<int,ll>;
// #define RANDOM_TEST
#if defined( DEBUG ) && defined( RANDOM_TEST )
  ll GetRand( const ll& Rand_min , const ll& Rand_max );
  #define SET_ASSERT( A , MIN , MAX ) CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) )
  #define CIN( LL , ... ) LL __VA_ARGS__; static_assert( false )
  #define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = bound_T; static_assert( bound_T > 1 )
  #define RETURN( ANSWER ) if( ( ANSWER ) == guchoku ){ CERR( ANSWER , "==" , guchoku ); goto END_MAIN; } else { CERR( ANSWER , "!=" , guchoku ); return 0; }
#else
  #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX )
  #define CIN( LL , ... ) LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
  #define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = 1; if constexpr( bound_T > 1 ){ SET_ASSERT( T , 1 , bound_T ); }
  #define RETURN( ANSWER ) COUT( ANSWER ); QUIT
#endif
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define TYPE_OF( VAR ) decay_t<decltype( VAR )>
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define CIN_A( LL , A , N ) LL A[N]; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; }
#define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
#define GETLINE( ... ) GETLINE_SEPARATE( " " , ... )
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ )
#define FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR >= FINAL ; VAR -- )
#define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end()
#define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES )
#define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS )
#define OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS
#define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.begin() , END_FOR_OUTPUT_ITR = A.end(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; while( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS
#define QUIT goto END_MAIN
#define START_MAIN REPEAT( T ){ { if constexpr( bound_T > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_T , ":" ); }
#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 FINISH_MAIN QUIT; } END_MAIN: CERR( "" ); }

// 入出力用関数
template <class Traits> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); }
template <class Traits> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg& arg ) { return os << arg; }
template <class Traits , typename Arg1 , typename Arg2 , typename... ARGS> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); }

// 算術用関数
template <typename T> inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }
inline ll MIN( const ll& a , const ll& b ){ return min( a , b ); }
inline ull MIN( const ull& a , const ull& b ){ return min( a , b ); }
inline ll MAX( const ll& a , const ll& b ){ return max( a , b ); }
inline ull MAX( const ull& a , const ull& b ){ return max( a , b ); }

#define POWER( ANSWER , ARGUMENT , EXPONENT )				\
  static_assert( ! is_same<TYPE_OF( ARGUMENT ),int>::value && ! is_same<TYPE_OF( ARGUMENT ),uint>::value ); \
  TYPE_OF( ARGUMENT ) ANSWER{ 1 };					\
  {									\
    TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT );	\
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;			\
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;	\
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO )		\
  ll ANSWER{ 1 };							\
  {									\
    ll ARGUMENT_FOR_SQUARE_FOR_POWER = ( ( MODULO ) + ( ( ARGUMENT ) % ( MODULO ) ) ) % ( MODULO ); \
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_INDEX , CONSTEXPR_LENGTH , MODULO ) \
  static ll ANSWER[CONSTEXPR_LENGTH];					\
  static ll ANSWER_INV[CONSTEXPR_LENGTH];				\
  static ll INVERSE[CONSTEXPR_LENGTH];					\
  {									\
    ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1;				\
    ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL;			\
    FOREQ( i , 1 , MAX_INDEX ){						\
      ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \
    }									\
    ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \
    FOREQ( i , 2 , MAX_INDEX ){						\
      ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \
    }									\
  }									\

// 二分探索テンプレート
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
  static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \
  ll ANSWER = MINIMUM;							\
  if( MINIMUM <= MAXIMUM ){						\
    ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM;				\
    ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM;				\
    ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
    ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH;			\
    while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \
      VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \
      CERR( "二分探索中： " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << "=" << VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ); \
      if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH INEQUALITY_FOR_CHECK 0 ){	\
	VARIABLE_FOR_BINARY_SEARCH_U = UPDATE_U;			\
      } else {								\
	VARIABLE_FOR_BINARY_SEARCH_L = UPDATE_L;			\
      }									\
      ANSWER = UPDATE_ANSWER;						\
    }									\
    CERR( "二分探索終了： " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << ( EXPRESSION > TARGET ? ">" : EXPRESSION < TARGET ? "<" : "=" ) << TARGET ); \
    if( EXPRESSION DESIRED_INEQUALITY TARGET ){				\
      CERR( "二分探索成功" );						\
    } else {								\
      CERR( "二分探索失敗" );						\
      ANSWER = MAXIMUM + 1;						\
    }									\
  } else {								\
    CERR( "二分探索失敗： " << MINIMUM << ">" << MAXIMUM );		\
    ANSWER = MAXIMUM + 1;						\
  }									\

// 単調増加の時にEXPRESSION >= TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , >= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調増加の時にEXPRESSION <= TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , > , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調減少の時にEXPRESSION >= TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , < , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調減少の時にEXPRESSION <= TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , <= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MaximumLeq( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.upper_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; }
// t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MaximumLt( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.lower_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; }
// t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MinimumGeq( set<T>& S , const T& t ) { return S.lower_bound( t ); }
// tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MinimumGt( set<T>& S , const T& t ) { return S.upper_bound( t ); }

// データ構造用関数
template <typename T> inline T add( const T& t0 , const T& t1 ) { return t0 + t1; }
template <typename T> inline T xor_add( const T& t0 , const T& t1 ){ return t0 ^ t1; }
template <typename T> inline T multiply( const T& t0 , const T& t1 ) { return t0 * t1; }
template <typename T> inline const T& zero() { static const T z = 0; return z; }
template <typename T> inline const T& one() { static const T o = 1; return o; }\
template <typename T> inline T add_inv( const T& t ) { return -t; }
template <typename T> inline T id( const T& v ) { return v; }

// グリッド問題用関数
int H , W , H_minus , W_minus , HW;
inline pair<int,int> EnumHW( const int& v ) { return { v / W , v % W }; }
inline int EnumHW_inv( const int& h , const int& w ) { return h * W + w; }
const string direction[4] = {"U","R","D","L"};
// (i,j)->(k,h)の方向番号を取得
inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return i<k?2:i>k?0:j<h?1:j>h?3:(assert(false),-1);}
// v->wの方向番号を取得
inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);return DirectionNumberOnGrid(i,j,k,h);}
// 方向番号の反転U<->D、R<->L
inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<int> ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back(v);}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back(v);}if(j>0){e[EnumHW_inv(i,j-1)].push_back(v);}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back(v);}}}}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<pair<int,ll> > ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){const int v=EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back({v,1});}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back({v,1});}if(j>0){e[EnumHW_inv(i,j-1)].push_back({v,1});}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back({v,1});}}}}
inline void SetWallOnGrid( const string& Si , const int& i , bool ( &non_wall_i )[] , const char& walkable = '.'  , const char& unwalkable = '#' ){FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]==unwalkable),false);}}

// グラフ用関数
template <typename path_type> list<path_type> E( const int& i ); // 本体をmain()の後に定義
template <typename path_type> vector<list<path_type> > e;

// デバッグ用関数
#ifdef DEBUG
  inline void AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); }
  void AutoCheck( int& auto_checked );
  void Jikken();
  void Debug();
#endif

// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#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 MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&

/*

C-x 3 C-x o C-x C-fによるファイル操作用

BIT:
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/compress.txt

BFS:
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt

DFS on Tree:
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepththFirstSearch/Tree/compress.txt

Divisor:
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt

Mod:
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/ConstexprModulo/compress.txt

Polynomial
c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt

*/

// VVV ライブラリは以下に挿入する。
TE <TY INT,INT val_limit,int LE_max = val_limit>CL PrimeEnumeration{PU:bool m_is_composite[val_limit];INT m_val[LE_max];int m_LE;CE PrimeEnumeration();CE CO INT& OP[](CRI n) CO;CE CO INT& Get(CRI n) CO;CE CO bool& IsComposite(CRI i) CO;CE CRI LE() CO NE;};
TE <TY INT,INT val_limit,int LE_max>CE PrimeEnumeration<INT,val_limit,LE_max>::PrimeEnumeration():m_is_composite(),m_val(),m_LE(0){for(INT i = 2;i < val_limit;i++){if(! m_is_composite[i]){INT j = i;WH((j += i)< val_limit){m_is_composite[j] = true;}m_val[m_LE++] = i;if(m_LE >= LE_max){break;}}}}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::OP[](CRI n)CO{assert(n < m_LE);RE m_val[n];}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::Get(CRI n)CO{RE OP[](n);}TE <TY INT,INT val_limit,int LE_max> CE CO bool& PrimeEnumeration<INT,val_limit,LE_max>::IsComposite(CRI i)CO{assert(i < val_limit);RE m_is_composite[i];}TE <TY INT,INT val_limit,int LE_max> CE CRI PrimeEnumeration<INT,val_limit,LE_max>::LE()CO NE{RE m_LE;}
TE <TY INT,INT val_limit,int LE_max>VO SetPrimeFactorisation(CO PrimeEnumeration<INT,val_limit,LE_max>& prime,CO INT& n,VE<INT>& P,VE<INT>& EX){INT n_copy = n;int i = 0;WH(i < prime.m_LE){CO INT& p = prime[i];if(p * p > n_copy){break;}if(n_copy % p == 0){P.push_back(p);EX.push_back(1);INT& EX_back = EX.back();n_copy /= p;WH(n_copy % p == 0){EX_back++;n_copy /= p;}}i++;}if(n_copy != 1){P.push_back(n_copy);EX.push_back(1);}RE;}

#define SFINAE_FOR_MA(DEFAULT) TY Arg,enable_if_t<is_constructible<T,Arg>::value>* DEFAULT

TE <uint Y,uint X,TY T>CL MA{PU:T m_M[Y][X];IN MA()NE;IN MA(CO T& t)NE;IN MA(CRI t)NE;TE <TY Arg0,TY Arg1,TY... Args> IN MA(Arg0&& t0,Arg1&& t1,Args&&... args)NE;IN MA(CO MA<Y,X,T>& mat)NE;IN MA(MA<Y,X,T>&& mat)NE;TE <TY... Args> IN MA(CO T (&mat)[Y][X])NE;TE <TY... Args> IN MA(T (&&mat)[Y][X])NE;IN MA<Y,X,T>& OP=(CO MA<Y,X,T>& mat)NE;IN MA<Y,X,T>& OP=(MA<Y,X,T>&& mat)NE;IN MA<Y,X,T>& OP=(CO T (&mat)[Y][X])NE;IN MA<Y,X,T>& OP=(T (&&mat)[Y][X])NE;IN MA<Y,X,T>& OP+=(CO MA<Y,X,T>& mat)NE;IN MA<Y,X,T>& OP-=(CO MA<Y,X,T>& mat)NE;IN MA<Y,X,T>& OP*=(CO T& scalar)NE;IN MA<Y,X,T>& OP*=(CO MA<X,X,T>& mat)NE;IN MA<Y,X,T>& OP/=(CO T& scalar);IN MA<Y,X,T>& OP%=(CO T& scalar);IN bool OP==(CO MA<Y,X,T>& mat) CO NE;TE <uint Z> IN MA<Y,Z,T> OP*(CO MA<X,Z,T>& mat) CO NE;IN MA<X,Y,T> Transpose() CO NE;IN T Trace() CO NE;IN CO T (&GetTable() CO NE)[Y][X];IN T (&RefTable()NE)[Y][X];ST IN CO MA<Y,X,T>& Zero()NE;ST IN CO MA<Y,X,T>& Unit()NE;ST IN MA<Y,X,T> Scalar(CO T& t)NE;ST IN VO SetArray(T (&M)[Y][X],T (&&array)[Y * X])NE;};

TE <uint Y,uint X,TY T> IN MA<Y,X,T>::MA()NE:m_M(){}TE <uint Y,uint X,TY T> IN MA<Y,X,T>::MA(CO T& t)NE:m_M(){OP=(Scalar(t));}TE <uint Y,uint X,TY T> IN MA<Y,X,T>::MA(CRI t)NE:MA(T(t)){}TE <uint Y,uint X,TY T> TE <TY Arg0,TY Arg1,TY... Args> IN MA<Y,X,T>::MA(Arg0&& t0,Arg1&& t1,Args&&... args)NE:m_M(){T array[Y * X] ={T(forward<Arg0>(t0)),T(forward<Arg1>(t1)),T(forward<Args>(args))...};SetArray(m_M,MO(array));}TE <uint Y,uint X,TY T> IN MA<Y,X,T>::MA(CO MA<Y,X,T>& mat)NE:m_M(){OP=(mat.m_M);}TE <uint Y,uint X,TY T> IN MA<Y,X,T>::MA(MA<Y,X,T>&& mat)NE:m_M(){swap(m_M,mat.m_M);}TE <uint Y,uint X,TY T> TE <TY... Args> IN MA<Y,X,T>::MA(CO T (&mat)[Y][X])NE:m_M(){OP=(mat);}TE <uint Y,uint X,TY T> TE <TY... Args> IN MA<Y,X,T>::MA(T (&&mat)[Y][X])NE:m_M(){swap(m_M,mat);}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP=(CO MA<Y,X,T>& mat)NE{RE OP=(mat.m_M);}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP=(MA<Y,X,T>&& mat)NE{RE OP=(MO(mat.m_M));}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP=(CO T (&mat)[Y][X])NE{for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];CO T (&mat_y)[X] = mat[y];for(uint x = 0;x < X;x++){m_M_y[x] = mat_y[x];}}RE *TH;}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP=(T (&&mat)[Y][X])NE{swap(m_M,mat);RE *TH;}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP+=(CO MA<Y,X,T>& mat)NE{for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];T (&mat_y)[X] = mat.m_M[y];for(uint x = 0;x < X;x++){m_M_y[x] += mat_y[x];}}RE *TH;}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP-=(CO MA<Y,X,T>& mat)NE{for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];T (&mat_y)[X] = mat.m_M[y];for(uint x = 0;x < X;x++){m_M_y[x] -= mat_y[x];}}RE *TH;}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP*=(CO T& scalar)NE{for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];for(uint x = 0;x < X;x++){m_M_y[x] *= scalar;}}RE *TH;}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP*=(CO MA<X,X,T>& mat)NE{RE OP=(MO(*TH * mat));}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP/=(CO T& scalar){RE OP*=(T(1) / scalar);}TE <uint Y,uint X,TY T> IN MA<Y,X,T>& MA<Y,X,T>::OP%=(CO T& scalar){for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];for(uint x = 0;x < X;x++){m_M_y[x] %= scalar;}}RE *TH;}TE <uint Y,uint X,TY T> TE <uint Z> IN MA<Y,Z,T> MA<Y,X,T>::OP*(CO MA<X,Z,T>& mat) CO NE{MA<Y,Z,T> prod{};for(uint y = 0;y < Y;y++){CO T (&m_M_y)[X] = m_M[y];T (&prod_y)[Z] = prod.m_M[y];for(uint x = 0;x < X;x++){CO T &m_M_yx = m_M_y[x];CO T (&mat_x)[Z] = mat.m_M[x];for(uint z = 0;z < Z;z++){prod_y[z] += m_M_yx * mat_x[z];}}}RE prod;}TE <uint Y,uint X,TY T> IN bool MA<Y,X,T>::OP==(CO MA<Y,X,T>& mat) CO NE{for(uint y = 0;y < Y;y++){CO T (&m_M_y)[X] = m_M[y];CO T (&mat_y)[X] = mat[y];for(uint x = 0;x < X;x++){if(m_M_y[x] != mat_y[x]){RE false;}}}RE true;}TE <uint Y,uint X,TY T> IN MA<X,Y,T> MA<Y,X,T>::Transpose() CO NE{MA<X,Y,T> M_t{};for(uint x = 0;x < X;x++){CO T (&M_t_x)[Y] = M_t.m_M[x];for(uint y = 0;y < Y;y++){M_t_x[y] = m_M[y][x];}}RE M_t;}TE <uint Y,uint X,TY T> IN T MA<Y,X,T>::Trace() CO NE{CE CO uint minXY = Y < X?Y:X;T AN{};for(uint y = 0;y < minXY;y++){AN += m_M[y][y];}RE AN;}TE <uint Y,uint X,TY T> IN T (&MA<Y,X,T>::RefTable()NE)[Y][X]{RE m_M;}TE <uint Y,uint X,TY T> IN CO T (&MA<Y,X,T>::GetTable() CO NE)[Y][X]{RE m_M;}TE <uint Y,uint X,TY T> IN CO MA<Y,X,T>& MA<Y,X,T>::Zero()NE{ST CO MA<Y,X,T> zero{};RE zero;}TE <uint Y,uint X,TY T> IN CO MA<Y,X,T>& MA<Y,X,T>::Unit()NE{ST CO MA<Y,X,T> unit{1};RE unit;}TE <uint Y,uint X,TY T> IN MA<Y,X,T> MA<Y,X,T>::Scalar(CO T& t)NE{CE CO uint minXY = Y < X?Y:X;MA<Y,X,T> M{};for(uint y = 0;y < minXY;y++){M.m_M[y][y] = t;}RE M;}TE <uint Y,uint X,TY T> IN VO MA<Y,X,T>::SetArray(T (&M)[Y][X],T (&&array)[Y * X])NE{uint i = 0;for(uint y = 0;y < Y;y++){T (&M_y)[X] = M[y];for(uint x = 0;x < X;x++){M_y[x] = MO(array[i + x]);}i += X;}}TE <uint Y,uint X,TY T> IN MA<Y,X,T> OP!=(CO MA<Y,X,T>& mat1,CO MA<Y,X,T>& mat2)NE{RE !(mat1 == mat2);}TE <uint Y,uint X,TY T> IN MA<Y,X,T> OP+(CO MA<Y,X,T>& mat1,CO MA<Y,X,T>& mat2)NE{RE MO(MA<Y,X,T>(mat1) += mat2);}TE <uint Y,uint X,TY T> IN MA<Y,X,T> OP-(CO MA<Y,X,T>& mat1,CO MA<Y,X,T>& mat2)NE{RE MO(MA<Y,X,T>(mat1) -= mat2);}TE <uint Y,uint X,TY T> IN MA<Y,X,T> OP*(CO MA<Y,X,T>& mat,CO T& scalar)NE{RE MO(MA<Y,X,T>(mat) *= scalar);}TE <uint Y,uint X,TY T> IN MA<Y,X,T> OP*(CO T& scalar,CO MA<Y,X,T>& mat)NE{RE MO(MA<Y,X,T>(mat) *= scalar);}TE <uint Y,uint X,TY T> IN MA<Y,X,T> OP/(CO MA<Y,X,T>& mat,CO T& scalar){RE MO(MA<Y,X,T>(mat) /= scalar);}TE <uint Y,uint X,TY T> IN MA<Y,X,T> OP%(CO MA<Y,X,T>& mat,CO T& scalar){RE MO(MA<Y,X,T>(mat) %= scalar);}

CEXPR(uint,P,998244353);TE <uint M,TY INT> CE INT& RS(INT& n)NE{RE n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n %= M;}TE <uint M> CE uint& RS(uint& n)NE{RE n %= M;}TE <uint M> CE ull& RS(ull& n)NE{RE 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 <> CE ull& RS<P,ull>(ull& n)NE{CE CO ull Pull = P;CE CO ull Pull2 = (Pull - 1)* (Pull - 1);RE RSP(n > Pull2?n -= Pull2:n);}TE <uint M,TY INT> CE INT RS(INT&& n)NE{RE MO(RS<M>(n));}TE <uint M,TY INT> CE INT RS(CO INT& n)NE{RE RS<M>(INT(n));}

#define SFINAE_FOR_MOD(DEFAULT)TY T,enable_if_t<is_constructible<uint,decay_t<T> >::value>* DEFAULT
#define DC_OF_CM_FOR_MOD(FUNC)CE bool OP FUNC(CO Mod<M>& n)CO NE
#define DC_OF_AR_FOR_MOD(FUNC)CE Mod<M> OP FUNC(CO Mod<M>& n)CO NE;TE <SFINAE_FOR_MOD(= nullptr)> CE Mod<M> OP FUNC(T&& n)CO NE;
#define DF_OF_CM_FOR_MOD(FUNC)TE <uint M> CE bool Mod<M>::OP FUNC(CO Mod<M>& n)CO NE{RE m_n FUNC n.m_n;}
#define DF_OF_AR_FOR_MOD(FUNC,FORMULA)TE <uint M> CE Mod<M> Mod<M>::OP FUNC(CO Mod<M>& n)CO NE{RE MO(Mod<M>(*TH)FUNC ## = n);}TE <uint M> TE <SFINAE_FOR_MOD()> CE Mod<M> Mod<M>::OP FUNC(T&& n)CO NE{RE FORMULA;}TE <uint M,SFINAE_FOR_MOD(= nullptr)> CE Mod<M> OP FUNC(T&& n0,CO Mod<M>& n1)NE{RE MO(Mod<M>(forward<T>(n0))FUNC ## = 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;CE Mod(Mod<M>&& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> CE Mod(CO T& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> CE Mod(T& n)NE;TE <SFINAE_FOR_MOD(= nullptr)> CE Mod(T&& n)NE;CE Mod<M>& OP=(CO Mod<M>& 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/=(CO Mod<M>& n);CE Mod<M>& OP<<=(int n)NE;CE Mod<M>& OP>>=(int n)NE;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(+);DC_OF_AR_FOR_MOD(-);DC_OF_AR_FOR_MOD(*);DC_OF_AR_FOR_MOD(/);CE Mod<M> OP<<(int n)CO NE;CE Mod<M> OP>>(int n)CO NE;CE Mod<M> OP-()CO NE;CE Mod<M>& SignInvert()NE;CE Mod<M>& Double()NE;CE Mod<M>& Halve()NE;IN Mod<M>& Invert();TE <TY T> CE Mod<M>& PositivePW(T&& EX)NE;TE <TY T> CE Mod<M>& NonNegativePW(T&& EX)NE;TE <TY T> CE Mod<M>& PW(T&& EX);CE VO swap(Mod<M>& n)NE;CE CRUI RP()CO NE;ST CE Mod<M> DeRP(CRUI n)NE;ST CE uint& Normalise(uint& n)NE;ST IN CO Mod<M>& Inverse(CRUI n)NE;ST IN CO Mod<M>& Factorial(CRUI n)NE;ST IN CO Mod<M>& FactorialInverse(CRUI n)NE;ST IN Mod<M> Combination(CRUI n,CRUI i)NE;ST IN CO Mod<M>& zero()NE;ST IN CO Mod<M>& one()NE;TE <TY T> CE Mod<M>& Ref(T&& n)NE;};

#define SFINAE_FOR_MN(DEFAULT)TY T,enable_if_t<is_constructible<Mod<M>,decay_t<T> >::value>* DEFAULT
#define DC_OF_AR_FOR_MN(FUNC)IN MN<M> OP FUNC(CO MN<M>& n)CO NE;TE <SFINAE_FOR_MOD(= nullptr)> IN MN<M> OP FUNC(T&& n)CO NE;
#define DF_OF_CM_FOR_MN(FUNC)TE <uint M> IN bool MN<M>::OP FUNC(CO MN<M>& n)CO NE{RE m_n FUNC n.m_n;}
#define DF_OF_AR_FOR_MN(FUNC,FORMULA)TE <uint M> IN MN<M> MN<M>::OP FUNC(CO MN<M>& n)CO NE{RE MO(MN<M>(*TH)FUNC ## = n);}TE <uint M> TE <SFINAE_FOR_MOD()> IN MN<M> MN<M>::OP FUNC(T&& n)CO NE{RE FORMULA;}TE <uint M,SFINAE_FOR_MOD(= nullptr)> IN MN<M> OP FUNC(T&& n0,CO MN<M>& n1)NE{RE MO(MN<M>(forward<T>(n0))FUNC ## = n1);}

TE <uint M>CL MN:PU Mod<M>{PU:CE MN()NE;CE MN(CO MN<M>& n)NE;CE MN(MN<M>& n)NE;CE MN(MN<M>&& n)NE;TE <SFINAE_FOR_MN(= nullptr)> CE MN(CO T& n)NE;TE <SFINAE_FOR_MN(= nullptr)> CE MN(T&& n)NE;CE MN<M>& OP=(CO MN<M>& n)NE;CE MN<M>& OP=(MN<M>&& n)NE;CE MN<M>& OP+=(CO MN<M>& n)NE;CE MN<M>& OP-=(CO MN<M>& n)NE;CE MN<M>& OP*=(CO MN<M>& n)NE;IN MN<M>& OP/=(CO MN<M>& n);CE MN<M>& OP<<=(int n)NE;CE MN<M>& OP>>=(int n)NE;CE MN<M>& OP++()NE;CE MN<M> OP++(int)NE;CE MN<M>& OP--()NE;CE MN<M> OP--(int)NE;DC_OF_AR_FOR_MN(+);DC_OF_AR_FOR_MN(-);DC_OF_AR_FOR_MN(*);DC_OF_AR_FOR_MN(/);CE MN<M> OP<<(int n)CO NE;CE MN<M> OP>>(int n)CO NE;CE MN<M> OP-()CO NE;CE MN<M>& SignInvert()NE;CE MN<M>& Double()NE;CE MN<M>& Halve()NE;CE MN<M>& Invert();TE <TY T> CE MN<M>& PositivePW(T&& EX)NE;TE <TY T> CE MN<M>& NonNegativePW(T&& EX)NE;TE <TY T> CE MN<M>& PW(T&& EX);CE uint RP()CO NE;CE Mod<M> Reduce()CO NE;ST CE MN<M> DeRP(CRUI n)NE;ST IN CO MN<M>& Formise(CRUI n)NE;ST IN CO MN<M>& Inverse(CRUI n)NE;ST IN CO MN<M>& Factorial(CRUI n)NE;ST IN CO MN<M>& FactorialInverse(CRUI n)NE;ST IN MN<M> Combination(CRUI n,CRUI i)NE;ST IN CO MN<M>& zero()NE;ST IN CO MN<M>& one()NE;ST CE uint Form(CRUI n)NE;ST CE ull& Reduction(ull& n)NE;ST CE ull& ReducedMU(ull& n,CRUI m)NE;ST CE uint MU(CRUI n0,CRUI n1)NE;ST CE uint BaseSquareTruncation(uint& n)NE;TE <TY T> CE MN<M>& Ref(T&& n)NE;};TE <uint M> CE MN<M> Twice(CO MN<M>& n)NE;TE <uint M> CE MN<M> Half(CO MN<M>& n)NE;TE <uint M> CE MN<M> Inverse(CO MN<M>& n);TE <uint M,TY T> CE MN<M> PW(MN<M> n,T EX);TE <TY T> CE MN<2> PW(CO MN<2>& n,CO T& p);TE <TY T> CE T Square(CO T& t);TE <> CE MN<2> Square<MN<2> >(CO MN<2>& t);TE <uint M> CE VO swap(MN<M>& n0,MN<M>& n1)NE;TE <uint M> IN string to_string(CO MN<M>& n)NE;TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO MN<M>& n);

TE <uint M>CL COantsForMod{PU:COantsForMod()= delete;ST CE CO bool g_even = ((M & 1)== 0);ST CE CO uint g_memory_bound = 1000000;ST CE CO uint g_memory_LE = M < g_memory_bound?M:g_memory_bound;ST CE ull MNBasePW(ull&& EX)NE;ST CE uint g_M_minus = M - 1;ST CE uint g_M_minus_2 = M - 2;ST CE uint g_M_minus_2_neg = 2 - M;ST CE CO int g_MN_digit = 32;ST CE CO ull g_MN_base = ull(1)<< g_MN_digit;ST CE CO uint g_MN_base_minus = uint(g_MN_base - 1);ST CE CO uint g_MN_digit_half = (g_MN_digit + 1)>> 1;ST CE CO uint g_MN_base_sqrt_minus = (1 << g_MN_digit_half)- 1;ST CE CO uint g_MN_M_neg_inverse = uint((g_MN_base - MNBasePW((ull(1)<< (g_MN_digit - 1))- 1))& g_MN_base_minus);ST CE CO uint g_MN_base_mod = uint(g_MN_base % M);ST CE CO uint g_MN_base_square_mod = uint(((g_MN_base % M)* (g_MN_base % M))% M);};TE <uint M> CE ull COantsForMod<M>::MNBasePW(ull&& EX)NE{ull prod = 1;ull PW = M;WH(EX != 0){(EX & 1)== 1?(prod *= PW)&= g_MN_base_minus:prod;EX >>= 1;(PW *= PW)&= g_MN_base_minus;}RE prod;}

US MP = Mod<P>;US MNP = MN<P>;TE <uint M> CE uint MN<M>::Form(CRUI n)NE{ull n_copy = n;RE uint(MO(Reduction(n_copy *= COantsForMod<M>::g_MN_base_square_mod)));}TE <uint M> CE ull& MN<M>::Reduction(ull& n)NE{ull n_sub = n & COantsForMod<M>::g_MN_base_minus;RE ((n += ((n_sub *= COantsForMod<M>::g_MN_M_neg_inverse)&= COantsForMod<M>::g_MN_base_minus)*= M)>>= COantsForMod<M>::g_MN_digit)< M?n:n -= M;}TE <uint M> CE ull& MN<M>::ReducedMU(ull& n,CRUI m)NE{RE Reduction(n *= m);}TE <uint M> CE uint MN<M>::MU(CRUI n0,CRUI n1)NE{ull n0_copy = n0;RE uint(MO(ReducedMU(ReducedMU(n0_copy,n1),COantsForMod<M>::g_MN_base_square_mod)));}TE <uint M> CE uint MN<M>::BaseSquareTruncation(uint& n)NE{CO uint n_u = n >> COantsForMod<M>::g_MN_digit_half;n &= COantsForMod<M>::g_MN_base_sqrt_minus;RE n_u;}TE <uint M> CE MN<M>::MN()NE:Mod<M>(){static_assert(! COantsForMod<M>::g_even);}TE <uint M> CE MN<M>::MN(CO MN<M>& n)NE:Mod<M>(n){}TE <uint M> CE MN<M>::MN(MN<M>& n)NE:Mod<M>(n){}TE <uint M> CE MN<M>::MN(MN<M>&& n)NE:Mod<M>(MO(n)){}TE <uint M> TE <SFINAE_FOR_MN()> CE MN<M>::MN(CO T& n)NE:Mod<M>(n){static_assert(! COantsForMod<M>::g_even);Mod<M>::m_n = Form(Mod<M>::m_n);}TE <uint M> TE <SFINAE_FOR_MN()> CE MN<M>::MN(T&& n)NE:Mod<M>(forward<T>(n)){static_assert(! COantsForMod<M>::g_even);Mod<M>::m_n = Form(Mod<M>::m_n);}TE <uint M> CE MN<M>& MN<M>::OP=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP=(n));}TE <uint M> CE MN<M>& MN<M>::OP=(MN<M>&& n)NE{RE Ref(Mod<M>::OP=(MO(n)));}TE <uint M> CE MN<M>& MN<M>::OP+=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP+=(n));}TE <uint M> CE MN<M>& MN<M>::OP-=(CO MN<M>& n)NE{RE Ref(Mod<M>::OP-=(n));}TE <uint M> CE MN<M>& MN<M>::OP*=(CO MN<M>& n)NE{ull m_n_copy = Mod<M>::m_n;RE Ref(Mod<M>::m_n = MO(ReducedMU(m_n_copy,n.m_n)));}TE <uint M> IN MN<M>& MN<M>::OP/=(CO MN<M>& n){RE OP*=(MN<M>(n).Invert());}TE <uint M> CE MN<M>& MN<M>::OP<<=(int n)NE{RE Ref(Mod<M>::OP<<=(n));}TE <uint M> CE MN<M>& MN<M>::OP>>=(int n)NE{RE Ref(Mod<M>::OP>>=(n));}TE <uint M> CE MN<M>& MN<M>::OP++()NE{RE Ref(Mod<M>::Normalise(Mod<M>::m_n += COantsForMod<M>::g_MN_base_mod));}TE <uint M> CE MN<M> MN<M>::OP++(int)NE{MN<M> n{*TH};OP++();RE n;}TE <uint M> CE MN<M>& MN<M>::OP--()NE{RE Ref(Mod<M>::m_n < COantsForMod<M>::g_MN_base_mod?((Mod<M>::m_n += M)-= COantsForMod<M>::g_MN_base_mod):Mod<M>::m_n -= COantsForMod<M>::g_MN_base_mod);}TE <uint M> CE MN<M> MN<M>::OP--(int)NE{MN<M> n{*TH};OP--();RE n;}DF_OF_AR_FOR_MN(+,MN<M>(forward<T>(n))+= *TH);DF_OF_AR_FOR_MN(-,MN<M>(forward<T>(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MN(*,MN<M>(forward<T>(n))*= *TH);DF_OF_AR_FOR_MN(/,MN<M>(forward<T>(n)).Invert()*= *TH);TE <uint M> CE MN<M> MN<M>::OP<<(int n)CO NE{RE MO(MN<M>(*TH)<<= n);}TE <uint M> CE MN<M> MN<M>::OP>>(int n)CO NE{RE MO(MN<M>(*TH)>>= n);}TE <uint M> CE MN<M> MN<M>::OP-()CO NE{RE MO(MN<M>(*TH).SignInvert());}TE <uint M> CE MN<M>& MN<M>::SignInvert()NE{RE Ref(Mod<M>::m_n > 0?Mod<M>::m_n = M - Mod<M>::m_n:Mod<M>::m_n);}TE <uint M> CE MN<M>& MN<M>::Double()NE{RE Ref(Mod<M>::Double());}TE <uint M> CE MN<M>& MN<M>::Halve()NE{RE Ref(Mod<M>::Halve());}TE <uint M> CE MN<M>& MN<M>::Invert(){assert(Mod<M>::m_n > 0);RE PositivePW(uint(COantsForMod<M>::g_M_minus_2));}TE <uint M> TE <TY T> CE MN<M>& MN<M>::PositivePW(T&& EX)NE{MN<M> PW{*TH};(--EX)%= COantsForMod<M>::g_M_minus_2;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <uint M> TE <TY T> CE MN<M>& MN<M>::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(Mod<M>::m_n = COantsForMod<M>::g_MN_base_mod):PositivePW(forward<T>(EX));}TE <uint M> TE <TY T> CE MN<M>& MN<M>::PW(T&& EX){bool neg = EX < 0;assert(!(neg && Mod<M>::m_n == 0));RE neg?PositivePW(forward<T>(EX *= COantsForMod<M>::g_M_minus_2_neg)):NonNegativePW(forward<T>(EX));}TE <uint M> CE uint MN<M>::RP()CO NE{ull m_n_copy = Mod<M>::m_n;RE MO(Reduction(m_n_copy));}TE <uint M> CE Mod<M> MN<M>::Reduce()CO NE{ull m_n_copy = Mod<M>::m_n;RE Mod<M>::DeRP(MO(Reduction(m_n_copy)));}TE <uint M> CE MN<M> MN<M>::DeRP(CRUI n)NE{RE MN<M>(Mod<M>::DeRP(n));}TE <uint M> IN CO MN<M>& MN<M>::Formise(CRUI n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = DeRP(LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::Inverse(CRUI n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>(Mod<M>::Inverse(LE_curr));LE_curr++;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::Factorial(CRUI n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN<M> val_curr{one()};ST MN<M> val_last{one()};WH(LE_curr <= n){memory[LE_curr++] = val_curr *= ++val_last;}RE memory[n];}TE <uint M> IN CO MN<M>& MN<M>::FactorialInverse(CRUI n)NE{ST MN<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;ST MN<M> val_curr{one()};ST MN<M> val_last{one()};WH(LE_curr <= n){memory[LE_curr] = val_curr *= Inverse(LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN MN<M> MN<M>::Combination(CRUI n,CRUI i)NE{RE i <= n?Factorial(n)*FactorialInverse(i)*FactorialInverse(n - i):zero();}TE <uint M> IN CO MN<M>& MN<M>::zero()NE{ST CE CO MN<M> z{};RE z;}TE <uint M> IN CO MN<M>& MN<M>::one()NE{ST CE CO MN<M> o{DeRP(1)};RE o;}TE <uint M> TE <TY T> CE MN<M>& MN<M>::Ref(T&& n)NE{RE *TH;}TE <uint M> CE MN<M> Twice(CO MN<M>& n)NE{RE MO(MN<M>(n).Double());}TE <uint M> CE MN<M> Half(CO MN<M>& n)NE{RE MO(MN<M>(n).Halve());}TE <uint M> CE MN<M> Inverse(CO MN<M>& n){RE MO(MN<M>(n).Invert());}TE <uint M,TY T> CE MN<M> PW(MN<M> n,T EX){RE MO(n.PW(EX));}TE <uint M> CE VO swap(MN<M>& n0,MN<M>& n1)NE{n0.swap(n1);}TE <uint M> IN string to_string(CO MN<M>& n)NE{RE to_string(n.RP())+ " + MZ";}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO MN<M>& n){RE os << n.RP();}

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(n.m_n){}TE <uint M> CE Mod<M>::Mod(Mod<M>&& n)NE:m_n(MO(n.m_n)){}TE <uint M> TE <SFINAE_FOR_MOD()> CE Mod<M>::Mod(CO T& n)NE:m_n(RS<M>(n)){}TE <uint M> TE <SFINAE_FOR_MOD()> CE Mod<M>::Mod(T& n)NE:m_n(RS<M>(decay_t<T>(n))){}TE <uint M> TE <SFINAE_FOR_MOD()> CE Mod<M>::Mod(T&& n)NE:m_n(RS<M>(forward<T>(n))){}TE <uint M> CE Mod<M>& Mod<M>::OP=(CO Mod<M>& n)NE{RE Ref(m_n = n.m_n);}TE <uint M> CE Mod<M>& Mod<M>::OP=(Mod<M>&& n)NE{RE Ref(m_n = MO(n.m_n));}TE <uint M> CE Mod<M>& Mod<M>::OP+=(CO Mod<M>& n)NE{RE Ref(Normalise(m_n += n.m_n));}TE <uint M> CE Mod<M>& Mod<M>::OP-=(CO Mod<M>& n)NE{RE Ref(m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n);}TE <uint M> CE Mod<M>& Mod<M>::OP*=(CO Mod<M>& n)NE{RE Ref(m_n = COantsForMod<M>::g_even?RS<M>(ull(m_n)* n.m_n):MN<M>::MU(m_n,n.m_n));}TE <> CE MP& MP::OP*=(CO MP& n)NE{ull m_n_copy = m_n;RE Ref(m_n = MO((m_n_copy *= n.m_n)< P?m_n_copy:RSP(m_n_copy)));}TE <uint M> IN Mod<M>& Mod<M>::OP/=(CO Mod<M>& n){RE OP*=(Mod<M>(n).Invert());}TE <uint M> CE Mod<M>& Mod<M>::OP<<=(int n)NE{WH(n-- > 0){Normalise(m_n <<= 1);}RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP>>=(int n)NE{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{RE Ref(m_n < COantsForMod<M>::g_M_minus?++m_n:m_n = 0);}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{RE Ref(m_n == 0?m_n = COantsForMod<M>::g_M_minus:--m_n);}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(+,Mod<M>(forward<T>(n))+= *TH);DF_OF_AR_FOR_MOD(-,Mod<M>(forward<T>(n)).SignInvert()+= *TH);DF_OF_AR_FOR_MOD(*,Mod<M>(forward<T>(n))*= *TH);DF_OF_AR_FOR_MOD(/,Mod<M>(forward<T>(n)).Invert()*= *TH);TE <uint M> CE Mod<M> Mod<M>::OP<<(int n)CO NE{RE MO(Mod<M>(*TH)<<= n);}TE <uint M> CE Mod<M> Mod<M>::OP>>(int n)CO NE{RE MO(Mod<M>(*TH)>>= 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{RE Ref(m_n > 0?m_n = M - m_n:m_n);}TE <uint M> CE Mod<M>& Mod<M>::Double()NE{RE Ref(Normalise(m_n <<= 1));}TE <uint M> CE Mod<M>& Mod<M>::Halve()NE{RE Ref(((m_n & 1)== 0?m_n:m_n += M)>>= 1);}TE <uint M> IN Mod<M>& Mod<M>::Invert(){assert(m_n > 0);uint m_n_neg;RE m_n < COantsForMod<M>::g_memory_LE?Ref(m_n = Inverse(m_n).m_n):(m_n_neg = M - m_n < COantsForMod<M>::g_memory_LE)?Ref(m_n = M - Inverse(m_n_neg).m_n):PositivePW(uint(COantsForMod<M>::g_M_minus_2));}TE <> IN Mod<2>& Mod<2>::Invert(){assert(m_n > 0);RE *TH;}TE <uint M> TE <TY T> CE Mod<M>& Mod<M>::PositivePW(T&& EX)NE{Mod<M> PW{*TH};EX--;WH(EX != 0){(EX & 1)== 1?OP*=(PW):*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <> TE <TY T> CE Mod<2>& Mod<2>::PositivePW(T&& EX)NE{RE *TH;}TE <uint M> TE <TY T> CE Mod<M>& Mod<M>::NonNegativePW(T&& EX)NE{RE EX == 0?Ref(m_n = 1):Ref(PositivePW(forward<T>(EX)));}TE <uint M> TE <TY T> CE Mod<M>& Mod<M>::PW(T&& EX){bool neg = EX < 0;assert(!(neg && m_n == 0));neg?EX *= COantsForMod<M>::g_M_minus_2_neg:EX;RE m_n == 0?*TH:(EX %= COantsForMod<M>::g_M_minus)== 0?Ref(m_n = 1):PositivePW(forward<T>(EX));}TE <uint M> IN CO Mod<M>& Mod<M>::Inverse(CRUI n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr].m_n = M - MN<M>::MU(memory[M % LE_curr].m_n,M / LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::Factorial(CRUI n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>::Factorial(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::FactorialInverse(CRUI n)NE{ST Mod<M> memory[COantsForMod<M>::g_memory_LE] ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory[LE_curr] = MN<M>::FactorialInverse(LE_curr).Reduce();LE_curr++;}RE memory[n];}TE <uint M> IN Mod<M> Mod<M>::Combination(CRUI n,CRUI i)NE{RE MN<M>::Combination(n,i).Reduce();}TE <uint M> CE VO Mod<M>::swap(Mod<M>& n)NE{std::swap(m_n,n.m_n);}TE <uint M> CE CRUI Mod<M>::RP()CO NE{RE m_n;}TE <uint M> CE Mod<M> Mod<M>::DeRP(CRUI n)NE{Mod<M> n_copy{};n_copy.m_n = n;RE n_copy;}TE <uint M> CE uint& Mod<M>::Normalise(uint& n)NE{RE n < M?n:n -= M;}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{DeRP(1)};RE o;}TE <uint M> TE <TY T> CE Mod<M>& Mod<M>::Ref(T&& n)NE{RE *TH;}TE <uint M> CE Mod<M> Twice(CO Mod<M>& n)NE{RE MO(Mod<M>(n).Double());}TE <uint M> CE Mod<M> Half(CO Mod<M>& n)NE{RE MO(Mod<M>(n).Halve());}TE <uint M> IN Mod<M> Inverse(CO Mod<M>& n){RE MO(Mod<M>(n).Invert());}TE <uint M> CE Mod<M> Inverse_COrexpr(CRUI n)NE{RE MO(Mod<M>::DeRP(RS<M>(n)).NonNegativePW(M - 2));}TE <uint M,TY T> CE Mod<M> PW(Mod<M> n,T EX){RE MO(n.PW(EX));}TE <TY T>CE Mod<2> PW(Mod<2> n,const T& p){RE p == 0?Mod<2>::one():move(n);}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())+ " + MZ";}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO Mod<M>& n){RE os << n.RP();}


// AAA ライブラリは以上に挿入する。

template <typename path_type> list<path_type> E( const int& i )
{
  // list<path_type> answer{};
  list<path_type> answer = e<path_type>[i];
  // VVV 入力によらない処理は以下に挿入する。

  // AAA 入力によらない処理は以上に挿入する。
  return answer;
}

ll Guchoku( int N , int M , int K )
{
  ll answer = 0;
  ll A[N];
  FOR( d , 0 , N ){
    A[d] = 1;
  }
  ll prod[N] = { 1 };
  FOR( d , 1 , N ){
    prod[d] = prod[d-1] * K % M;
  }
  POWER( power , ll( M - 1 ) , N );
  REPEAT( power ){
    ll sum = 0;
    FOR( d , 0 , N ){
      sum += A[d] * prod[d];
    }
    sum % M == 0 ? ++answer : answer;
    FOR( d , 0 , N ){
      if( ++A[d] == M ){
	A[d] = 1;
      } else {
	break;
      }
    }
  }
  return answer;
}

MP Answer( int N , int M , int K )
{
  if( N == 1 ){
    return 0;
  }
  constexpr PrimeEnumeration<int,31622> pe{};
  vector<int> prime;
  vector<int> exponent;
  SetPrimeFactorisation( pe , M , prime , exponent );
  int size = prime.size();
  int e_max = 0;
  FOR( i , 0 , size ){
    e_max = max( e_max , exponent[i] );
  }
  ll K_div[e_max+2];
  FOREQ( j , 0 , e_max ){
    K_div[j] = 1;
  }
  K_div[e_max+1] = M;
  FOR( i , 0 , size ){
    int d = 0;
    while( K % prime[i] == 0 ){
      K /= prime[i];
      d++;
    }
    int d_mul = 0;
    ll power = 1;
    FOREQ( j , 1 , e_max ){
      int d_mul_new = min( d * j , exponent[i] );
      FOR( k , d_mul , d_mul_new ){
	power *= prime[i];
      }
      K_div[j] *= power;
      d_mul = d_mul_new;
    }
  }
  ll K_dif[e_max+2] = { K_div[0] };
  FOREQ( j , 1 , e_max + 1 ){
    K_dif[j] = K_div[j] - K_div[j-1];
  }
  CEXPR( int , length , 30 );
  MA<length,1,MP> dp{};
  {
    auto& dp_ref = dp.RefTable();
    dp_ref[0][0] = 0;  
    FOREQ( j , 1 , e_max + 1 ){
      dp_ref[j][0] = K_dif[j];
    }
  }
  MA<length,length,MP> A{};
  auto& A_ref = A.RefTable();
  FOREQ( j , 0 , e_max + 1 ){
    FOREQ( k , 0 , e_max + 1 ){
      A_ref[j][k] = K_dif[j];
    }
    if( j == 0 ){
      A_ref[j][0]--;
    }
    if( j < e_max ){
      A_ref[j][j+1]--;
    } else if( j == e_max + 1 ){
      A_ref[j][j]--;
    }
  }
  POWER( A_power , A , N - 2 );
  dp = A_power * dp;
  auto& dp_ref = dp.RefTable();
  MP answer = 0;
  FOREQ( j , 2 , e_max + 1 ){
    answer += dp_ref[j][0];
  }
  return answer;
}


int main()
{
  UNTIE;
  AUTO_CHECK;
  // START_WATCH;
  TEST_CASE_NUM( 1 );
  START_MAIN;

  // // 大きな素数
  // CEXPR( ll , P , 998244353 );
  // // CEXPR( ll , P , 1000000007 ); // Mod<P>を使う時はP2に変更。

  // // データ構造使用畤のNの上限
  DEXPR( int , bound_N , 1000000000 , 1000 ); // 0が9個
  // // CEXPR( int , bound_N , 1000000000 ); // 0が9個
  // // CEXPR( ll , bound_N , 1000000000000000000 ); // 0が18個

  // // データ構造使用畤のMの上限
  // // CEXPR( TYPE_OF( bound_N ) , bound_M , bound_N );
  DEXPR( int , bound_M , 1000000000 , 1000 ); // 0が9個
  // // CEXPR( int , bound_M , 1000000000 ); // 0が9個
  // // CEXPR( ll , bound_M , 1000000000000000000 ); // 0が18個
  DEXPR( int , bound_K , 1000000000 , 1000 ); // 0が9個

  // // 数
  // CIN( ll , N );
  // CIN( ll , M );
  // CIN( int , N , M , K );
  CIN_ASSERT( N , 1 , bound_N ); // ランダムテスト用。上限のデフォルト値は10^5。
  CIN_ASSERT( M , 1 , bound_M ); // ランダムテスト用。上限のデフォルト値は10^5。
  CIN_ASSERT( K , 1 , bound_K ); // ランダムテスト用。上限のデフォルト値は10^5。

  // // 文字列
  // CIN( string , S );
  // CIN( string , T );

  // // 配列
  // CIN_A( ll , A , N );
  // // CIN_A( ll , B , N );
  // // ll A[N];
  // // ll B[N];
  // // ll A[bound_N]; // 関数（コンストラクタ）の引数に使う。長さのデフォルト値は10^5。
  // // ll B[bound_N]; // 関数（コンストラクタ）の引数に使う。長さのデフォルト値は10^5。
  // // FOR( i , 0 , N ){
  // //   cin >> A[i] >> B[i];
  // // }

  // // 順列
  // int P[N];
  // int P_inv[N];
  // FOR( i , 0 , N ){
  //   cin >> P[i];
  //   P_inv[--P[i]] = i;
  // }
  
  // // グラフ
  // FOR( j , 0 , M ){
  //   CIN_ASSERT( uj , 1 , N );
  //   CIN_ASSERT( vj , 1 , N );
  //   uj--;
  //   vj--;
  //   e<int>[uj].push_back( vj );
  //   e<int>[vj].push_back( uj );
  //   // CIN( ll , wj );
  //   // e<path>[uj].push_back( { vj , wj } );
  //   // e<path>[vj].push_back( { uj , wj } );
  // }

  // // 座標圧縮や単一クエリタイプなどのための入力格納
  // T3<ll> data[M];
  // FOR( j , 0 , M ){
  //   CIN( ll , x , y , z );
  //   data[j] = { x , y , z };
  // }

  // // 一般のクエリ
  // CIN( int , Q );
  // // DEXPR( int , bound_Q , 100000 , 100 ); // 基本不要。
  // // CIN_ASSERT( Q , 1 , bound_Q ); // 基本不要。
  // // T3<int> query[Q];
  // // T2<int> query[Q];
  // FOR( q , 0 , Q ){
  //   CIN( int , type );
  //   if( type == 1 ){
  //     CIN( int , x , y );
  //     // query[q] = { type , x , y };
  //   } else if( type == 2 ){
  //     CIN( int , x , y );
  //     // query[q] = { type , x , y };
  //   } else {
  //     CIN( int , x , y );
  //     // query[q] = { type , x , y };
  //   }
  //   // CIN( int , x , y );
  //   // // query[q] = { x , y };
  // }
  // // sort( query , query + Q );
  // // FOR( q , 0 , Q ){
  // //   auto& [x,y] = query[q];
  // //   // auto& [type,x,y] = query[q];
  // // }
  
  // // データ構造や壁配列使用畤のH,Wの上限
  // DEXPR( int , bound_H , 1000 , 20 );
  // // DEXPR( int , bound_H , 100000 , 10 ); // 0が5個
  // // CEXPR( int , bound_H , 1000000000 ); // 0が9個
  // CEXPR( int , bound_W , bound_H );
  // static_assert( ll( bound_H ) * bound_W < ll( 1 ) << 31 );
  // CEXPR( int , bound_HW , bound_H * bound_W );
  // // CEXPR( int , bound_HW , 100000 ); // 0が5個
  // // CEXPR( int , bound_HW , 1000000 ); // 0が6個

  // // グリッド
  // cin >> H >> W;
  // // SET_ASSERT( H , 1 , bound_H ); // ランダムテスト用。上限のデフォルト値は10^3。
  // // SET_ASSERT( W , 1 , bound_W ); // ランダムテスト用。上限のデフォルト値は10^3。
  // H_minus = H - 1;
  // W_minus = W - 1;
  // HW = H * W;
  // // assert( HW <= bound_HW ); // 基本不要。上限のデフォルト値は10^6。
  // string S[H];
  // // bool non_wall[H+1][W+1]={};
  // FOR( i , 0 , H ){
  //   cin >> S[i];
  //   // SetEdgeOnGrid( S[i] , i , e<int> );
  //   // SetWallOnGrid( S[i] , i , non_wall[i] );
  // }
  // // {h,w}へデコード: EnumHW( v )
  // // {h,w}をコード: EnumHW_inv( h , w );
  // // (i,j)->(k,h)の方向番号を取得: DirectionNumberOnGrid( i , j , k , h );
  // // v->wの方向番号を取得: DirectionNumberOnGrid( v , w );
  // // 方向番号の反転U<->D、R<->L: ReverseDirectionNumberOnGrid( n );

  // // 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 ) ){

  // }

  // // ランダムテスト用の愚直解
  // auto guchoku = Guchoku( N , M , K );
  auto answer = Answer( N , M , K );
  // // MP answer{};
  // FOR( i , 0 , N ){
  //   answer += A[i];
  // }
  RETURN( answer );
  // // COUT( answer );
  // // COUT_A( A , N );
  
  FINISH_MAIN;
}

void Jikken()
{
  // CEXPR( int , bound , 10 );
  // FOREQ( N , 1 , bound ){
  //   FOREQ( M , 2 , bound ){
  //     FOREQ( K , 1 , bound ){
  //   	COUT( N , M , K , ":" , Guchoku( N , M , K ) );
  //     }
  //   }
  //   // cout << Guchoku( N ) << ",\n"[N==bound];
  // }
}

void Debug()
{
  CEXPR( int , bound , 10 );
  FOREQ( N , 1 , bound ){
    FOREQ( M , 2 , bound ){
      FOREQ( K , 1 , bound ){
	auto guchoku = Guchoku( N , M , K );
	auto answer = Answer( N , M , K );
	bool match = guchoku == answer.RP();
    	COUT( N , M , K , ":" , guchoku , match ? "==" : "!=" , answer );
	if( !match ){
	  return;
	}
      }
    }
    // auto guchoku = Guchoku( N );
    // auto answer = Answer( N );
    // bool match = guchoku == answer;
    // COUT( N , ":" , guchoku , match ? "==" : "!=" , answer );
    // if( !match ){
    //   return;
    // }
  }
}
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