結果
| 問題 | No.2592 おでぶなおばけさん 2 |
| ユーザー |
👑  p-adic
|
| 提出日時 | 2023-12-20 09:14:12 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 60,763 bytes |
| コンパイル時間 | 3,659 ms |
| コンパイル使用メモリ | 234,496 KB |
| 実行使用メモリ | 15,220 KB |
| 最終ジャッジ日時 | 2024-09-27 09:25:35 |
| 合計ジャッジ時間 | 13,738 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / 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 | 6 ms
14,428 KB |
| testcase_01 | AC | 20 ms
14,652 KB |
| testcase_02 | AC | 26 ms
14,488 KB |
| testcase_03 | AC | 14 ms
14,636 KB |
| testcase_04 | AC | 15 ms
14,620 KB |
| testcase_05 | AC | 40 ms
15,072 KB |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | AC | 54 ms
14,800 KB |
| testcase_14 | AC | 55 ms
14,752 KB |
| testcase_15 | AC | 45 ms
14,628 KB |
| testcase_16 | AC | 55 ms
14,804 KB |
| testcase_17 | AC | 59 ms
14,896 KB |
| testcase_18 | AC | 45 ms
14,500 KB |
| testcase_19 | AC | 40 ms
14,620 KB |
| testcase_20 | AC | 54 ms
14,516 KB |
| testcase_21 | AC | 45 ms
14,616 KB |
| testcase_22 | AC | 69 ms
14,704 KB |
| testcase_23 | AC | 59 ms
14,868 KB |
| testcase_24 | AC | 49 ms
14,840 KB |
| testcase_25 | AC | 37 ms
14,716 KB |
| testcase_26 | AC | 37 ms
14,716 KB |
| testcase_27 | AC | 67 ms
15,092 KB |
| testcase_28 | AC | 67 ms
15,092 KB |
| testcase_29 | AC | 68 ms
15,092 KB |
| testcase_30 | AC | 69 ms
15,092 KB |
| testcase_31 | AC | 70 ms
14,964 KB |
| testcase_32 | AC | 69 ms
15,092 KB |
| testcase_33 | AC | 68 ms
15,052 KB |
| testcase_34 | AC | 68 ms
15,096 KB |
| testcase_35 | AC | 68 ms
15,096 KB |
| testcase_36 | AC | 68 ms
15,092 KB |
| testcase_37 | AC | 68 ms
15,048 KB |
| testcase_38 | AC | 68 ms
15,080 KB |
| testcase_39 | AC | 69 ms
15,012 KB |
| testcase_40 | AC | 67 ms
15,096 KB |
| testcase_41 | AC | 68 ms
15,024 KB |
| testcase_42 | AC | 67 ms
14,968 KB |
| testcase_43 | AC | 68 ms
15,056 KB |
| testcase_44 | AC | 67 ms
15,084 KB |
| testcase_45 | AC | 68 ms
15,088 KB |
| testcase_46 | AC | 68 ms
15,096 KB |
| testcase_47 | AC | 60 ms
15,220 KB |
| testcase_48 | AC | 62 ms
14,992 KB |
| testcase_49 | AC | 61 ms
14,960 KB |
| testcase_50 | AC | 61 ms
15,220 KB |
| testcase_51 | AC | 63 ms
15,096 KB |
| testcase_52 | AC | 68 ms
14,960 KB |
| testcase_53 | AC | 68 ms
14,968 KB |
| testcase_54 | AC | 67 ms
15,096 KB |
| testcase_55 | AC | 68 ms
15,096 KB |
| testcase_56 | AC | 69 ms
14,908 KB |
| testcase_57 | AC | 31 ms
15,032 KB |
| testcase_58 | AC | 67 ms
14,968 KB |
| testcase_59 | AC | 69 ms
15,092 KB |
| testcase_60 | AC | 70 ms
15,056 KB |
| testcase_61 | AC | 68 ms
15,096 KB |
| testcase_62 | AC | 69 ms
15,020 KB |
| testcase_63 | AC | 68 ms
14,992 KB |
| testcase_64 | AC | 68 ms
14,968 KB |
| testcase_65 | AC | 65 ms
15,092 KB |
| testcase_66 | AC | 64 ms
14,920 KB |
| testcase_67 | AC | 62 ms
14,968 KB |
| testcase_68 | AC | 63 ms
15,092 KB |
| testcase_69 | AC | 62 ms
15,092 KB |
| testcase_70 | AC | 63 ms
15,136 KB |
| testcase_71 | AC | 63 ms
15,020 KB |
| testcase_72 | AC | 65 ms
14,968 KB |
| testcase_73 | AC | 64 ms
15,036 KB |
| testcase_74 | AC | 6 ms
14,440 KB |
| testcase_75 | AC | 70 ms
15,092 KB |
| testcase_76 | AC | 67 ms
14,964 KB |
| testcase_77 | AC | 67 ms
15,020 KB |
| testcase_78 | AC | 67 ms
14,968 KB |
| testcase_79 | AC | 68 ms
14,948 KB |
| testcase_80 | AC | 69 ms
15,180 KB |
| testcase_81 | AC | 67 ms
14,968 KB |
| testcase_82 | AC | 71 ms
15,096 KB |
| testcase_83 | AC | 69 ms
15,032 KB |
ソースコード
#ifdef INCLUDE_MAIN
inline void Solve()
{
DEXPR( ll , bound_N , 100000 , 100 ); // 0が5個
CIN( ll , N , Q , K );
CIN_A( ll , A , N );
using QR = QuotientRing<ll>;
CumulativeProd<QR,Add<QR>,Zero<QR>,AddInv<QR>,bound_N> cp[3];
ll MOD[3];
FOR( i , 0 , 3 ){
MOD[i] = GetRand( 999000000 , 1000000009 );
cerr << "MOD[" << i << "] == " << MOD[i] << endl;
QR power{ 1 , &MOD[i] };
QR B[bound_N];
FOR( i , 0 , N ){
B[i] = power * A[i];
power *= K;
}
cp[i].Set( B , N );
}
FOR( q , 0 , Q ){
CIN( int , x , y );
--x;
--y;
COUT( cp[0].RightProd( x , y ) == QR( 0 , &MOD[0] ) && cp[1].RightProd( x , y ) == QR( 0 , &MOD[1] ) && cp[2].RightProd( x , y ) == QR( 0 , &MOD[2] ) ? "No" : "Yes" );
}
}
REPEAT_MAIN(1);
#else // INCLUDE_MAIN
#ifdef INCLUDE_SUB
template <typename PATH> list<PATH> E( const int& i )
{
// list<PATH> answer{};
list<PATH> answer = e<PATH>[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;
}
template <typename T> inline T F( const T& t ){ return f<T>[t]; }
template <typename T> inline T G( const int& i ){ return g<T>[i]; }
// COMPAREに使用。圧縮時は削除する。
ll Naive( int N , int M , int K )
{
ll answer = N + M + K;
return answer;
}
// COMPAREに使用。圧縮時は削除する。
ll Answer( ll N , ll M , ll K )
{
// START_WATCH;
ll answer = N + M + K;
// // TLに準じる乱択や全探索。デフォルトの猶予は100.0[ms]。
// CEXPR( double , TL , 2000.0 );
// while( CHECK_WATCH( TL ) ){
// }
return answer;
}
// 圧縮時は中身だけ削除する。
inline void Experiment()
{
// CEXPR( int , bound , 10 );
// FOREQ( N , 0 , bound ){
// FOREQ( M , 0 , bound ){
// FOREQ( K , 0 , bound ){
// COUT( N , M , K , ":" , Naive( N , M , K ) );
// }
// }
// // cout << Naive( N ) << ",\n"[N==bound];
// }
}
// 圧縮時は中身だけ削除する。
inline void SmallTest()
{
// CEXPR( int , bound , 10 );
// FOREQ( N , 0 , bound ){
// FOREQ( M , 0 , bound ){
// FOREQ( K , 0 , bound ){
// COMPARE( N , M , K );
// }
// }
// // COMPARE( N );
// }
}
#define INCLUDE_MAIN
#include __FILE__
#else // INCLUDE_SUB
#ifdef INCLUDE_LIBRARY
/*
C-x 3 C-x o C-x C-fによるファイル操作用
BFS:
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt
CoordinateCompress:
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txt
DFSOnTree
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepthFirstSearch/Tree/a.hpp
Divisor:
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt
Polynomial
c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt
UnionFind
c:/Users/user/Documents/Programming/Utility/VLTree/UnionFindForest/compress.txt
*/
// VVV 常設でないライブラリは以下に挿入する。
template <typename INT>
class QuotientRing
{
protected:
INT m_n;
const INT* m_p_M;
static const INT* g_p_M;
public:
inline QuotientRing() noexcept;
inline QuotientRing( const INT& n , const INT* const& p_M = g_p_M ) noexcept;
inline QuotientRing( const QuotientRing<INT>& n ) noexcept;
inline QuotientRing<INT>& operator+=( const QuotientRing<INT>& n ) noexcept;
inline QuotientRing<INT>& operator+=( const INT& n ) noexcept;
// operator<が定義されていても負の数は正に直さず剰余を取ることに注意。
inline QuotientRing<INT>& operator-=( const QuotientRing<INT>& n ) noexcept;
inline QuotientRing<INT>& operator-=( const INT& n ) noexcept;
inline QuotientRing<INT>& operator*=( const QuotientRing<INT>& n ) noexcept;
inline QuotientRing<INT>& operator*=( const INT& n ) noexcept;
// *m_p_Mが素数でかつnの逆元が存在する場合のみサポート。
inline QuotientRing<INT>& operator/=( const QuotientRing<INT>& n );
inline QuotientRing<INT>& operator/=( const INT& n );
// m_nの正負やm_p_Mの一致込みの等号。
inline bool operator==( const QuotientRing<INT>& n ) const noexcept;
inline bool operator!=( const QuotientRing<INT>& n ) const noexcept;
template <typename T> inline QuotientRing<INT> operator+( const T& n1 ) const noexcept;
inline QuotientRing<INT> operator-() const noexcept;
template <typename T> inline QuotientRing<INT> operator-( const T& n1 ) const noexcept;
template <typename T> inline QuotientRing<INT> operator*( const T& n1 ) const noexcept;
// *m_p_Mが素数でかつn1の逆元が存在する場合のみサポート。
template <typename T> inline QuotientRing<INT> operator/( const T& n1 ) const;
inline const INT& Represent() const noexcept;
inline const INT& GetModulo() const noexcept;
inline void SetModulo( const INT* const& p_M = nullptr ) noexcept;
static inline const INT& GetStaticModulo() noexcept;
static inline void SetStaticModulo( const INT* const& p_M ) noexcept;
template <typename T> static QuotientRing<INT> Power( const QuotientRing<INT>& n , T exponent );
// *m_p_Mが素数でかつnの逆元が存在する場合のみサポート。
static QuotientRing<INT> Inverse( const QuotientRing<INT>& n );
};
template <typename INT , typename T> inline QuotientRing<INT> Power( const QuotientRing<INT>& n , T exponent );
// *(n.m_p_M)が素数でかつnの逆元が存在する場合のみサポート。
template <typename INT> inline QuotientRing<INT> Inverse( const QuotientRing<INT>& n );
template <typename INT> const INT* QuotientRing<INT>::g_p_M = nullptr;
template <typename INT> inline QuotientRing<INT>::QuotientRing() noexcept : m_n() , m_p_M( g_p_M ) {}
template <typename INT> inline QuotientRing<INT>::QuotientRing( const INT& n , const INT* const& p_M ) noexcept : m_n( p_M == nullptr ? n : n % *p_M ) , m_p_M( p_M ) {}
template <typename INT> inline QuotientRing<INT>::QuotientRing( const QuotientRing<INT>& n ) noexcept : m_n( n.m_n ) , m_p_M( n.m_p_M ) {}
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator+=( const QuotientRing<INT>& n ) noexcept { if( m_p_M == nullptr ){ m_p_M = n.m_p_M; } m_n += n.m_n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator+=( const INT& n ) noexcept { m_n += n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator-=( const QuotientRing<INT>& n ) noexcept { if( m_p_M == nullptr ){ m_p_M = n.m_p_M; } m_n -= n.m_n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator-=( const INT& n ) noexcept { m_n -= n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator*=( const QuotientRing<INT>& n ) noexcept { if( m_p_M == nullptr ){ m_p_M = n.m_p_M; } m_n *= n.m_n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator*=( const INT& n ) noexcept { m_n *= n; if( m_p_M != nullptr ){ m_n %= *m_p_M; } return *this; }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator/=( const QuotientRing<INT>& n ) { if( m_p_M == nullptr ){ if( n.m_p_M == nullptr ){ assert( n.m_n != 0 ); m_n /= n.m_n; return *this; } else { m_p_M = n.m_p_M; } } return operator*=( Inverse( QuotientRing<INT>( n.m_n , m_p_M ) ) ); }
template <typename INT> inline QuotientRing<INT>& QuotientRing<INT>::operator/=( const INT& n ) { if( m_p_M == nullptr ){ assert( n.m_n != 0 ); m_n /= n.m_n; return *this; } return operator*=( Inverse( Q( n.m_n , m_p_M ) ) ); }
template <typename INT> inline bool QuotientRing<INT>::operator==( const QuotientRing<INT>& n ) const noexcept { return m_p_M == n.m_p_M && m_n == n.m_n; }
template <typename INT> inline bool QuotientRing<INT>::operator!=( const QuotientRing<INT>& n ) const noexcept { return !operator==( n ); }
template <typename INT> template<typename T> inline QuotientRing<INT> QuotientRing<INT>::operator+( const T& n ) const noexcept { return QuotientRing<INT>( *this ).operator+=( n ); }
template <typename INT> inline QuotientRing<INT> QuotientRing<INT>::operator-() const noexcept { return QuotientRing<INT>( -m_n , m_p_M ); }
template <typename INT> template<typename T> inline QuotientRing<INT> QuotientRing<INT>::operator-( const T& n ) const noexcept { return QuotientRing<INT>( *this ).operator-=( n ); }
template <typename INT> template<typename T> inline QuotientRing<INT> QuotientRing<INT>::operator*( const T& n ) const noexcept { return QuotientRing<INT>( *this ).operator*=( n ); }
template <typename INT> template<typename T> inline QuotientRing<INT> QuotientRing<INT>::operator/( const T& n ) const { return QuotientRing<INT>( *this ).operator/=( n ); }
template <typename INT> inline const INT& QuotientRing<INT>::Represent() const noexcept { return m_n; }
template <typename INT> inline const INT& QuotientRing<INT>::GetModulo() const noexcept { static const INT zero{ 0 }; return m_p_M == nullptr ? zero : *m_p_M; }
template <typename INT> inline void QuotientRing<INT>::SetModulo( const INT* const& p_M ) noexcept { m_p_M = p_M; if( m_p_M != nullptr ){ m_n %= *m_p_M; } }
template <typename INT> inline const INT& QuotientRing<INT>::GetStaticModulo() noexcept { static const INT zero{ 0 }; return g_p_M == nullptr ? zero : *g_p_M; }
template <typename INT> inline void QuotientRing<INT>::SetStaticModulo( const INT* const& p_M ) noexcept { g_p_M = p_M; }
template <typename INT> template <typename T>
QuotientRing<INT> QuotientRing<INT>::Power( const QuotientRing<INT>& n , T exponent )
{
QuotientRing<INT> answer{ 1 , n.m_p_M };
QuotientRing<INT> power{ n };
while( exponent != 0 ){
if( exponent % 2 == 1 ){
answer *= power;
}
power *= power;
exponent /= 2;
}
return answer;
}
template <typename INT> inline QuotientRing<INT> QuotientRing<INT>::Inverse( const QuotientRing<INT>& n ) { assert( n.m_p_M != nullptr ); return Power( n , *( n.m_p_M ) - 2 ); }
template <typename INT , typename T> inline QuotientRing<INT> Power( const QuotientRing<INT>& n , T exponent ) { return QuotientRing<INT>::template Power<T>( n , exponent ); }
template <typename INT> inline QuotientRing<INT> Inverse( const QuotientRing<INT>& n ) { return QuotientRing<INT>::Inverse( n ); }
#define SFINAE_FOR_CUMULATIVE_PROD( DEFAULT ) enable_if_t<is_convertible_v<U,T> >* DEFAULT
// 入力の範囲内で要件
// (1) (T,m_T:T^2->T,i_T:T->T)が群である。
// が成り立つ場合のみサポート。（単位元はテンプレート引数に渡さなくてよい）
template <typename T , T m_T(const T&,const T&) , T i_T(const T&) , int size_max>
class CumulativeProd_Body
{
protected:
int m_size;
T m_right[size_max];
T m_left[size_max];
public:
inline CumulativeProd_Body( const int& size );
// 0 <= i,j < m_sizeの場合のみサポート。
// iからへのpathがi=v_0->...->v_k=jの時、Setした配列aに対する
// 右総乗a[v_0]...a[v_k]を計算する。
inline T PathProd( const int& i , const int& j );
private:
virtual int Parent( const int& i ) = 0;
virtual int LCA( const int& i , const int& j ) = 0;
};
// 通常の配列上の累積積。
// テンプレート引数に単位元e_T:1->Tも渡す。
// e_Tによる初期化O(size)
// 配列による初期化O(size)
// 一点左乗算O(size)
// 一点右乗算O(size)
// 右区間積取得O(1)
// 左区間積取得O(1)
// 区間積が単位元である区間の数え上げO(size log size)
// 区間積が単位元である区間の列挙O(size log size + 区間数)
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max>
class CumulativeProd :
public CumulativeProd_Body<T,m_T,i_T,size_max>
{
public:
inline CumulativeProd( const int& size = 0 );
template <typename U , SFINAE_FOR_CUMULATIVE_PROD( = nullptr )> inline CumulativeProd( const U ( &a )[size_max] , const int& size );
template <typename U , SFINAE_FOR_CUMULATIVE_PROD( = nullptr )> inline void Set( const U ( &a )[size_max] , const int& size );
// a[i]をm_T(t,a[i])に置き変える。
inline void LeftMultiply( const int& i , const T& t );
// a[i]をm_T(a[i],t)に置き変える。
inline void RightMultiply( const int& i , const T& t );
// 0 <= iかつi-1 <= j < m_sizeの場合のみサポート。
// 右区間積a[i]...a[j]をm_Tに関して計算する。
inline T RightProd( const int& i , const int& j );
// 左区間積a[j]...a[i]をm_Tに関して計算する。
inline T LeftProd( const int& i , const int& j );
// 区間積がe_T()と等しい区間の個数を計算する。
ll CountUnitProdRange();
// 区間積がe_T()と等しい区間を列挙する。
list<pair<int,int> > UnitProdRange();
private:
inline int Parent( const int& i );
inline int LCA( const int& i , const int& j );
};
template <typename T , T m_T(const T&,const T&) , T i_T(const T&) , int size_max> inline CumulativeProd_Body<T,m_T,i_T,size_max>::CumulativeProd_Body( const int& size ) : m_size( size ) , m_right() , m_left() { assert( size <= size_max ); }
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> inline CumulativeProd<T,m_T,e_T,i_T,size_max>::CumulativeProd( const int& size ) : CumulativeProd_Body<T,m_T,i_T,size_max>( size )
{
using base = CumulativeProd_Body<T,m_T,i_T,size_max>;
const T& unit = e_T();
if( base::m_size > 0 ? base::m_right[0] != unit : false ){
for( int i = 0 ; i < size ; i++ ){
base::m_right[i] = base::m_left[i] = unit;
}
}
}
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> template <typename U , SFINAE_FOR_CUMULATIVE_PROD()> inline CumulativeProd<T,m_T,e_T,i_T,size_max>::CumulativeProd( const U ( &a )[size_max] , const int& size ) : CumulativeProd_Body<T,m_T,i_T,size_max>( size ) { Set( a , size ); }
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> template <typename U , SFINAE_FOR_CUMULATIVE_PROD()> inline void CumulativeProd<T,m_T,e_T,i_T,size_max>::Set( const U ( &a )[size_max] , const int& size )
{
using base = CumulativeProd_Body<T,m_T,i_T,size_max>;
T temp , temp_reverse;
base::m_right[0] = base::m_left[0] = temp = temp_reverse = a[0];
for( int i = 1 ; i < size ; i++ ){
base::m_right[i] = temp = m_T( temp , a[i] );
base::m_left[i] = temp_reverse = m_T( a[i] , temp_reverse );
}
}
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> inline void CumulativeProd<T,m_T,e_T,i_T,size_max>::LeftMultiply( const int& i , const T& t )
{
using base = CumulativeProd_Body<T,m_T,i_T,size_max>;
const T m_right_i_prev_inv = i == 0 ? e_T() : i_T( base::m_right[i-1] );
const T m_right_i_prev = i == 0 ? t : m_T( base::m_right[i-1] , t );
for( int j = i ; j < base::m_size ; j++ ){
base::m_right[j] = m_T( m_right_i_prev , m_T( m_right_i_prev_inv , base::m_right[j] ) );
}
const T m_left_i_inv = i_T( base::m_left[i] );
const T& m_left_i = base::m_left[i] = m_T( t , base::m_left[i] );
for( int j = i + 1 ; j < base::m_size ; j++ ){
base::m_left[j] = m_T( m_T( base::m_left[j] , m_left_i_inv ) , m_left_i );
}
}
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> inline void CumulativeProd<T,m_T,e_T,i_T,size_max>::RightMultiply( const int& i , const T& t )
{
using base = CumulativeProd_Body<T,m_T,i_T,size_max>;
const T m_right_i_inv = i_T( base::m_right[i] );
const T& m_right_i = base::m_right[i] = m_T( base::m_right[i] , t );
for( int j = i + 1 ; j < base::m_size ; j++ ){
base::m_right[j] = m_T( m_right_i , m_T( m_right_i_inv , base::m_right[j] ) );
}
const T m_left_i_prev_inv = i == base::m_size - 1 ? e_T() : i_T( base::m_left[i-1] );
const T m_left_i_prev = m_T( t , base::m_left[i-1] );
for( int j = i + 1 ; j < base::m_size ; j++ ){
base::m_left[j] = m_T( m_T( base::m_left[j] , m_left_i_prev_inv ) , m_left_i_prev );
}
}
template <typename T , T m_T(const T&,const T&) , T i_T(const T&) , int size_max> inline T CumulativeProd_Body<T,m_T,i_T,size_max>::PathProd( const int& i , const int& j ) { assert( 0 <= i && i < m_size && 0 <= j && j < m_size ); const int k = LCA( i , j ); return m_T( m_T( m_left[i] , i_T( m_left[k] ) ) , k == 0 ? m_right[j] : m_T( i_T( m_right[Parent( k ) ] ) , m_right[j] )); }
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> inline T CumulativeProd<T,m_T,e_T,i_T,size_max>::RightProd( const int& i , const int& j )
{
assert( i - 1 <= j );
using base = CumulativeProd_Body<T,m_T,i_T,size_max>;
return i <= j ? i == 0 ? base::m_right[j] : m_T( i_T( base::m_right[i-1] ) , base::m_right[j] ) : e_T();
}
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> inline T CumulativeProd<T,m_T,e_T,i_T,size_max>::LeftProd( const int& i , const int& j )
{
assert( i - 1 <= j );
using base = CumulativeProd_Body<T,m_T,i_T,size_max>;
return i <= j ? i == 0 ? base::m_left[j] : m_T( base::m_left[j] , i_T( base::m_left[i - 1] ) ) : e_T();
}
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> ll CumulativeProd<T,m_T,e_T,i_T,size_max>::CountUnitProdRange()
{
using base = CumulativeProd_Body<T,m_T,i_T,size_max>;
map<T,ll> f{};
f[e_T()]++;
for( int i = 0 ; i < base::m_size ; i++ ){
f[base::m_right[i]]++;
}
ll answer = 0;
for( auto itr_f = f.begin() , end_f = f.end() ; itr_f != end_f ; itr_f++ ){
const ll& num = itr_f->second;
answer += num * ( num - 1 ) / 2;
}
return answer;
}
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> list<pair<int,int> > CumulativeProd<T,m_T,e_T,i_T,size_max>::UnitProdRange()
{
using base = CumulativeProd_Body<T,m_T,i_T,size_max>;
map<T,list<int> > f{};
f[e_T()].push_back( -1 );
for( int i = 0 ; i < base::m_size ; i++ ){
f[base::m_right[i]].push_back( i );
}
list<pair<int,int> > answer{};
for( auto itr_f = f.begin() , end_f = f.end() ; itr_f != end_f ; itr_f++ ){
const auto& a = itr_f->second;
for( auto itr_a_L = a.begin() , end_a = a.end() ; itr_a_L != end_a ; itr_a_L++ ){
const int i = *itr_a_L + 1;
auto itr_a_R = itr_a_R;
itr_a_R++;
while( itr_a_R != end_a ){
answer.push_back( i , *itr_a_R );
}
}
}
return answer;
}
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> inline int CumulativeProd<T,m_T,e_T,i_T,size_max>::Parent( const int& i ) { return i - 1; }
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T i_T(const T&) , int size_max> inline int CumulativeProd<T,m_T,e_T,i_T,size_max>::LCA( const int& i , const int& j ) { return min( i , j ); }
// 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
// #define REACTIVE
// #define USE_GETLINE
#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define REPEAT_MAIN( BOUND ) START_MAIN; signal( SIGABRT , &AlertAbort ); AutoCheck( exec_mode , use_getline ); if( exec_mode == sample_debug_mode || exec_mode == submission_debug_mode || exec_mode == library_search_mode ){ return 0; } else if( exec_mode == experiment_mode ){ Experiment(); return 0; } else if( exec_mode == small_test_mode ){ SmallTest(); return 0; }; DEXPR( int , bound_test_case_num , BOUND , min( BOUND , 100 ) ); int test_case_num = 1; if( exec_mode == solve_mode ){ if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } } else if( exec_mode == random_test_mode ){ CERR( "ランダムテストを行う回数を指定してください。" ); SET_LL( test_case_num ); } FINISH_MAIN
#define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE )
#define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
#define SET_ASSERT( A , MIN , MAX ) if( exec_mode == solve_mode ){ SET_LL( A ); ASSERT( A , MIN , MAX ); } else if( exec_mode == random_test_mode ){ CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ); } else { assert( false ); }
#define SOLVE_ONLY static_assert( __FUNCTION__[0] == 'S' )
#define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl
#define COUT( ... ) VariadicCout( cout << "出力： " , __VA_ARGS__ ) << endl
#define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl
#define COUT_A( A , N ) cout << "出力： "; OUTPUT_ARRAY( cout , A , N ) << endl
#define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl
#define COUT_ITR( A ) cout << "出力： "; OUTPUT_ITR( cout , A ) << endl
#else
#pragma GCC optimize ( "O3" )
#pragma GCC optimize ( "unroll-loops" )
#pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
#define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN
#define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE )
#define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
#define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX )
#define SOLVE_ONLY
#define CERR( ... )
#define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
#define CERR_A( A , N )
#define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL
#define CERR_ITR( A )
#define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL
#endif
#ifdef REACTIVE
#define ENDL endl
#else
#define ENDL "\n"
#endif
#ifdef USE_GETLINE
#define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); }
#define GETLINE_SEPARATE( SEPARATOR , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
#define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#else
#define SET_LL( A ) cin >> A
#define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
#define SET_A( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; }
#define CIN_A( LL , A , N ) vector<LL> A( N ); SET_A( A , N );
#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 ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define FINISH_MAIN REPEAT( test_case_num ){ if constexpr( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } }
#define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now()
#define CURRENT_TIME static_cast<double>( chrono::duration_cast<chrono::microseconds>( chrono::system_clock::now() - watch ).count() / 1000.0 )
#define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 )
#define 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 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 + 1 > 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 RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); return
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ return; }
// 入出力用
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>& operator<<( basic_ostream<char,Traits>& os , const vector<Arg>& arg ) { auto begin = arg.begin() , end = arg.end(); auto itr = begin; while( itr != end ){ ( itr == begin ? os : os << " " ) << *itr; itr++; } return os; }
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
template <typename T> constexpr T PositiveBaseResidue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }
template <typename T> constexpr T Residue( const T& a , const T& p ){ return PositiveBaseResidue( a , p < 0 ? -p : p ); }
template <typename T> constexpr T PositiveBaseQuotient( const T& a , const T& p ){ return ( a - PositiveBaseResidue( a , p ) ) / p; }
template <typename T> constexpr T Quotient( const T& a , const T& p ){ return p < 0 ? PositiveBaseQuotient( -a , -p ) : PositiveBaseQuotient( a , p ); }
#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 = ( ( ARGUMENT ) % ( MODULO ) ) % ( MODULO ); \
ARGUMENT_FOR_SQUARE_FOR_POWER < 0 ? ARGUMENT_FOR_SQUARE_FOR_POWER += ( MODULO ) : ARGUMENT_FOR_SQUARE_FOR_POWER; \
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 ) \
ll ANSWER[CONSTEXPR_LENGTH]; \
ll ANSWER_INV[CONSTEXPR_LENGTH]; \
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<TYPE_OF( CONST_TARGET ),uint>::value && ! is_same<TYPE_OF( CONST_TARGET ),ull>::value ); \
ll ANSWER = MINIMUM; \
{ \
ll L_BS = MINIMUM; \
ll U_BS = MAXIMUM; \
ANSWER = UPDATE_ANSWER; \
ll EXPRESSION_BS; \
const ll CONST_TARGET_BS = ( CONST_TARGET ); \
ll DIFFERENCE_BS; \
while( L_BS < U_BS ){ \
DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CONST_TARGET_BS; \
CERR( "二分探索中：" , "L_BS =" , L_BS , "<=" , ANSWER , "<=" , U_BS , "= U_BS :" , #EXPRESSION , "-" , #CONST_TARGET , "=" , EXPRESSION_BS , "-" , CONST_TARGET_BS , "=" , DIFFERENCE_BS ); \
if( DIFFERENCE_BS INEQUALITY_FOR_CHECK 0 ){ \
U_BS = UPDATE_U; \
} else { \
L_BS = UPDATE_L; \
} \
ANSWER = UPDATE_ANSWER; \
} \
if( L_BS > U_BS ){ \
CERR( "二分探索失敗：" , "L_BS =" , L_BS , ">" , U_BS , "= U_BS :" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \
CERR( "二分探索マクロにミスがある可能性があります。変更前の版に戻してください。" ); \
ANSWER = MAXIMUM + 1; \
} else { \
CERR( "二分探索終了：" , "L_BS =" , L_BS , "<=" , ANSWER , "<=" , U_BS , "= U_BS" ); \
CERR( "二分探索が成功したかを確認するために" , #EXPRESSION , "を計算します。" ); \
CERR( "成功判定が不要な場合はこの計算を削除しても構いません。" ); \
EXPRESSION_BS = ( EXPRESSION ); \
CERR( "二分探索結果：" , #EXPRESSION , "=" , EXPRESSION_BS , ( EXPRESSION_BS > 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 , ( L_BS + U_BS ) / 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 , ( L_BS + 1 + U_BS ) / 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 , ( L_BS + 1 + U_BS ) / 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 , ( L_BS + U_BS ) / 2 ) \
// t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。
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
template <typename T> inline T Add( const T& t0 , const T& t1 ) { return t0 + t1; }
template <typename T> inline T XorAdd( 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 AddInv( const T& t ) { return -t; }
template <typename T> inline T Id( const T& v ) { return v; }
template <typename T> inline T Min( const T& a , const T& b ){ return a < b ? a : b; }
template <typename T> inline T Max( const T& a , const T& b ){ return a < b ? b : a; }
// グリッド問題用
int H , W , H_minus , W_minus , HW;
vector<vector<bool> > non_wall;
inline T2<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<path> ( &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 , vector<vector<bool> >& non_wall , const char& walkable = '.' , const char& unwalkable = '#' ){non_wall.push_back(vector<bool>(W));auto& non_wall_i=non_wall[i];FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]==unwalkable),false);}}
// グラフ用
template <typename PATH> vector<list<PATH> > e;
template <typename T> map<T,T> f;
template <typename T> vector<T> g;
// デバッグ用
#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& exec_mode , const bool& use_getline );
inline void Solve();
inline void Experiment();
inline void SmallTest();
inline void RandomTest();
ll GetRand( const ll& Rand_min , const ll& Rand_max );
int exec_mode;
CEXPR( int , solve_mode , 0 );
CEXPR( int , sample_debug_mode , 1 );
CEXPR( int , submission_debug_mode , 2 );
CEXPR( int , library_search_mode , 3 );
CEXPR( int , experiment_mode , 4 );
CEXPR( int , small_test_mode , 5 );
CEXPR( int , random_test_mode , 6 );
#ifdef USE_GETLINE
CEXPR( bool , use_getline , true );
#else
CEXPR( bool , use_getline , false );
#endif
#else
ll GetRand( const ll& Rand_min , const ll& Rand_max ) { ll answer = time( NULL ); return answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; }
#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&
// VVV 常設ライブラリは以下に挿入する。
// ConstexprModulo
// c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/ConstexprModulo/a.hpp
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_istream<char,Traits>& OP>>(basic_istream<char,Traits>& is,MN<M>& n);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_istream<char,Traits>& OP>>(basic_istream<char,Traits>& is,MN<M>& n){ll m;is >> m;n = m;RE is;}TE<uint M,CL Traits> IN basic_ostream<char,Traits>& OP<<(basic_ostream<char,Traits>& os,CO 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();}
// IntervalAddBIT
// c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/IntervalAdd/a.hpp
TE<int N>CL PWInverse_CE{PU:int m_val;CE PWInverse_CE();};
TE<int N>CE PWInverse_CE<N>::PWInverse_CE():m_val(1){WH(m_val < N){m_val <<= 1;}}
TE <TY T,int N>CL BIT{PU:T m_fenwick[N + 1];IN BIT();BIT(CO T(&a)[N]);IN T Get(CRI i)CO;IN VO Set(CRI i,CO T& n);IN VO Set(CO T(&a)[N]);IN VO Initialise();IN BIT<T,N>& OP+=(CO T(&a)[N]);VO Add(CRI i,CO T& n);T InitialSegmentSum(CRI i_final)CO;IN T IntervalSum(CRI i_start,CRI i_final)CO;int BinarySearch(CO T& n)CO;IN int BinarySearch(CRI i_start,CO T& n)CO;};
TE <TY T,int N> IN BIT<T,N>::BIT():m_fenwick(){static_assert(! is_same<T,int>::value);}TE <TY T,int N>BIT<T,N>::BIT(CO T(&a)[N]):m_fenwick(){static_assert(! is_same<T,int>::value);for(int j = 1;j <= N;j++){T& fenwick_j = m_fenwick[j];int i = j - 1;fenwick_j = a[i];int i_lim = j -(j & -j);WH(i != i_lim){fenwick_j += m_fenwick[i];i -=(i & -i);}}}TE <TY T,int N> IN T BIT<T,N>::Get(CRI i)CO{RE IntervalSum(i,i);}TE <TY T,int N> IN VO BIT<T,N>::Set(CRI i,CO T& n){Add(i,n - IntervalSum(i,i));}TE <TY T,int N> IN VO BIT<T,N>::Set(CO T(&a)[N]){BIT<T,N> a_copy{a};swap(m_fenwick,a_copy.m_fenwick);}TE <TY T,int N> IN VO BIT<T,N>::Initialise(){for(int j = 1;j <= N;j++){m_fenwick[j] = 0;}}TE <TY T,int N> IN BIT<T,N>& BIT<T,N>::OP+=(CO T(&a)[N]){for(int i = 0;i < N;i++){Add(i,a[i]);}RE *TH;}TE <TY T,int N>VO BIT<T,N>::Add(CRI i,CO T& n){int j = i + 1;WH(j <= N){m_fenwick[j] += n;j +=(j & -j);}RE;}TE <TY T,int N>T BIT<T,N>::InitialSegmentSum(CRI i_final)CO{T sum = 0;int j =(i_final < N?i_final:N - 1)+ 1;WH(j > 0){sum += m_fenwick[j];j -= j & -j;}RE sum;}TE <TY T,int N> IN T BIT<T,N>::IntervalSum(CRI i_start,CRI i_final)CO{RE InitialSegmentSum(i_final)- InitialSegmentSum(i_start - 1);}TE <TY T,int N>int BIT<T,N>::BinarySearch(CO T& n)CO{int j = 0;int PW = PWInverse_CE<N>().m_val;T sum{};T sum_next{};WH(PW > 0){int j_next = j | PW;if(j_next < N){sum_next += m_fenwick[j_next];if(sum_next < n){sum = sum_next;j = j_next;}else{sum_next = sum;}}PW >>= 1;}RE j;}TE <TY T,int N> IN int BIT<T,N>::BinarySearch(CRI i_start,CO T& n)CO{RE max(i_start,BinarySearch(InitialSegmentSum(i_start)+ n));}
TE <TY T,int N>CL IntervalAddBIT{PU:BIT<T,N> m_bit_0;BIT<T,N> m_bit_1;IN IntervalAddBIT();IN IntervalAddBIT(CO T(&a)[N]);IN T Get(CRI i)CO;IN VO Set(CRI i,CO T& n);IN VO Set(CO T(&a)[N]);IN VO Initialise();IN IntervalAddBIT<T,N>& OP+=(CO T(&a)[N]);IN VO Add(CRI i,CO T& n);IN VO IntervalAdd(CRI i_start,CRI i_final,CO T& n);IN T InitialSegmentSum(CRI i_final)CO;IN T IntervalSum(CRI i_start,CRI i_final)CO;};
TE <TY T,int N> IN IntervalAddBIT<T,N>::IntervalAddBIT():m_bit_0(),m_bit_1(){}TE <TY T,int N> IN IntervalAddBIT<T,N>::IntervalAddBIT(CO T(&a)[N]):m_bit_0(),m_bit_1(){OP+=(a);}TE <TY T,int N> IN T IntervalAddBIT<T,N>::Get(CRI i)CO{RE IntervalSum(i,i);}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Set(CRI i,CO T& n){Add(i,n - IntervalSum(i,i));}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Set(CO T(&a)[N]){IntervalAddBIT<T,N> a_copy{a};swap(m_bit_0,a_copy.m_bit_0);swap(m_bit_1,a_copy.m_bit_1);}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Initialise(){m_bit_0.Initialise();m_bit_1.Initialise();}TE <TY T,int N> IN IntervalAddBIT<T,N>& IntervalAddBIT<T,N>::OP+=(CO T(&a)[N]){for(int i = 0;i < N;i++){Add(i,a[i]);}RE *TH;}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::Add(CRI i,CO T& n){IntervalAdd(i,i,n);}TE <TY T,int N> IN VO IntervalAddBIT<T,N>::IntervalAdd(CRI i_start,CRI i_final,CO T& n){m_bit_0.Add(i_start,-(i_start - 1)* n);m_bit_0.Add(i_final + 1,i_final * n);m_bit_1.Add(i_start,n);m_bit_1.Add(i_final + 1,- n);}TE <TY T,int N> IN T IntervalAddBIT<T,N>::InitialSegmentSum(CRI i_final)CO{RE m_bit_0.InitialSegmentSum(i_final)+ i_final * m_bit_1.InitialSegmentSum(i_final);}TE <TY T,int N> IN T IntervalAddBIT<T,N>::IntervalSum(CRI i_start,CRI i_final)CO{RE InitialSegmentSum(i_final)- InitialSegmentSum(i_start - 1);}
// 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