#ifdef DEBUG #define _GLIBCXX_DEBUG #define CERR( ANSWER ) cerr << ANSWER << "\n"; #else #pragma GCC optimize ( "O3" ) #pragma GCC optimize( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #define CERR( ANSWER ) #endif #include <bits/stdc++.h> using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; #define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) ) #define TYPE_OF( VAR ) decay_t<decltype( VAR )> #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE #define CIN( LL , A ) LL A; cin >> A #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #define CIN_ASSERT( A , MIN , MAX ) CIN( TYPE_OF( MAX ) , A ); ASSERT( A , MIN , MAX ) #define GETLINE( A ) string A; getline( cin , A ) #define GETLINE_SEPARATE( A , SEPARATOR ) string A; getline( cin , A , SEPARATOR ) #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 FOR_ITR( ARRAY , ITR , END ) for( auto ITR = ARRAY .begin() , END = ARRAY .end() ; ITR != END ; ITR ++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT , 0 , HOW_MANY_TIMES ) #define QUIT return 0 #define COUT( ANSWER ) cout << ( ANSWER ) << "\n" #define RETURN( ANSWER ) COUT( ANSWER ); QUIT #define SET_PRECISION( PRECISION ) cout << fixed << setprecision( PRECISION ) #define DOUBLE( PRECISION , ANSWER ) SET_PRECISION << ( ANSWER ) << "\n"; QUIT template <typename T> inline T Absolute( const T& a ){ return a > 0 ? a : -a; } template <typename T> inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : ( a % p ) + 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 = ( 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_I , LENGTH , MODULO ) \ static ll ANSWER[LENGTH]; \ static ll ANSWER_INV[LENGTH]; \ static ll INVERSE[LENGTH]; \ { \ ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL; \ FOREQ( i , 1 , MAX_I ){ \ 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_I ){ \ ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = MODULO - ( ( ( MODULO / i ) * INVERSE[MODULO % i] ) % MODULO ) ) %= MODULO; \ } \ } \ // 通常の二分探索その1 // EXPRESSIONがANSWERの狭義単調増加関数の時、EXPRESSION >= TARGETを満たす最小の整数を返す。 // 広義単調増加関数を扱いたい時は等号成立の処理を消して続く>に等号を付ける。 #define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \ ll ANSWER; \ { \ 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( 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 == 0 ){ \ break; \ } else { \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH > 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_U = ANSWER; \ } else { \ VARIABLE_FOR_BINARY_SEARCH_L = ANSWER + 1; \ } \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ } \ } \ CERR( VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << ">=0" ); \ } \ // 通常の二分探索その2 // EXPRESSIONがANSWERの狭義単調増加関数の時、EXPRESSION <= TARGETを満たす最大の整数を返す。 // 広義単調増加関数を扱いたい時は等号成立の処理を消して続く<に等号を付ける。 #define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \ ll ANSWER; \ { \ 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( 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 == 0 ){ \ break; \ } else { \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH < 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_L = ANSWER; \ } else { \ VARIABLE_FOR_BINARY_SEARCH_U = ANSWER - 1; \ } \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ } \ } \ CERR( VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << "<=0" ); \ } \ // 通常の二分探索その3 // EXPRESSIONがANSWERの狭義単調減少関数の時、EXPRESSION >= TARGETを満たす最大の整数を返す。 // 広義単調増加関数を扱いたい時は等号成立の処理を消して続く>に等号を付ける。 #define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \ ll ANSWER; \ { \ 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( 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 == 0 ){ \ break; \ } else { \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH > 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_L = ANSWER; \ } else { \ VARIABLE_FOR_BINARY_SEARCH_U = ANSWER - 1; \ } \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ } \ } \ CERR( VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << ">=0" ); \ } \ // 通常の二分探索その4 // EXPRESSIONがANSWERの狭義単調減少関数の時、EXPRESSION <= TARGETを満たす最小の整数を返す。 // 広義単調増加関数を扱いたい時は等号成立の処理を消して続く<に等号を付ける。 #define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \ ll ANSWER; \ { \ 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( 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 == 0 ){ \ break; \ } else { \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH < 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_U = ANSWER; \ } else { \ VARIABLE_FOR_BINARY_SEARCH_L = ANSWER + 1; \ } \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ } \ } \ CERR( VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << "<=0" ); \ } \ // 二進法の二分探索 // EXPRESSIONがANSWERの狭義単調増加関数の時、EXPRESSION <= TARGETを満たす最大の整数を返す。 #define BBS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ ll ANSWER = MINIMUM; \ { \ ll VARIABLE_FOR_POWER_FOR_BINARY_SEARCH = 1; \ ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( MAXIMUM ) - ANSWER; \ while( VARIABLE_FOR_POWER_FOR_BINARY_SEARCH <= VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ){ \ VARIABLE_FOR_POWER_FOR_BINARY_SEARCH *= 2; \ } \ VARIABLE_FOR_POWER_FOR_BINARY_SEARCH /= 2; \ ll VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH = ANSWER; \ while( VARIABLE_FOR_POWER_FOR_BINARY_SEARCH != 0 ){ \ ANSWER = VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH + VARIABLE_FOR_POWER_FOR_BINARY_SEARCH; \ VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){ \ VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH = ANSWER; \ break; \ } else if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH < 0 ){ \ VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH = ANSWER; \ } \ VARIABLE_FOR_POWER_FOR_BINARY_SEARCH /= 2; \ } \ ANSWER = VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH; \ } \ // 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& inline CEXPR( int , bound_NQ , 200000 ); list<int> edge[bound_NQ] = {}; inline list<int> E( const int& i ) { return edge[i]; } // Resetはm_foundとm_prevを初期化 // Shiftはm_foundとm_prevを非初期化 #define DECLARATION_OF_FIRST_SEARCH( BREADTH ) \ template <int V_max,list<int> E(const int&)> \ class BREADTH ## FirstSearch \ { \ \ private: \ int m_V; \ int m_init; \ list<int> m_next; \ bool m_found[V_max]; \ int m_prev[V_max]; \ \ public: \ inline BREADTH ## FirstSearch( const int& V ); \ inline BREADTH ## FirstSearch( const int& V , const int& init ); \ \ inline void Reset( const int& init ); \ inline void Shift( const int& init ); \ \ inline const int& size() const; \ inline const int& init() const; \ inline bool& found( const int& i ); \ inline const int& prev( const int& i ) const; \ \ int Next(); \ \ }; \ #define DEFINITION_OF_FIRST_SEARCH( BREADTH , PUSH ) \ template <int V_max,list<int> E(const int&)> inline BREADTH ## FirstSearch<V_max,E>::BREADTH ## FirstSearch( const int& V ) : m_V( V ) , m_init() , m_next() , m_found() , m_prev() { for( int i = 0 ; i < m_V ; i++ ){ m_prev[i] = -1; } } \ template <int V_max,list<int> E(const int&)> inline BREADTH ## FirstSearch<V_max,E>::BREADTH ## FirstSearch( const int& V , const int& init ) : BREADTH ## FirstSearch( V ) { m_init = init; m_next.push_back( m_init ); m_found[m_init] = true; } \ \ template <int V_max,list<int> E(const int&)> inline void BREADTH ## FirstSearch<V_max,E>::Reset( const int& init ) { m_init = init; assert( m_init < m_V ); m_next.clear(); m_next.push_back( m_init ); for( int i = 0 ; i < m_V ; i++ ){ m_found[i] = i == m_init; m_prev[i] = -1; } } \ template <int V_max,list<int> E(const int&)> inline void BREADTH ## FirstSearch<V_max,E>::Shift( const int& init ) { m_init = init; assert( m_init < m_V ); m_next.clear(); if( ! m_found[m_init] ){ m_next.push_back( m_init ); m_found[m_init] = true; } } \ \ template <int V_max,list<int> E(const int&)> inline const int& BREADTH ## FirstSearch<V_max,E>::size() const { return m_V; } \ template <int V_max,list<int> E(const int&)> inline const int& BREADTH ## FirstSearch<V_max,E>::init() const { return m_init; } \ template <int V_max,list<int> E(const int&)> inline bool& BREADTH ## FirstSearch<V_max,E>::found( const int& i ) { assert( i < m_V ); return m_found[i]; } \ template <int V_max,list<int> E(const int&)> inline const int& BREADTH ## FirstSearch<V_max,E>::prev( const int& i ) const { assert( i < m_V ); return m_prev[i]; } \ \ template <int V_max,list<int> E(const int&)> \ int BREADTH ## FirstSearch<V_max,E>::Next() \ { \ \ if( m_next.empty() ){ \ \ return -1; \ \ } \ \ const int i_curr = m_next.front(); \ m_next.pop_front(); \ list<int> edge = E( i_curr ); \ \ while( ! edge.empty() ){ \ \ const int& i = edge.front(); \ bool& found_i = found( i ); \ \ if( ! found_i ){ \ \ m_next.PUSH( i ); \ m_prev[i] = i_curr; \ found_i = true; \ \ } \ \ edge.pop_front(); \ \ } \ \ return i_curr; \ \ } \ DECLARATION_OF_FIRST_SEARCH( Depth ); DEFINITION_OF_FIRST_SEARCH( Depth , push_front ); template <int V_max,list<int> E(const int&),int digit = 0> class DepthFirstSearchOnTree : public DepthFirstSearch<V_max,E> { private: // メモリが厳しい場合、以下で不要なものを消す。 int m_reversed[V_max]; list<int> m_children[V_max]; bool m_set_children; int m_depth[V_max]; int m_height[V_max]; bool m_set_height; int m_weight[V_max]; bool m_set_weight; int m_doubling[digit][V_max]; bool m_set_doubling; public: inline DepthFirstSearchOnTree( const int& V , const int& root ); inline void Reset( const int& init ) = delete; inline void Shift( const int& init ) = delete; inline const int& Root() const; inline const int& Parent( const int& i ) const; inline const list<int>& Children( const int& i ); inline const int& Depth( const int& i ) const; inline const int& Height( const int& i ); inline const int& Weight( const int& i ); // 各ノードの高さ < 2^digitの時のみサポート。 int Ancestor( int i , int n ); int LCA( int i , int j ); int LCA( int i , int j , int& i_prev , int& j_prev ); private: void SetChildren(); void SetHeight(); void SetWeight(); // 各ノードの高さ < 2^digitの時のみサポート。 // LCA()を呼ぶ前にAncestor()経由で完全にダブリングを設定するため、 // 遅延評価する../../../../Mathematics/Function/Iteration/Doubling/のダブリングで代用しない。 void SetDoubling(); }; template <int V_max,list<int> E(const int&),int digit> inline DepthFirstSearchOnTree<V_max,E,digit>::DepthFirstSearchOnTree( const int& V , const int& root ) : DepthFirstSearch<V_max,E>( V , root ) , m_reversed() , m_children() , m_set_children() , m_depth() , m_height() , m_set_height() , m_weight() , m_set_weight() , m_doubling() , m_set_doubling() { int n = DepthFirstSearch<V_max,E>::size(); while( --n >= 0 ){ const int& i = m_reversed[n] = DepthFirstSearch<V_max,E>::Next(); const int& j = Parent( i ); if( j != -1 ){ m_depth[i] = m_depth[j] + 1; } } } template <int V_max,list<int> E(const int&),int digit> inline const int& DepthFirstSearchOnTree<V_max,E,digit>::Root() const { return DepthFirstSearch<V_max,E>::init(); } template <int V_max,list<int> E(const int&),int digit> inline const int& DepthFirstSearchOnTree<V_max,E,digit>::Parent( const int& i ) const { return DepthFirstSearch<V_max,E>::prev( i ); } template <int V_max,list<int> E(const int&),int digit> inline const list<int>& DepthFirstSearchOnTree<V_max,E,digit>::Children( const int& i ) { if( ! m_set_children ){ SetChildren(); } return m_children[i]; } template <int V_max,list<int> E(const int&),int digit> inline const int& DepthFirstSearchOnTree<V_max,E,digit>::Depth( const int& i ) const { return m_depth[i]; } template <int V_max,list<int> E(const int&),int digit> inline const int& DepthFirstSearchOnTree<V_max,E,digit>::Height( const int& i ) { if( ! m_set_height ){ SetHeight(); } return m_height[i]; } template <int V_max,list<int> E(const int&),int digit> inline const int& DepthFirstSearchOnTree<V_max,E,digit>::Weight( const int& i ) { if( ! m_set_weight ){ SetWeight(); } return m_weight[i]; } template <int V_max,list<int> E(const int&),int digit> int DepthFirstSearchOnTree<V_max,E,digit>::Ancestor( int i , int n ) { if( ! m_set_doubling ){ SetDoubling(); } if( ( n >> digit ) != 0 ){ return Root(); } int d = 0; while( n != 0 ){ ( ( n & 1 ) == 1 ) ? i = m_doubling[d++][i] : i; n >>= 1; } return i; } template <int V_max,list<int> E(const int&),int digit> int DepthFirstSearchOnTree<V_max,E,digit>::LCA( int i , int j ) { int diff = Depth( i ) - Depth( j ); if( diff < 0 ){ swap( i , j ); diff *= -1; } i = Ancestor( i , diff ); if( i == j ){ return i; } int d = digit; while( --d >= 0 ){ const int ( &doubling_d )[V_max] = m_doubling[d]; const int& doubling_d_i = doubling_d[i]; const int& doubling_d_j = doubling_d[j]; if( doubling_d_i != doubling_d_j ){ i = doubling_d_i; j = doubling_d_j; } } return Parent( i ); } template <int V_max,list<int> E(const int&),int digit> int DepthFirstSearchOnTree<V_max,E,digit>::LCA( int i , int j , int& i_prev , int& j_prev ) { if( i == j ){ i_prev = j_prev = -1; return i; } int diff = Depth( i ) - Depth( j ); if( diff < 0 ){ return LCA( j , i , j_prev , i_prev ); } if( diff > 0 ){ i_prev = Ancestor( i , diff - 1 ); i = Parent( i_prev ); if( i == j ){ j_prev = -1; return i; } } else if( ! m_set_doubling ){ SetDoubling(); } int d = digit; while( --d >= 0 ){ const int ( &doubling_d )[V_max] = m_doubling[d]; const int& doubling_d_i = doubling_d[i]; const int& doubling_d_j = doubling_d[j]; if( doubling_d_i != doubling_d_j ){ i = doubling_d_i; j = doubling_d_j; } } i_prev = i; j_prev = j; return Parent( i_prev ); } template <int V_max,list<int> E(const int&),int digit> void DepthFirstSearchOnTree<V_max,E,digit>::SetChildren() { assert( !m_set_children ); m_set_children = true; const int& V = DepthFirstSearch<V_max,E>::size(); for( int i = 0 ; i < V ; i++ ){ const int& parent_i = Parent( i ); if( parent_i != -1 ){ m_children[parent_i].push_back( i ); } } return; } template <int V_max,list<int> E(const int&),int digit> void DepthFirstSearchOnTree<V_max,E,digit>::SetHeight() { assert( !m_set_height ); m_set_height = true; const int& V = DepthFirstSearch<V_max,E>::size(); for( int i = 0 ; i < V ; i++ ){ const int& reversed_i = m_reversed[i]; const int& parent_i = Parent( reversed_i ); if( parent_i != -1 ){ int& height_parent_i = m_height[parent_i]; const int& height_i = m_height[reversed_i]; height_parent_i > height_i ? height_parent_i : height_parent_i = height_i + 1; } } return; } template <int V_max,list<int> E(const int&),int digit> void DepthFirstSearchOnTree<V_max,E,digit>::SetWeight() { assert( !m_set_weight ); m_set_weight = true; const int& V = DepthFirstSearch<V_max,E>::size(); for( int i = 0 ; i < V ; i++ ){ const int& reversed_i = m_reversed[i]; const int& parent_i = Parent( reversed_i ); if( parent_i != -1 ){ m_weight[parent_i] += m_weight[reversed_i] + 1; } } return; } template <int V_max,list<int> E(const int&),int digit> void DepthFirstSearchOnTree<V_max,E,digit>::SetDoubling() { assert( !m_set_doubling ); m_set_doubling = true; const int& V = DepthFirstSearch<V_max,E>::size(); { int ( &doubling_0 )[V_max] = m_doubling[0]; const int& r = Root(); for( int i = 0 ; i < V ; i++ ){ doubling_0[i] = i == r ? r : Parent( i ); } } for( int d = 1 ; d < digit ; d++ ){ int ( &doubling_d )[V_max] = m_doubling[d]; int ( &doubling_d_minus )[V_max] = m_doubling[d-1]; for( int i = 0 ; i < V ; i++ ){ doubling_d[i] = doubling_d_minus[doubling_d_minus[i]]; } } return; } int main() { UNTIE; CIN_ASSERT( N , 2 , bound_NQ ); CIN_ASSERT( Q , 1 , bound_NQ ); int N_minus = N - 1; REPEAT( N_minus ){ CIN_ASSERT( A , 1 , N ); CIN_ASSERT( B , 1 , N ); A--; B--; edge[A].push_back( B ); edge[B].push_back( A ); } static DepthFirstSearchOnTree<bound_NQ,E,15> dfs{ N , 0 }; REPEAT( Q ){ CIN_ASSERT( S , 1 , N ); CIN_ASSERT( T , 1 , N ); S--; T--; int depth_S = dfs.Depth( S ); int depth_T = dfs.Depth( T ); int diff = depth_S - depth_T; if( diff < 0 ){ swap( S , T ); swap( depth_S , depth_T ); diff *= -1; } if( S == T ){ COUT( N ); } else if( diff % 2 == 1 ){ COUT( 0 ); } else if( diff == 0 ){ int S_prev; int T_prev; dfs.LCA( S , T , S_prev , T_prev ); COUT( N - dfs.Weight( S_prev ) - dfs.Weight( T_prev ) - 2 ); } else { int LCA = dfs.LCA( S , T ); int centre_prev = dfs.Ancestor( S , depth_S - 1 - dfs.Depth( LCA ) ); const int& centre = dfs.Parent( centre_prev ); COUT( dfs.Weight( centre ) - dfs.Weight( centre_prev ) ); } } QUIT; }