#ifdef DEBUG
  #define _GLIBCXX_DEBUG
  #define CERR( ANSWER ) cerr << ANSWER << endl;
  #define LIBRARY_SEARCH if( LibrarySearch() != 0 ){ QUIT; };
#else
  #pragma GCC optimize ( "O3" )
  #pragma GCC optimize( "unroll-loops" )
  #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
  #define CERR( ANSWER ) 
  #define LIBRARY_SEARCH
#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_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; \
    }									\
  }									\

// 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&

int LibrarySearch()
{
  CERR( "ライブラリーを探索しますか？[y/n]" );
  CIN( string , reply );
  if( reply == "n" ){
    CERR( "ライブラリーを探索せずに続行します。" );
    CERR( "" );
    return 0;
  } else if( reply != "y" ){
    CERR( "y/nのいずれかで答えてください。" );
    CERR( "終了します。" );
    CERR( "" );
    return -1;
  }
  CERR( "" );
  CERR( "ライブラリーを探索します。" );
  CERR( "問題の種類を番号で指定してください；" );
  vector<string> problems =
    {
      "数に関する問題。" ,
      "配列に関する問題。" ,
      "文字列に関する問題。" ,
      "順列に関する問題。" ,
      "グラフに関する問題。" ,
      "格子点に関する問題。"
    };
  int problems_size = problems.size();
  FOR( i , 0 , problems_size ){
    CERR( i << ": " << problems[i] );
  }
  CIN( int , num );
  CERR( "" );
  if( num < 0 || num >= problems_size ){
    cerr << "返答は" << problems_size - 1 << "以下の非負整数にしてください。";
    CERR( "終了します。" );
    CERR( "" );
    return -1;
  } else if( num == 0 ){
    CERR( "入力は１つの数か、１つの数と法を表す数ですか？[y/n/c]" );
    cin >> reply;
    CERR( "" );
    if( reply == "y" ){
      CERR( "まずは小さい入力の場合を愚直に計算し、OEISで検索しましょう。" );
      CERR( "https://oeis.org/?language=japanese" );
      CERR( "" );
      CERR( "次に出力の定義と等価な式を考察しましょう。" );
      CERR( "もし単調ならば、冪乗や階乗を検討しましょう。" );
      CERR( "もし定義にp進法が使われていれば、探索アルゴリズムを検討しましょう。" );
      CERR( "もし入力が素数に近い場合に規則性があれば、p進付値、p進法、オイラー関数、約数の個数などを検討しましょう。" );
    } else if( reply == "n" ){
      CERR( "このケースのライブラリー探索は未実装です。" );
    } else if( reply == "c" ){
      CERR( "終了します。" );
      CERR( "" );
      return -1;
    } else {
      CERR( "y/n/cのいずれかで答えてください。" );
      CERR( "終了します。" );
      CERR( "" );
      return -1;
    }
    CERR( "" );
    CERR( "マルチテストケースの場合は以下の前計算を検討しましょう；" );
    CERR( "素数列挙、約数列挙、サブゴールとなる関係式を満たす解列挙。" );
  } else if( num == 3 ){
    CERR( "符号の計算は転倒数の計算に帰着させましょう。" );
    CERR( "符号と何かの積の和は行列式に帰着させましょう。余因子展開のメモ化再帰でO(N 2^N)です。" );
    CERR( "" );
    CERR( "１つの順列の転倒数は、" );
    CERR( "- O(N^2)が通るなら愚直な二重ループ" );
    CERR( "- O(N log_2 N)が必要なら可換群に対するBIT" );
    CERR( "  \\Mathematics\\SetTheory\\DirectProduct\\AffineSpace\\BIT" );
    CERR( "で計算しましょう。" );
    CERR( "" );
    CERR( "条件を満たす順列全体をわたる転倒数の総和は、各i<jごとにそこで転倒が生じる順列の個数を計算し、その総和を取りましょう。" );
    CERR( "条件が良ければ、転倒が生じる順列の個数は転倒が生じるとは限らない順列の個数の半分となります。" );
  } else {
    CERR( "このケースのライブラリー探索は未実装です。" );
  }
  CERR( "" );
  CERR( "終了します。" );
  CERR( "" );
  return -1;
}

// InitialSegmentSumで負の入力を扱うためにuintではなくintをテンプレート引数にする。
// 使用演算：
// T& T::operator=( const T& )
// T& T::operator+=( const T& )
// T operator-( const T& , const T& )（ただしIntervalSumを用いない場合は不要）
// T operator<( const T& , const T& )（ただしBinarySearchを用いない場合は不要）
template <typename T , int N>
class BIT
{
private:
  T m_fenwick[N + 1];

public:
  inline BIT();
  BIT( const T ( & a )[N] );

  inline void Set( const int& i , const T& n );

  inline BIT<T,N>& operator+=( const T ( & a )[N] );
  void Add( const int& i , const T& n );

  T InitialSegmentSum( const int& i_final ) const;
  inline T IntervalSum( const int& i_start , const int& i_final ) const;
  
  // operator+=の単位元T()より小さくない要素のみを成分に持つ場合のみサポート。
  // InitialSegmentSum( i )がn以上となるiが存在する場合にその最小値を2進法で探索。
  int BinarySearch( const T& n ) const;
  // IntervalSum( i_start , i )がt以上となるi_start以上のiが存在する場合にその最小値を2進法で探索。
  inline int BinarySearch( const int& i_start , const T& n ) const;
  
};

template <typename T , int N> inline BIT<T,N>::BIT() : m_fenwick() {}
template <typename T , int N>
BIT<T,N>::BIT( const T ( & a )[N] ) : m_fenwick()
{

  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 );

    while( i != i_lim ){

      fenwick_j += m_fenwick[i];
      i -= ( i & -i );

    }

  }

}

template <typename T , int N> inline void BIT<T,N>::Set( const int& i , const T& n ) { Add( i , n - IntervalSum( i , i ) ); }

template <typename T , int N> inline BIT<T,N>& BIT<T,N>::operator+=( const T ( & a )[N] ) { for( int i = 0 ; i < N ; i++ ){ Add( i , a[i] ); } return *this; }

template <typename T , int N>
void BIT<T,N>::Add( const int& i , const T& n )
{
  
  int j = i + 1;

  while( j <= N ){

    m_fenwick[j] += n;
    j += ( j & -j );

  }

  return;
  
}

template <typename T , int N> 
T BIT<T,N>::InitialSegmentSum( const int& i_final ) const
{

  T sum = 0;
  int j = ( i_final < N ? i_final : N - 1 ) + 1;

  while( j > 0 ){

    sum += m_fenwick[j];
    j -= j & -j;
    
  }

  return sum;
  
}

template <typename T , int N> inline T BIT<T,N>::IntervalSum( const int& i_start , const int& i_final ) const { return InitialSegmentSum( i_final ) - InitialSegmentSum( i_start - 1 ); }

// template <typename T , int N>
// int BIT<T,N>::BinarySearch( const T& n ) const
// {

//   int j = 0;
//   int power = PowerCalculation<N>.m_val;
//   T sum{};
//   T sum_next{};
  
//   while( power > 0 ){

//     int j_next = j | power;

//     if( j_next < N ){
      
//       sum_next += m_fenwick[j_next];

//       if( sum_next < n ){
	
// 	sum = sum_next;
// 	j = j_next;

//       } else {

// 	sum_next = sum;
	
//       }
      
//     }
    
//     power >>= 1;

//   }

//   // InitialSegmentSum( i )がt未満となるiが存在するならばjはその最大値に1を足したものとなり、
//   // InitialSegmentSum( i )がt未満となるiが存在しないならばj=0となり、
//   // いずれの場合もjはInitialSegmentSum( i )がt以上となる最小のiと等しい。
//   return j;

// }

// template <typename T , int N> inline int BIT<T,N>::BinarySearch( const int& i_start , const T& n ) const { return max( i_start , BinarySearch( InitialSegmentSum( i_start ) + n ) ); }


int main()
{
  UNTIE;
  LIBRARY_SEARCH;
  CEXPR( int , bound_N , 100000 );
  CIN_ASSERT( N , 1 , bound_N );
  CIN_ASSERT( M , 0 , N );
  CEXPR( ll , P , 998244353 );
  static pair<int,int> PK[bound_N];
  static pair<int,int> KP[bound_N];
  static BIT<int,bound_N> bitP{};
  FOR( m , 0 , M ){
    CIN_ASSERT( Pi , 1 , N );
    CIN_ASSERT( Ki , 1 , N );
    Pi--;
    Ki--;
    PK[m] = pair<int,int>( Pi , Ki );
    KP[m] = pair<int,int>( Ki , Pi );
    bitP.Add( Pi , 1 );
  }
  int max_index = max( N - M , 2 );
  FACTORIAL_MOD( factorial , factorial_inv , inv , max_index , bound_N , P );
  ll& factorial_N_M = factorial[N - M];
  ll answer0 = ll( N - M ) * ( N - M - 1 ) / 2 % P * factorial_N_M % P * inv[2] % P;
  CERR( "answer0: " << ll( N - M ) * ( N - M - 1 ) / 2 << "," << factorial_N_M % P * inv[2] % P );
  sort( PK , PK + M );
  sort( KP , KP + M );
  ll& factorial_N_M_1 = factorial[ max( N - M - 1 , 0 ) ];
  ll answer1 = 0;
  FOR( i , 0 , M ){
    pair<int,int>& KPi = KP[i];
    answer1 += ll( KPi.first - i ) * ( N - KPi.second - bitP.IntervalSum( KPi.second , N - 1 ) );
    CERR( "answer1," << i << ": " << KPi.first << "," << KPi.second << "," << KPi.first - i << "," << N - KPi.second - bitP.IntervalSum( KPi.second , N - 1 ) << "," << factorial_N_M_1 );
  }
  ( ( answer1 %= P ) *= factorial_N_M_1 ) %= P;
  ll answer2 = 0;
  FOREQINV( i , M - 1 , 0 ){
    pair<int,int>& KPi = KP[i];
    answer2 += ll( N - KPi.first - M + i ) * ( KPi.second - bitP.IntervalSum( 0 , KPi.second - 1 ) );
    CERR( "answer2," << i << ": " << KPi.first << "," << KPi.second << "," << N - KPi.first - M + i << "," << KPi.second - bitP.IntervalSum( 0 , KPi.second - 1 ) << "," << factorial_N_M_1 );
  }
  ( ( answer2 %= P ) *= factorial_N_M_1 ) %= P;
  static BIT<int,bound_N> bitK{};
  ll answer3 = 0;
  FOREQINV( i , M - 1 , 0 ){
    pair<int,int>& PKi = PK[i];
    bitK.Add( PKi.second , 1 );
    answer3 += bitK.IntervalSum( 0 , PKi.second - 1 );
    CERR( "answer1," << i << ": " << PKi.first << "," << PKi.second << "," << bitK.IntervalSum( 0 , PKi.second - 1 ) << "," << factorial_N_M );
  }
  ( answer3 *= factorial_N_M ) %= P;
  CERR( answer0 << "," << answer1 << "," << answer2 << "," << answer3 );
  RETURN( ( answer0 + answer1 + answer2 + answer3 ) % P );
}