結果

問題 No.2127 Mod, Sum, Sum, Mod
コンテスト
ユーザー 👑 p-adic
提出日時 2022-10-28 12:29:46
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 4,858 bytes
コンパイル時間 1,985 ms
コンパイル使用メモリ 194,172 KB
最終ジャッジ日時 2025-02-08 13:49:28
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 2 WA * 1
other AC * 23 WA * 4
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<bits/stdc++.h>
using namespace std;

using ll = long long;

#define TYPE_OF( VAR ) remove_const<remove_reference<decltype( VAR )>::type >::type
#define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) 
#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 FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ )  
#define QUIT return 0 
#define RETURN( ANSWER ) cout << ( ANSWER ) << "\n"; QUIT 
#define MIN( A , B ) ( A < B ? A : B )

#define CHECK_REDUNDANT_INPUT string VARIABLE_FOR_CHECK_REDUNDANT_INPUT = ""; cin >> VARIABLE_FOR_CHECK_REDUNDANT_INPUT; assert( VARIABLE_FOR_CHECK_REDUNDANT_INPUT == "" ); assert( ! cin );
// #define CHECK_REDUNDANT_INPUT string VARIABLE_FOR_CHECK_REDUNDANT_INPUT = ""; getline( cin , VARIABLE_FOR_CHECK_REDUNDANT_INPUT ); assert( VARIABLE_FOR_CHECK_REDUNDANT_INPUT == "" ); assert( ! cin );

int main()
{
  UNTIE;
  constexpr const ll bound = 1000000000;
  CIN_ASSERT( N , 1 , bound );
  CIN_ASSERT( M , 1 , bound );
  // CHECK_REDUNDANT_INPUT;
  // sum( ll i = 1 ; i <= N ; i++ ) sum( ll j = 1 ; j <= M ; j++ ){ i % j }
  // = sum( ll i = 1 ; i <= N ; i++ ) sum( ll j = 1 ; j <= M ; j++ ){ i - ( i / j ) * j }
  // = M * sum( ll i = 1 ; i <= N ; i++ ){ i }
  //   - sum( ll i = 1 ; i <= N ; i++ ) sum( ll j = 1 ; j <= M ; j++ ){ ( i / j ) * j }
  // = M * ( N * ( N + 1 ) ) / 2
  //   - sum( ll j = 1 ; j <= M ; j++ ){ j * sum( ll i = 1 ; i <= N ; i++ ){ i / j } }
  // = M * ( N * ( N + 1 ) ) / 2
  //   - sum( ll j = 1 ; j <= M ; j++ ){ j * ( j * ( ( N / j - 1 ) * ( N / j ) ) / 2 + ( N - j * ( N / j ) + 1 ) * ( N / j ) ) }
  // = M * ( N * ( N + 1 ) ) / 2
  //   - sum( ll j = 1 ; j <= M ; j++ ){ j ^ 2 * ( ( ( N / j - 1 ) * ( N / j ) ) / 2 - ( N / j ) ^ 2 ) + j * ( N + 1 ) * ( N / j ) }
  // = M * ( N * ( N + 1 ) ) / 2
  //   - sum( ll j = 1 ; j <= M ; j++ ){ j * ( N + 1 ) * ( N / j ) - j ^ 2 * ( ( ( N / j ) * ( N / j + 1 ) ) / 2 ) }
  // = M * ( N * ( N + 1 ) ) / 2
  //   - sum( ll j = 1 ; j <= min( 31622 , M ) ; j++ ){ j * ( N + 1 ) * ( N / j ) - j ^ 2 * ( ( ( N / j ) * ( N / j + 1 ) ) / 2 ) }
  //   - sum( ll j = 31622 ; j <= M ; j++ ){ j * ( N + 1 ) * ( N / j ) - j ^ 2 * ( ( ( N / j ) * ( N / j + 1 ) ) / 2 ) }
  // = M * ( N * ( N + 1 ) ) / 2
  //   - sum( ll j = 1 ; j <= min( 31622 , M ) ; j++ ){ j * ( ( N + 1 ) * ( N / j ) - j * ( ( ( N / j ) * ( N / j + 1 ) ) / 2 ) }
  //   - sum( ll h = N / M ; h <= N / 31622 ) sum( ll j = N / ( h + 1 ) + 1 ; j <= N / h ; j++ ){ j * ( N + 1 ) * ( N / j ) - j ^ 2 * ( ( ( N / j ) * ( N / j + 1 ) ) / 2 ) }
  // = M * ( N * ( N + 1 ) ) / 2
  //   - sum( ll j = 1 ; j <= min( 31622 , M ) ; j++ ){ j * ( ( N + 1 ) * ( N / j ) - j * ( ( ( N / j ) * ( N / j + 1 ) ) / 2 ) }
  //   - sum( ll h = N / M ; h <= N / 31622 ){ ( N + 1 ) * ( ( ( N / h - N / ( h + 1 ) ) * ( N / h + N / ( h + 1 ) + 1 ) ) / 2 ) * h - ( ( ( N / h ) * ( N / h ) * ( 2 * ( N / h ) + 1 ) ) / 6 - ( ( N / ( h + 1 ) ) * ( N / ( h + 1 ) ) * ( 2 * ( N / ( h + 1 ) ) + 1 ) ) / 6 ) * ( ( h * ( h + 1 ) ) / 2 ) }
  // = M * ( N * ( N + 1 ) ) / 2
  //   - sum( ll j = 1 ; j <= min( 31622 , M ) ; j++ ){ j * ( ( N + 1 ) * ( N / j ) - j * ( ( ( N / j ) * ( N / j + 1 ) ) / 2 ) }
  //   - ( ( N + 1 ) * sum( ll h = N / M ; h <= N / 31622 ){ ( N / h - N / ( h + 1 ) ) * ( N / h + N / ( h + 1 ) + 1 ) * h } ) / 2
  //   + ( sum( ll h = N / M ; h <= N / 31622 ){ ( ( N / h ) * ( N / h + 1 ) * ( 2 * ( N / h ) + 1 ) - ( N / ( h + 1 ) ) * ( N / ( h + 1 ) + 1 ) * ( 2 * ( N / ( h + 1 ) ) + 1 ) ) * h * ( h + 1 ) } ) / 12
  constexpr const ll P = 998244353;
  ll answer0 = ( M * ( ( ( N * ( N + 1 ) ) / 2 ) % P ) ) % P;
  ll answer1 = 0;
  ll answer2 = 0;
  ll answer3 = 0;
  constexpr const ll sqrt_bound = 31622;
  ll border = MIN( sqrt_bound , M );
  if( border > N ){
    border = N;
  }
  FOREQ( j , 1 , border ){
    answer1 += ( j * ( ( N + 1 ) * ( N / j ) - j * ( ( ( N / j ) * ( N / j + 1 ) ) / 2 ) ) ) % P;
  }
  answer1 %= P;
  ll N_div_min = N > M ? N / M : 1;
  ll N_div_max = N / sqrt_bound;
  FOREQ( h , N_div_min , N_div_max ){
    answer2 += ( ( N / h - N / ( h + 1 ) ) * ( N / h + N / ( h + 1 ) + 1 ) * h ) % P;
    answer3 += ( ( ( ( ( N / h ) * ( ( ( N / h + 1 ) * ( 2 * ( N / h ) + 1 ) ) % P ) - ( N / ( h + 1 ) ) * ( ( ( N / ( h + 1 ) + 1 ) * ( 2 * ( N / ( h + 1 ) ) + 1 ) ) % P ) ) * h ) % P ) * ( h + 1 ) ) % P;
  }
  constexpr const ll inv_2 = ( P + 1 ) / 2;
  constexpr const ll inv_3 = P - ( ( P / 3 ) * inv_2 ) % P;
  constexpr const ll inv_12 = ( inv_2 * ( ( inv_3 * inv_3 ) % P ) ) % P;
  answer2 = ( ( ( ( N + 1 ) * ( answer2 % P ) ) % P ) * inv_2 ) % P;
  answer3 = ( ( answer3 % P ) * inv_12 ) % P;
  RETURN( ( answer0 + ( P - answer1 ) + ( P - answer2 ) + answer3 ) % P );
}
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