結果

問題 No.3106 Simple Math Problem 3
コンテスト
ユーザー hos.lyric
提出日時 2025-04-11 21:54:09
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,330 ms / 2,000 ms
コード長 5,927 bytes
コンパイル時間 1,146 ms
コンパイル使用メモリ 121,512 KB
実行使用メモリ 131,356 KB
最終ジャッジ日時 2025-04-11 21:54:47
合計ジャッジ時間 34,455 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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 * 4
other AC * 42
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 <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;


constexpr int LIM = 1'000'010;

Int N, sqrtN;

int lpf[LIM];

int main() {
  for (; ~scanf("%lld", &N); ) {
    sqrtN = floor(sqrt((long double)N));
    
    for (int p = 2; p <= sqrtN; ++p) lpf[p] = p;
    for (int p = 2; p <= sqrtN; ++p) if (lpf[p] == p) {
      for (int n = p; n <= sqrtN; n += p) chmin(lpf[n], p);
    }
    const Int off = N - sqrtN;
    vector<Int> sieve(sqrtN + 1);
    for (int i = 0; i <= sqrtN; ++i) sieve[i] = off + i;
    vector<vector<pair<Int, int>>> pess(sqrtN + 1);
    for (int p = 2; p <= sqrtN; ++p) if (lpf[p] == p) {
      for (Int n = max((off + p - 1) / p, 1LL) * p; n <= N; n += p) {
        const int i = n - off;
        int e = 0;
        do {
          ++e;
          sieve[i] /= p;
        } while (sieve[i] % p == 0);
        pess[i].emplace_back(p, e);
      }
    }
    for (int i = 0; i <= sqrtN; ++i) if (sieve[i] > 1) {
      pess[i].emplace_back(sieve[i], 1);
    }
// if(N<=100)cerr<<off<<" "<<pess<<endl;
    
    Mint ans = 0;
    
    const Int lim = off - 1;
    if (lim >= 1) {
      // B > q >= r
      for (Int q = 1; q <= sqrtN; ++q) {
        const Int b = lim / q;
        ans += Mint(max(b - q, 0LL)) * (Mint(q) * Mint(q+1) / 2);
      }
      // r < B <= q
      for (Int b = 1; b <= sqrtN; ++b) {
        const Int q = lim / b;
        ans += Mint(max(q - b + 1, 0LL)) * (Mint(b-1) * Mint(b) / 2);
      }
    }
cerr<<"lim = "<<lim<<": ans = "<<ans<<endl;
    
    for (int i = 0; i <= sqrtN; ++i) {
      vector<Int> ds{1};
      for (const auto &pe : pess[i]) {
        const Int p = pe.first;
        const int e = pe.second;
        const int len = ds.size();
        ds.resize(len * (e + 1));
        for (int h = len; h < len * (e + 1); ++h) ds[h] = ds[h - len] * p;
      }
      const int len = ds.size();
      __int128 sum = 0;
      for (int h = 0; h < len; ++h) {
        const Int b = ds[h];
        const Int q = ds[len - 1 - h];
        const Int r = min({b - 1, q, sqrtN - i});
// if(N<=100)cerr<<"b = "<<b<<", q = "<<q<<", r = "<<r<<endl;
        sum += r * (r + 1);
      }
      ans += (int)((sum / 2) % MO);
    }
    printf("%u\n", ans.x);
  }
  return 0;
}
0