#567965 (C++17) No.1260 たくさんの多項式

• 問題: No.1260 たくさんの多項式
• ユーザー: 👑 emthrm
• 提出日時: 2020-10-16 22:51:34
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 89 ms / 2,000 ms
• コード長: 4,805 bytes
• コンパイル時間: 1,694 ms
• コンパイル使用メモリ: 199,444 KB
• 実行使用メモリ: 4,384 KB
• 最終ジャッジ日時: 2023-09-28 04:39:32
• 合計ジャッジ時間: 6,131 ms
• ジャッジサーバーID （参考情報）: judge11 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 4,376 KB
testcase_01	AC	2 ms; 4,376 KB
testcase_02	AC	2 ms; 4,376 KB
testcase_03	AC	2 ms; 4,376 KB
testcase_04	AC	2 ms; 4,376 KB
testcase_05	AC	2 ms; 4,376 KB
testcase_06	AC	1 ms; 4,380 KB
testcase_07	AC	2 ms; 4,380 KB
testcase_08	AC	2 ms; 4,376 KB
testcase_09	AC	2 ms; 4,380 KB
testcase_10	AC	2 ms; 4,376 KB
testcase_11	AC	2 ms; 4,380 KB
testcase_12	AC	2 ms; 4,376 KB
testcase_13	AC	2 ms; 4,380 KB
testcase_14	AC	2 ms; 4,376 KB
testcase_15	AC	1 ms; 4,376 KB
testcase_16	AC	1 ms; 4,376 KB
testcase_17	AC	2 ms; 4,380 KB
testcase_18	AC	2 ms; 4,376 KB
testcase_19	AC	2 ms; 4,376 KB
testcase_20	AC	89 ms; 4,376 KB
testcase_21	AC	26 ms; 4,380 KB
testcase_22	AC	75 ms; 4,376 KB
testcase_23	AC	60 ms; 4,380 KB
testcase_24	AC	63 ms; 4,376 KB
testcase_25	AC	51 ms; 4,380 KB
testcase_26	AC	61 ms; 4,376 KB
testcase_27	AC	48 ms; 4,376 KB
testcase_28	AC	86 ms; 4,380 KB
testcase_29	AC	65 ms; 4,376 KB
testcase_30	AC	40 ms; 4,376 KB
testcase_31	AC	63 ms; 4,376 KB
testcase_32	AC	62 ms; 4,380 KB
testcase_33	AC	51 ms; 4,376 KB
testcase_34	AC	80 ms; 4,376 KB
testcase_35	AC	37 ms; 4,376 KB
testcase_36	AC	34 ms; 4,376 KB
testcase_37	AC	64 ms; 4,376 KB
testcase_38	AC	68 ms; 4,376 KB
testcase_39	AC	84 ms; 4,376 KB
testcase_40	AC	65 ms; 4,376 KB
testcase_41	AC	78 ms; 4,380 KB
testcase_42	AC	57 ms; 4,380 KB
testcase_43	AC	82 ms; 4,376 KB
testcase_44	AC	52 ms; 4,376 KB
testcase_45	AC	50 ms; 4,376 KB
testcase_46	AC	47 ms; 4,380 KB
testcase_47	AC	58 ms; 4,380 KB
testcase_48	AC	13 ms; 4,380 KB
testcase_49	AC	43 ms; 4,376 KB
testcase_50	AC	23 ms; 4,380 KB
testcase_51	AC	83 ms; 4,376 KB
testcase_52	AC	28 ms; 4,380 KB
testcase_53	AC	38 ms; 4,376 KB
testcase_54	AC	86 ms; 4,384 KB
testcase_55	AC	89 ms; 4,380 KB
testcase_56	AC	41 ms; 4,376 KB
testcase_57	AC	58 ms; 4,376 KB
testcase_58	AC	38 ms; 4,376 KB
testcase_59	AC	62 ms; 4,376 KB
testcase_60	AC	86 ms; 4,376 KB

ソースコード

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr ll LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

template <int MOD>
struct MInt {
  unsigned val;
  MInt(): val(0) {}
  MInt(long long x) : val(x >= 0 ? x % MOD : x % MOD + MOD) {}
  static int get_mod() { return MOD; }
  static void set_mod(int divisor) { assert(divisor == MOD); }
  MInt pow(long long exponent) const {
    MInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  MInt &operator+=(const MInt &x) { if((val += x.val) >= MOD) val -= MOD; return *this; }
  MInt &operator-=(const MInt &x) { if((val += MOD - x.val) >= MOD) val -= MOD; return *this; }
  MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % MOD; return *this; }
  MInt &operator/=(const MInt &x) {
    // assert(std::__gcd(static_cast<int>(x.val), MOD) == 1);
    unsigned a = x.val, b = MOD; int u = 1, v = 0;
    while (b) {
      unsigned tmp = a / b;
      std::swap(a -= tmp * b, b);
      std::swap(u -= tmp * v, v);
    }
    return *this *= u;
  }
  bool operator==(const MInt &x) const { return val == x.val; }
  bool operator!=(const MInt &x) const { return val != x.val; }
  bool operator<(const MInt &x) const { return val < x.val; }
  bool operator<=(const MInt &x) const { return val <= x.val; }
  bool operator>(const MInt &x) const { return val > x.val; }
  bool operator>=(const MInt &x) const { return val >= x.val; }
  MInt &operator++() { if (++val == MOD) val = 0; return *this; }
  MInt operator++(int) { MInt res = *this; ++*this; return res; }
  MInt &operator--() { val = (val == 0 ? MOD : val) - 1; return *this; }
  MInt operator--(int) { MInt res = *this; --*this; return res; }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(val ? MOD - val : 0); }
  MInt operator+(const MInt &x) const { return MInt(*this) += x; }
  MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt &x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt &x) const { return MInt(*this) /= x; }
  friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; }
  friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
};
namespace std { template <int MOD> MInt<MOD> abs(const MInt<MOD> &x) { return x; } }
template <int MOD>
struct Combinatorics {
  using ModInt = MInt<MOD>;
  int val;  // "val!" and "mod" must be disjoint.
  std::vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    for (int i = 1; i <= val; ++i) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
    for (int i = 1; i <= val; ++i) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) const {
    if (n < 0 || n < k || k < 0) return 0;
    assert(n <= val && k <= val);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) const {
    if (n < 0 || n < k || k < 0) return 0;
    assert(n <= val);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) const {
    if (n < 0 || k < 0) return 0;
    return k == 0 ? 1 : nCk(n + k - 1, k);
  }
};
using ModInt = MInt<MOD>;

int main() {
  ll n; cin >> n;
  ModInt ans = 0;
  ll i = 2;
  for (; i * i <= n; ++i) {
    ll tmp = n;
    while (tmp > 0) {
      ans += tmp % i;
      tmp /= i;
    }
  }
  while (i <= n) {
    int j = n / i;
    ll nx = n / j, term = nx - i + 1;
    ans += ModInt(j) * term;
    ll fr = n - nx * j;
    ans += (ModInt(fr) + fr + 1LL * (term - 1) * j) * term / 2;
    i = nx + 1;
  }
  cout << ans << '\n';
  // ans = 0;
  // for (int i = 2; i <= n; ++i) {
  //   ll tmp = n;
  //   while (tmp > 0) {
  //     ans += tmp % i;
  //     tmp /= i;
  //   }
  // }
  // cout << ans << '\n';
  return 0;
}