Problem p02715 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
const long long INF = 1LL << 60;
const long long MOD = 1000000007;
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n - 1); i >= 0; --i)
#define perm(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define ALL(obj) (obj).begin(), (obj).end()
#define RALL(obj) (obj).rbegin(), (obj).rend()
#define MAX max<ll>
#define MIN min<ll>
#define pb push_back
#define to_s to_string
#define len(v) (ll) v.size()
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define print(x) cout << (x) << '\\n'
#define drop(x) cout << (x) << '\\n', exit(0)
#define debug(x) cout << #x << ": " << (x) << '\\n'
using namespace std;
using ll = long long;
typedef pair<ll, ll> P;
typedef vector<ll> vec;
typedef vector<vector<ll>> vec2;
typedef vector<vector<vector<ll>>> vec3;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
ll devc(ll x, ll y) { return (x + y - 1) / y; }

template <int MOD> struct modint {
  ll val;
  constexpr modint(ll v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      val += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr modint operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr modint operator+(const modint &r) const noexcept {
    return modint(*this) += r;
  }
  constexpr modint operator-(const modint &r) const noexcept {
    return modint(*this) -= r;
  }
  constexpr modint operator*(const modint &r) const noexcept {
    return modint(*this) *= r;
  }
  constexpr modint operator/(const modint &r) const noexcept {
    return modint(*this) /= r;
  }
  constexpr modint &operator++() noexcept {
    val += 1;
    return *this;
  }
  constexpr modint &operator--() noexcept {
    val -= 1;
    return *this;
  }
  constexpr modint &operator+=(const modint &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr modint &operator-=(const modint &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr modint &operator*=(const modint &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr modint &operator/=(const modint &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const modint &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const modint &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr istream &operator>>(istream &is, modint<MOD> &x) noexcept {
    is >> x.val;
    x += 0;
    return is;
  }
  friend constexpr ostream &operator<<(ostream &os,
                                       const modint<MOD> &x) noexcept {
    return os << x.val;
  }
  friend constexpr modint<MOD> modpow(const modint<MOD> &a,
                                      long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};
using mint = modint<MOD>;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);

  ll N, K;
  cin >> N >> K;
  vector<mint> ans(K + 1);
  for (ll D = K; D >= 1; --D) {
    ans[D] += modpow(mint(K / D), N);

    for (ll i = 2; i * i <= D; ++i) {
      if (D % i == 0) {
        ans[D / i] -= ans[D];
        if (D / i != i)
          ans[i] -= ans[D];
      }
    }

    if (D != 1)
      ans[1] -= ans[D];
  }

  mint res = 0;
  rep1(i, K) res += ans[i] * i;
  print(res);

  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
const long long INF = 1LL << 60;
const long long MOD = 1000000007;
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n - 1); i >= 0; --i)
#define perm(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define ALL(obj) (obj).begin(), (obj).end()
#define RALL(obj) (obj).rbegin(), (obj).rend()
#define MAX max<ll>
#define MIN min<ll>
#define pb push_back
#define to_s to_string
#define len(v) (ll) v.size()
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define print(x) cout << (x) << '\\n'
#define drop(x) cout << (x) << '\\n', exit(0)
#define debug(x) cout << #x << ": " << (x) << '\\n'
using namespace std;
using ll = long long;
typedef pair<ll, ll> P;
typedef vector<ll> vec;
typedef vector<vector<ll>> vec2;
typedef vector<vector<vector<ll>>> vec3;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
ll devc(ll x, ll y) { return (x + y - 1) / y; }

template <int MOD> struct modint {
  ll val;
  constexpr modint(ll v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      val += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr modint operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr modint operator+(const modint &r) const noexcept {
    return modint(*this) += r;
  }
  constexpr modint operator-(const modint &r) const noexcept {
    return modint(*this) -= r;
  }
  constexpr modint operator*(const modint &r) const noexcept {
    return modint(*this) *= r;
  }
  constexpr modint operator/(const modint &r) const noexcept {
    return modint(*this) /= r;
  }
  constexpr modint &operator++() noexcept {
    val += 1;
    return *this;
  }
  constexpr modint &operator--() noexcept {
    val -= 1;
    return *this;
  }
  constexpr modint &operator+=(const modint &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr modint &operator-=(const modint &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr modint &operator*=(const modint &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr modint &operator/=(const modint &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const modint &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const modint &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr istream &operator>>(istream &is, modint<MOD> &x) noexcept {
    is >> x.val;
    x += 0;
    return is;
  }
  friend constexpr ostream &operator<<(ostream &os,
                                       const modint<MOD> &x) noexcept {
    return os << x.val;
  }
  friend constexpr modint<MOD> modpow(const modint<MOD> &a,
                                      long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};
using mint = modint<MOD>;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);

  ll N, K;
  cin >> N >> K;
  vector<mint> ans(K + 1);
  for (ll D = K; D >= 1; --D) {
    ans[D] += modpow(mint(K / D), N);

    for (ll i = 2; i <= D; ++i) {
      if (D % i == 0)
        ans[D / i] -= ans[D];
    }
  }

  mint res = 0;
  rep1(i, K) res += ans[i] * i;
  print(res);

  return 0;
}