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

#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
const ll mod = 1e9 + 7;
// const ll mod = 998244353;
#define REP(i, n) for (int i = 0; i < (int)n; ++i)
// debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \\
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \\
       << " " << __FILE__ << endl;
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 (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class S, class T>
ostream &operator<<(ostream &os, const pair<S, T> v) {
  os << "(" << v.first << ", " << v.second << ")";
  return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << " ";
    }
    os << v[i];
  }
  return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<vector<T>> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << endl;
    }
    os << v[i];
  }
  return os;
}
string num2bit(ll num, ll len) {
  string bit = "";
  REP(i, len) { bit += char('0' + (num >> i & 1)); }
  return bit;
}

template <std::uint_fast64_t Modulus> class modint {
  // long long から modint
  // を作るときは必ず正の数にしてからコンストラクタに入れること！
  // そうしないとバグります
  using u64 = std::uint_fast64_t;

public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
};
using mint = modint<mod>;

template <class T, class U> constexpr T power(T x, U exp) {
  T ret = static_cast<T>(1);
  while (exp) {
    if (exp % static_cast<U>(2) == static_cast<U>(1))
      ret *= x;
    exp /= static_cast<U>(2);
    x *= x;
  }
  return ::std::move(ret);
}

ll N, K;

mint calc(ll x, vector<ll> &meb) {
  mint res = 0;
  for (int i = x; i <= K; i += x) {
    mint tmp = 0;
    mint val = K / i;
    tmp += power(val, N) * mint(-meb[i / x] + mod);
    res += tmp;
  }
  res *= x;
  return res;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  vector<ll> is_prime(101010, 1);
  vector<ll> meb(101010, -1);
  meb[0] = 0;
  meb[1] = 0;
  is_prime[0] = 0;
  is_prime[1] = 0;
  ll m = 101000;
  REP(i, m) {
    if (is_prime[i] == 0)
      continue;
    for (int j = 2; j * i <= m; j++) {
      is_prime[i * j] = 0;
    }
    for (int j = 1; j * i <= m; j++) {
      meb[i * j] *= -1;
      if (j % i == 0)
        meb[i * j] = 0;
    }
  }
  meb[1] = -1;

  cin >> N >> K;

  mint res = 0;
  for (int i = 1; i <= K; i++) {
    mint tmp = calc(i, meb);
    res += tmp;
  }
  cout << res.value() << endl;

  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
const ll mod = 1e9 + 7;
// const ll mod = 998244353;
#define REP(i, n) for (int i = 0; i < (int)n; ++i)
// debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \\
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \\
       << " " << __FILE__ << endl;
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 (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class S, class T>
ostream &operator<<(ostream &os, const pair<S, T> v) {
  os << "(" << v.first << ", " << v.second << ")";
  return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << " ";
    }
    os << v[i];
  }
  return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<vector<T>> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << endl;
    }
    os << v[i];
  }
  return os;
}
string num2bit(ll num, ll len) {
  string bit = "";
  REP(i, len) { bit += char('0' + (num >> i & 1)); }
  return bit;
}

template <std::uint_fast64_t Modulus> class modint {
  // long long から modint
  // を作るときは必ず正の数にしてからコンストラクタに入れること！
  // そうしないとバグります
  using u64 = std::uint_fast64_t;

public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
};
using mint = modint<mod>;

template <class T, class U> constexpr T power(T x, U exp) {
  T ret = static_cast<T>(1);
  while (exp) {
    if (exp % static_cast<U>(2) == static_cast<U>(1))
      ret *= x;
    exp /= static_cast<U>(2);
    x *= x;
  }
  return ::std::move(ret);
}

ll N, K;

mint calc(ll x, vector<ll> meb) {
  mint res = 0;
  for (int i = x; i <= K; i += x) {
    mint tmp = 0;
    mint val = K / i;
    tmp += power(val, N) * mint(-meb[i / x] + mod);
    res += tmp;
  }
  res *= x;
  return res;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  vector<ll> is_prime(101010, 1);
  vector<ll> meb(101010, -1);
  meb[0] = 0;
  meb[1] = 0;
  is_prime[0] = 0;
  is_prime[1] = 0;
  ll m = 101000;
  REP(i, m) {
    if (is_prime[i] == 0)
      continue;
    for (int j = 2; j * i <= m; j++) {
      is_prime[i * j] = 0;
    }
    for (int j = 1; j * i <= m; j++) {
      meb[i * j] *= -1;
      if (j % i == 0)
        meb[i * j] = 0;
    }
  }
  meb[1] = -1;

  cin >> N >> K;

  mint res = 0;
  for (int i = 1; i <= K; i++) {
    mint tmp = calc(i, meb);
    res += tmp;
  }
  cout << res.value() << endl;

  return 0;
}