Problem p02793 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define FOR(i, k, n) for (int(i) = (k); (i) < (n); ++(i))
#define rep(i, n) FOR(i, 0, n)
#define all(v) begin(v), end(v)
#define debug(x) std::cerr << #x << ": " << x << "\n"
#define debug2(x, y)                                                           \
  std::cerr << #x << ": " << x << ", " << #y << ": " << y << "\n"
#define debug3(x, y, z)                                                        \
  std::cerr << #x << ": " << x << ", " << #y << ": " << y << ", " << #z        \
            << ": " << z << "\n"

using ll = long long;
using vi = std::vector<int>;
using vvi = std::vector<vi>;
using vll = std::vector<ll>;
using vvll = std::vector<vll>;
template <typename T> std::vector<T> vec(int l, T e) {
  return std::vector<T>(l, e);
}
template <typename T> using MaxHeap = std::priority_queue<T>;
template <typename T>
using MinHeap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T> inline void chmax(T &a, T b) { a = std::max(a, b); }

template <typename T>
std::ostream &operator<<(std::ostream &s, const std::vector<T> &v) {
  int sz = v.size();
  s << "\n";
  rep(i, sz) {
    s << v[i];
    if (i < sz - 1) {
      s << "\t";
    }
  }
  s << "\n";
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s,
                         const std::vector<std::vector<T>> &v) {
  for (auto &&w : v) {
    s << w;
  }
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::deque<T> &v) {
  int sz = v.size();
  s << "\n";
  rep(i, sz) {
    s << v[i];
    if (i < sz - 1) {
      s << "\t";
    }
  }
  s << "\n";
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::deque<std::deque<T>> &v) {
  for (auto &&w : v) {
    s << w;
  }
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::set<T> &v) {
  s << "\n";
  for (auto &&elm : v) {
    s << elm << "\t";
  }
  s << "\n";
  return s;
}

inline void scan(int &a) { scanf("%d", &a); }
inline void scan(ll &a) { scanf("%lld", &a); }
inline void scan(char &a) { scanf(" %c", &a); }
inline void scan(double &a) { scanf("%lf", &a); }
template <typename T> inline void scan(std::vector<T> &v) {
  for (auto &&sv : v) {
    scan(sv);
  }
}
template <typename First, typename... Args>
inline void scan(First &f, Args &...args) {
  scan(f);
  scan(args...);
}
inline void scan(std::string &s) {
  char BUF[3000000];
  scanf(" %s", BUF);
  s = std::string(BUF);
}
inline void print(int a) { printf("%d\n", a); }
inline void print(ll a) { printf("%lld\n", a); }
inline void print(double a) { printf("%.12f\n", a); }
inline void print(std::string s) { std::cout << s << "\n"; }

using namespace std;

struct Prime {
  int max_check;
  int max_prime;
  int prime_number;
  vector<int> primes;
  map<int, int> prime_id;
  Prime(){};
  Prime(int m) { initialize(m); };
  void initialize(int m) {
    sieve(m);
    prime_number = (int)primes.size();
    max_check = m;
  }

  void sieve(int m) {
    max_prime = 2;
    deque<bool> is_prime(m + 1, true);
    is_prime[0] = is_prime[1] = false;
    int i;
    for (i = 2; i <= m; ++i) {
      if (!is_prime[i]) {
        continue;
      }
      if (i * i > m) {
        break;
      }
      for (int j = i * 2; j <= m; j += i) {
        is_prime[j] = false;
      }
      prime_id[i] = (int)primes.size();
      primes.push_back(i);
      max_prime = i;
    }
    for (int j = i; j <= m; ++j) {
      if (!is_prime[j]) {
        continue;
      }
      prime_id[j] = (int)primes.size();
      primes.push_back(j);
      max_prime = j;
    }
  }

  unordered_map<int, int> prime_factor(ll x) {
    unordered_map<int, int> ret;
    if ((ll)max_check * (ll)max_check < x) {
      return ret;
    }
    for (int i = 0; i < prime_number; ++i) {
      if (x == 1) {
        break;
      }
      while (x % primes[i] == 0) {
        x /= primes[i];
        ret[primes[i]] += 1;
      }
    }
    if (x != 1) {
      ret[x] += 1;
    }
    return ret;
  }
};

int mod = 1000000007;

ll po(ll k, ll x) {
  if (x == 0) {
    return 1;
  }
  if (x == 1) {
    return k % mod;
  }
  ll y = po(k, x / 2);
  y = y * y % mod;
  if (x % 2 == 1) {
    y = y * k % mod;
  }
  return y;
}

int main() {
  int n;
  scan(n);
  vi a(n);
  scan(a);
  Prime pr(1000000);
  //  cout << pr.primes;
  unordered_map<int, int> lcm;
  rep(i, n) {
    auto pf = pr.prime_factor(a[i]);
    for (auto p : pf) {
      chmax(lcm[p.first], p.second);
    }
  }
  ll l = 1;
  for (auto p : lcm) {
    l = l * po(p.first, p.second) % mod;
  }

  ll ans = 0;
  rep(i, n) {
    ans = ans + po(a[i], mod - 2);
    if (ans >= mod) {
      ans -= mod;
    }
  }
  ans = ans * l % mod;
  print(ans);

  return 0;
}


Fixed submission:
#include <algorithm>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define FOR(i, k, n) for (int(i) = (k); (i) < (n); ++(i))
#define rep(i, n) FOR(i, 0, n)
#define all(v) begin(v), end(v)
#define debug(x) std::cerr << #x << ": " << x << "\n"
#define debug2(x, y)                                                           \
  std::cerr << #x << ": " << x << ", " << #y << ": " << y << "\n"
#define debug3(x, y, z)                                                        \
  std::cerr << #x << ": " << x << ", " << #y << ": " << y << ", " << #z        \
            << ": " << z << "\n"

using ll = long long;
using vi = std::vector<int>;
using vvi = std::vector<vi>;
using vll = std::vector<ll>;
using vvll = std::vector<vll>;
template <typename T> std::vector<T> vec(int l, T e) {
  return std::vector<T>(l, e);
}
template <typename T> using MaxHeap = std::priority_queue<T>;
template <typename T>
using MinHeap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T> inline void chmax(T &a, T b) { a = std::max(a, b); }

template <typename T>
std::ostream &operator<<(std::ostream &s, const std::vector<T> &v) {
  int sz = v.size();
  s << "\n";
  rep(i, sz) {
    s << v[i];
    if (i < sz - 1) {
      s << "\t";
    }
  }
  s << "\n";
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s,
                         const std::vector<std::vector<T>> &v) {
  for (auto &&w : v) {
    s << w;
  }
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::deque<T> &v) {
  int sz = v.size();
  s << "\n";
  rep(i, sz) {
    s << v[i];
    if (i < sz - 1) {
      s << "\t";
    }
  }
  s << "\n";
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::deque<std::deque<T>> &v) {
  for (auto &&w : v) {
    s << w;
  }
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::set<T> &v) {
  s << "\n";
  for (auto &&elm : v) {
    s << elm << "\t";
  }
  s << "\n";
  return s;
}

inline void scan(int &a) { scanf("%d", &a); }
inline void scan(ll &a) { scanf("%lld", &a); }
inline void scan(char &a) { scanf(" %c", &a); }
inline void scan(double &a) { scanf("%lf", &a); }
template <typename T> inline void scan(std::vector<T> &v) {
  for (auto &&sv : v) {
    scan(sv);
  }
}
template <typename First, typename... Args>
inline void scan(First &f, Args &...args) {
  scan(f);
  scan(args...);
}
inline void scan(std::string &s) {
  char BUF[3000000];
  scanf(" %s", BUF);
  s = std::string(BUF);
}
inline void print(int a) { printf("%d\n", a); }
inline void print(ll a) { printf("%lld\n", a); }
inline void print(double a) { printf("%.12f\n", a); }
inline void print(std::string s) { std::cout << s << "\n"; }

using namespace std;

struct Prime {
  int max_check;
  int max_prime;
  int prime_number;
  vector<int> primes;
  map<int, int> prime_id;
  Prime(){};
  Prime(int m) { initialize(m); };
  void initialize(int m) {
    sieve(m);
    prime_number = (int)primes.size();
    max_check = m;
  }

  void sieve(int m) {
    max_prime = 2;
    deque<bool> is_prime(m + 1, true);
    is_prime[0] = is_prime[1] = false;
    int i;
    for (i = 2; i <= m; ++i) {
      if (!is_prime[i]) {
        continue;
      }
      if (i * i > m) {
        break;
      }
      for (int j = i * 2; j <= m; j += i) {
        is_prime[j] = false;
      }
      prime_id[i] = (int)primes.size();
      primes.push_back(i);
      max_prime = i;
    }
    for (int j = i; j <= m; ++j) {
      if (!is_prime[j]) {
        continue;
      }
      prime_id[j] = (int)primes.size();
      primes.push_back(j);
      max_prime = j;
    }
  }

  unordered_map<int, int> prime_factor(ll x) {
    unordered_map<int, int> ret;
    if ((ll)max_check * (ll)max_check < x) {
      return ret;
    }
    for (int i = 0; i < prime_number; ++i) {
      if (x == 1) {
        break;
      }
      while (x % primes[i] == 0) {
        x /= primes[i];
        ret[primes[i]] += 1;
      }
    }
    if (x != 1) {
      ret[x] += 1;
    }
    return ret;
  }
};

int mod = 1000000007;

ll po(ll k, ll x) {
  if (x == 0) {
    return 1;
  }
  if (x == 1) {
    return k % mod;
  }
  ll y = po(k, x / 2);
  y = y * y % mod;
  if (x % 2 == 1) {
    y = y * k % mod;
  }
  return y;
}

int main() {
  int n;
  scan(n);
  vi a(n);
  scan(a);
  Prime pr(2000);
  unordered_map<int, int> lcm;
  rep(i, n) {
    auto pf = pr.prime_factor(a[i]);
    for (auto p : pf) {
      chmax(lcm[p.first], p.second);
    }
  }
  ll l = 1;
  for (auto p : lcm) {
    l = l * po(p.first, p.second) % mod;
  }

  ll ans = 0;
  rep(i, n) {
    ans = ans + po(a[i], mod - 2);
    if (ans >= mod) {
      ans -= mod;
    }
  }
  ans = ans * l % mod;
  print(ans);

  return 0;
}