Problem:
Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <bitset>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <cmath>
#include <limits>
#include <numeric>
#include <iomanip>
#include <cstdlib>
#include <iterator>
#include <functional>
#include <unordered_map>
#include <unordered_set>

using namespace std;

typedef unsigned                    ui;
typedef int                         si;
typedef long                        sl;
typedef long long                   ll;
typedef unsigned long long          ull;

// ----------------

template <typename A, typename B>
string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string& s) {
  return '"' + s + '"';
}

string to_string(const char* s) {
  return to_string((string) s);
}

string to_string(bool b) {
  return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

// ----------------

template <typename T>
struct PairHash {
  size_t operator() (const pair<T, T>& v) const {
    return hash<ll>()((static_cast<ll>(v.first)) ^ (static_cast<ll>(v.second)) << 32);
  }
};

template <typename T>
T gcd(T a, T b) {
    while (b) {
        a %= b;
        swap(a, b);
    }

    return a;
}

template <typename T>
T lcm(T a, T b) {
    return (a / gcd(a, b) * b);
}

const ll mod = 1e9 + 7;

int main(int argc, char *argv[])
{
    std::ios_base::sync_with_stdio(false);

    ll n;
    cin >> n;

    vector<ll> a(n, 0);
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }

    ll l = a[0];
    for (int i = 1; i < n; ++i) {
        l = l * a[i] / gcd(l, a[i]);
    }

    debug(l);

    ll answer = 0;
    for (int i = 0; i < n; ++i) {
        ll cur = l / a[i];
        debug(cur);

        answer += cur;
        answer %= mod;
    }

    cout << answer << endl;

    return 0;
}