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 <bits/stdc++.h>
using namespace std;
using ll = unsigned long long;

ll gcd(ll m, ll n) {
  ll tmp;
  while (m % n != 0) {
    tmp = n;
    n = m % n;
    m = tmp;
  }
  return n;
}

ll lcm(ll m, ll n) {
  return (m / gcd(m, n)) * n;
}

int main() {
  ll n;
  cin >> n;

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

  ll lcm_all = a[0];
  for (ll i = 1; i < n; i++) {
    lcm_all = lcm(lcm_all, a[i]);
  }

  ll ans = 0;
  ll mod = 1000000007;

  for (ll i = 0; i < n; i++) {
    ans += (lcm_all / a[i]) % mod;
    ans %= mod;
  }

  cout << ans << endl;
}