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>
#define MOD 1000000007
#define mp make_pair
#define pb push_back
#define rep(i, n) for (int i = 0; i < (n); i++)
#define reps(i, n, s) for (int i = (s); i < (n); i++)
typedef long long int ll;
using namespace std;
using Graph = vector<vector<int>>;

ll gcd(ll a, ll b)
{
    if (a % b == 0)
    {
        return (b);
    }
    else
    {
        return (gcd(b, a % b));
    }
}
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N;
    cin >> N;
    vector<ll> A(N);
    bool memo[1000005];

    ll lcm;
    rep(i, N)
    {
        cin >> A[i];
        if (memo[A[i]])
        {
            continue;
        }
        memo[A[i]] = true;
        if (i == 0)
        {
            lcm = A[i];
        }
        else
        {
            lcm = (lcm * A[i]) / gcd(lcm, A[i]);
        }
    }
    ll total = 0;
    rep(i, N)
    {
        total = (total + (lcm / A[i])) % (MOD);
    }
    cout << total << endl;
 //   system("pause");
    return 0;
}