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>
#include <boost/range/irange.hpp>

using namespace std;
using boost::irange;
typedef long long ll;
const ll mod = 1e9 + 7;

long long GCD(long long a, long long b) {
    if (b == 0) return a;
    else return GCD(b, a % b);
}

long long LCM(long long a, long long b) {
    long long g = GCD(a, b);
    return a / g * b;
}
int main() {
    int N;
    cin >> N;
    vector<int> A(N);
    for (int i: irange(0, N)) cin >> A[i];

    ll l = A[0];
    for (int i: irange(0, N))
        l = LCM(l, A[i]);
        // l %= MOD;


    ll ans = 0;
    for (int i: irange(0, N)) {

        ans += l / A[i];
        ans %= mod;
    }
    cout << ans<< endl;
    return 0;
}