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 <iostream>
#include <bits/stdc++.h>

#define ll long long int

using namespace std;

// Utility function to find
// GCD of 'a' and 'b'
ll gcd(ll a, ll b)
{
	if (b == 0)
		return a;
	return gcd(b, a % b);
}

// Returns LCM of array elements
ll findlcm(ll arr[], ll n)
{
	// Initialize result
	ll ans = arr[0];

	// ans contains LCM of arr[0], ..arr[i]
	// after i'th iteration,
	for (ll i = 1; i < n; i++)
		ans = (((arr[i] * ans)) /
				(gcd(arr[i], ans)));

	return ans;
}

// Driver Code
int main()
{
    ll n;
    cin >> n;

	ll arr[n];

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

    ll ans = 0;

    ll mag = pow(10,9)+8;

    for(int i=0;i<n;i++){

        ans = (ans + (findlcm(arr,n)/arr[i])%mag)%mag;

    }

    cout << ans%mag << endl;

	return 0;
}