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;

typedef long long int ll;

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

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

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

    return ans;
}

// Driver Code
int main()
{
    long long int i,j,k,l,m,n,a,b,sum=0;
    cin>>n;
    long long int arr[n];
    for(i=0;i<n;i++)
    {
        cin>>arr[i];
    }

    l= findlcm(arr, n);
    for(i=0;i<n;i++)
    {
        m=l/arr[i];
        sum+=m;
sum%=1000000007;
    }
    sum%=1000000007;
    cout<<sum;
    return 0;
}