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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#define devi 1000000007

long int gl(long int a,long int b)
{
    long int tmp;
    long int p,q;
    p=a;
    q=b;

    if(a<b)
    {
        tmp=a;
        a=b;
        b=tmp;
    }
    long int r;

    r=a%b;
    while (r!=0)
    {
        a=b;
        b=r;
        r=a%b;
    } 
    return p*q/b;
}

long int main ()
{
    long int n;
    long int i;
    long int A;
    long int G;
    long int seki=1;
    long int sum=0;


    scanf("%ld",&n);

    long int num[n];

    for(i=0;i<n;i++)
    {
        scanf("%ld",&A);

        num[i]=A;

        seki=seki*A;

        if(i==0)
        {
            G=num[i];
        }

        else if(i>0)
        {
            G=gl(G,num[i]);
        }

    }
    for(i=0;i<n;i++)
    {
        sum+=G/num[i];
    }

    
    printf("%ld",sum%devi);

    return 0;

}