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>
long long int lcm(long long int a, long long int b)
{
     long long int n1,c,d,i,n2;
    n1=a;
    n2=b;
    for(i=1;;i++)
    {
        c=n1%n2;
        n1=n2;
        n2=c;
        if(n2==0)break;
    }
    d=(a*b)/n1;
    return d;
}
int main()
{
    long long int n,i,g,s,sum=0,k;
   scanf("%lld",&n);
   long long int a[n+5];
   for(i=1;i<=n;i++)
    scanf("%lld",&a[i]);
    g=a[1];
    for(i=2;i<=n;i++)
    {
        g=lcm(g,a[i]);
    }
    for(i=1;i<=n;i++)
    {
        s=g/a[i];
        sum=sum+s;
        sum=sum%1000000007;
    }
    printf("%lld\n",sum);
    return 0;
}