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;
int gcd(int a, int b) {
   if (b == 0)
   return a;
   return gcd(b, a % b);
}
int lcm(int a,int b){
    return (a*b)/gcd(a,b);
}

int main(){
    int n;
  cin>>n;
  int arr[n],l,s=0;
  for(int i=0;i<n;i++){
      cin>>arr[i];
     }
   l=lcm(arr[0],arr[1]);
   for(int i=0;i<n;i++){ 
       l=lcm(l,arr[i]);
         }
         
      for(int i=0;i<n;i++){ 
            s=s+(l/arr[i]);
         }     
    cout<<s%(1000000000+7);
}