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;
#define pi 3.14159265359
#define int long long
#define pii pair<int,int>
const int mod=1e9 + 7;
 
int dx[]={-1, 0, 1, 0};
int dy[]={0, -1, 0, 1};



int32_t main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
 

 

int n;
cin>>n;

vector<int>v(n);
int l=1;
for(int i=0;i<n;i++){
  cin>>v[i];
 
  int y=l/__gcd(v[i],l);
  l=v[i]*y;
}
int ans=0;

for(int i=0;i<n;i++)
{
  ans=(ans+l/v[i])%mod;
}
 
 cout<<ans<<"\n";
   
}