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;

int64_t gcd(int64_t a,int64_t b)
{
	while((a%=b) && (b%=a)) ;
	return a+b;
} 
int64_t lcm(int64_t a,int64_t b)
{
	return a*b/gcd(a,b);
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int n;
	cin>>n;
	int a[n];
	int64_t g=1;
	for(int i=0;i<n;i++)
	{
		cin>>a[i];	
		g = lcm(g,a[i]);
	}		
	int64_t ans=0;
	for(int i=0;i<n;i++)
	{
		ans+=g/a[i];
		ans%=1000000007;
	}
	cout<<ans<<"\n";
	return 0;
}