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>
#define lli long long int
#define rep(i,a,b)	for(i=a;i<b;i++)
#define M 1000000007
#define vll vector<long long int>
#define pb push_back
#define pi 3.1415926535897932384626433832795028841971
#define MOD(x) ((x>=M)?((x)%M):(x<0?((M+x)%M):x))
lli gcd(lli a,lli b){if(b==0) return a;if(a==0) return b;if(a>=b) return gcd(b,a%b);else return gcd(a,b%a);}
lli lcm(lli a,lli b){lli p=a*b;return p/gcd(a,b);}
using namespace std;


int main()
{
	char ch,ch1,ch2;
	string s1,s2,s3;
    lli i,j,k,a,b,t,c,n,m,sum=0,ans=0,temp;
	scanf("%lld",&n);
	vll v(n);
	rep(i,0,n)	scanf("%lld",&v[i]);
	if(n==1)	printf("0");
	else if(n==2){
		a=lcm(v[0],v[1]);
		ans=(a/v[0])+(a/v[1]);
		printf("%lld",ans%M);
	}
	else{
		a=lcm(v[0],v[1]);
		for(i=2;i<n;i++)
		{
			t=__gcd(a,v[i]);
			temp=(a*v[i]);
			a=temp/t;
		}
		for(i=0;i<n;i++)
		{
			temp=(a/v[i]);
			ans+=(temp%M);
		}
		printf("%lld",ans%M);
		//cout << ans%M << endl;
	}
	
	
	return 0;
}