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>

int gcd(unsigned long long a,unsigned long long b){
    if(a%b){
        b=gcd(b,a%b);
        return b;
    }else{
        return b;
    }
}

unsigned long long l_cm(unsigned long long lcm,unsigned long long a){
    if(lcm%a){
        return lcm*a/gcd(lcm,a);
    }else{
        return lcm;
    }
}

int main(void){
    int n;
    unsigned long long a[10000];
    unsigned long long min=0;

    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d",&a[i]);
    }

    unsigned long long lcm=1;

    for(int i=0;i<n;i++){
        lcm=l_cm(lcm,a[i]);
    }

    for(int i=0;i<n;i++){
        min+=(lcm/a[i])%1000000007;
        if(min>=1000000007){
            min-=1000000007;
        }
    }

    printf("%llu",min);

}