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>

long GCD(unsigned long long a,unsigned long long b){
    unsigned long long r;
    r = a%b;
    if(r==0)    return b;
    return GCD(b,r);
}

long LCM(unsigned long long a,unsigned long long b){
    if(a<b) return a*b/GCD(b,a);
    else return a*b/GCD(a,b);
}

int main(void){
    int n,i,c=0;
    unsigned long long lcm;
    scanf("%d",&n);
    int a[1000000];
    scanf("%d ",&a[0]);
    lcm = a[0];
    for(i=1;i<n;i++){
        scanf("%d ",&a[i]);
        lcm = LCM(a[i],lcm);
    }
    for(i=0;i<n;i++){
        c += (lcm/a[i])% (1000000000 + 7);
        c %= (1000000000 + 7);
    }
    

    
    printf("%d\n", c);
    return 0;
}