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>
#include <stdlib.h>
#include <stdbool.h>
#include <math.h>
int main(void){
int N,x,a,b,r,tmp;
int count = 0;
int P[10000];
    scanf("%d",&N);
    for(int i=0;i<N;i++)scanf("%d",&P[i]);
    b = P[0];
    for(int i=1;i<N;i++){
        a = P[i];
x = a*b;
 if(a<b){
    tmp = a;
    a = b;
    b = tmp;
  }
   r = a % b;
  while(r!=0){
    a = b;
    b = r;
    r = a % b;
  }
  b = x/b;
    }
    for(int i=0;i<N;i++){
        count += b/P[i];
    }
  printf("%d",count);
}