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: Runtime Error)

#include <math.h>
#include <stdio.h>
long long int modValue = pow(10, 9) + 7;
 
long long int gcd(long long int a, long long int b) {
  if (b > a) {
    long long int _b = b;
    b = a;
    a = _b;
  }
      
    while(b > 0) {
        long long int tb = b;
          b = a % b;
          a = tb;
      }
      return a;
  } 
 
long long int lcm(long long int a, long long int b) {
    return a * b / gcd(a, b);
}
 
int main() {
 
  int n;
  long long int ne[1000];
  scanf("%d", &n);
  
    long long int _lcm = 1;
  for (int i = 0; i < n; i++) {
    scanf("%lld", &ne[i]);
    _lcm = lcm(_lcm, ne[i]);
  }
    
    long long int cnt = 0;
    for (int i = 0; i < n; i++) {
        cnt += _lcm / ne[i];
        cnt = cnt % modValue;
    }
    
  printf("%lld", cnt);
    return 0;
}