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 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

static inline int gcd(unsigned s, unsigned t)
{
  int r;
  if (t == 0) return s;
  for ( ;(r = s % t) != 0; s = t, t = r);
  return t;
}

#define M 1000000007

int
main(int ac, char *av[])
{
  int n;
  unsigned a, g = 0;
  unsigned long u, l = 1, z = 0;
  scanf("%d", &n);

  for (int i = 0; i < n; ++i) {
    scanf("%u", &a);
    g = gcd(l, a);
    u = a / g;
    z = z * u + l / g;
    z %= M;
    l *= u;
  }

  printf("%lu\n", z);

  return 0;
}