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: Accepted)

#include <stdio.h>

#define M 1000000007

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

static inline int inverse(int a)
{
  int x = 1, g = a % M, v = 0, w = M, s, t, q;

  while (w != 0) {
    q = g / w;
    t = g - q * w;
    s = x - q * v;
    x = v;
    g = w;
    v = s;
    w = t;
  }

  x %= M;

  if (x < 0) x += M;

  return x;
}

int
main(int ac, char *av[])
{
  int n;
  unsigned A[10000];
  unsigned L[10000];
  unsigned g, u;
  unsigned long ll = 1, z = 0;

  scanf("%d", &n);

  for (int i = 0; i < n; ++i) {
    scanf("%u", &A[i]);
    L[i] = 1u;
  }

  for (int i = 0; i < n; ++i) {
    unsigned a = A[i];

    g = gcd(L[i], a);

    u = a / g;

    z = (z * u + ll * inverse(g)) % M;

    ll = (ll * u) % M;

    for (int j = i + 1; j < n; ++j) {
      L[j] = (unsigned long) L[j] * u % A[j];
    }
  }

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

  return 0;
}