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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll gcd(ll a,ll b)
{
	if (a%b==0)
	{
		return(b);
    }
	else
	{
		return(gcd(b,a%b));
    }
}
 
ll lcm(ll a, ll b)
{
    return a * b / gcd(a, b);
}
long long modinv(long long a, long long m) {
    long long b = m, u = 1, v = 0;
    while (b) {
        long long t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m; 
    if (u < 0) u += m;
    return u;
}

int main(){
  ll n; cin >> n;
  ll MOD = 1000000007;
  vector<ll> vec(n);
  for(ll i=0; i<n; i++){
    cin >> vec.at(i);
  }
  ll LCM = 1;
  for(ll i=0; i<n; i++){
    LCM = LCM*vec.at(i)%MOD;
    LCM = LCM%MOD;
  }
  for(ll i=0; i<n; i++){
    ll fac = vec.at(i);
    for(ll j=i+1; j<n; j++){
      ll GCD = gcd(fac,vec.at(j));
      fac = fac/GCD;
      if(GCD!=1){
        LCM = LCM*modinv(GCD,MOD)%MOD;
      }
    }
  }
  ll ans =0;
  for(ll i=0; i<n; i++){
    ans += LCM*modinv(vec.at(i),MOD)%MOD;
    ans = ans%MOD;
  }
  cout << ans << endl;
}