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: Time Limit Exceeded)

#include<bits/stdc++.h>
#include <boost/multiprecision/cpp_int.hpp>

#define rep(i,n) for(int i = 0; i < (n); i++)
#define ll long long
#define MOD 1000000007

using namespace std;
using bigint=boost::multiprecision::cpp_int;

bigint gcd(bigint a, bigint b){
  if(a==1 || b==1)return 1;
  if (a < b)swap(a,b);
  
  return b ? gcd(b, a % b) : a;
}

bigint lcm(bigint a, bigint b){
  return a * b / gcd(a, b);
}

// x^n in mod
ll mod_pow(ll x, ll n){
  if(n==0) return 1;

  if(n%2==0){
    return mod_pow(x*x%MOD, n/2) % MOD;
  }else{
    return x * mod_pow(x, (n-1)) % MOD;
  }
}

ll mod_pow_r(ll x, ll n){
  if(x==0)return 0;
  if(n==0) return 1;

  ll ret = 1;
  while(n){
    if(n&1) ret=ret*x%MOD;
    n /= 2;
    x=x*x%MOD;
  }
  
  return ret;
}

int main(){
  ll n;cin>>n;
  vector<ll> a(n);
  rep(i,n)cin>>a[i];
//  sort(a.begin(), a.end());
//  a.erase(unique(a.begin(),a.end()), a.end());

  bigint all_lcm=1;
  rep(i, a.size()) all_lcm = lcm(all_lcm, a[i]);
  all_lcm%=MOD;

//cout<<all_lcm<<endl<<endl;

  ll result=0;
  ll ll_lcm = (ll)all_lcm%MOD;
  rep(i, a.size()){
    ll inv = mod_pow_r(a[i], MOD-2);
//cout<<all_lcm<<'*'<<inv<<'='<<(all_lcm*inv)%MOD<<endl;
    result += (ll_lcm*inv)%MOD;
//cout<<result<<endl;
  }

  result%=MOD;
  cout<<result;

  return 0;
}