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 <bits/stdc++.h>
using namespace std;
static const long long MOD=1000000007;

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(){
  int N;
  cin>>N;
  long long A[N];
  for(int i=0;i<N;i++){
    cin>>A[i];  
  }
  
  //A[i]を素因数分解しmapに記録
  map<int,int>mp;
  map<int,int>mp2;    
  for(int j=0;j<N;j++){
    int temp=A[j];    
    for(int i=2;i*i<=A[j];i++){
      mp[i]=0;
      while(temp%i == 0){
        mp[i]++;
        temp/=i;
      }
      if(mp2[i]<mp[i]) mp2[i]=mp[i];
    }  
  }
  long long M=1;
  
  for(auto it=mp2.begin();it != mp2.end();it++){
    for(int i=0;i<it->second;i++){
      M*=it->first;
    }
    M%=MOD;
  }
  //cout<<M<<endl;
  long long ans=0;
  for(int i=0;i<N;i++){
    ans+=M*modinv(A[i],MOD);
    ans%=MOD;
    //cout<<M<<" "<<A[i]<<" "<<ans<<endl;
  }
  cout<<ans<<endl;

  return 0;
}