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;
const int MOD=1e9+7;

int max_n=1000009;

ll mod_pow(ll x, ll n){ //べき乗
    ll ans=1;
    while(n!=0){
        if(n&1) ans=ans*x%MOD;
        x=x*x%MOD;
        n=n>>1;
    }
    return ans;
}

int main(){
    int N; cin >> N;
    int a[N]; for(int i=0;i<N;i++) cin >> a[i];
    vector<ll> result(max_n,0);
    for(int i=0;i<N;i++){
        ll res=a[i];
        for(ll j=2;j*j<=res;j++){
            if(res%j!=0) continue;
            ll cnt=0;
            while(res%j==0){
                res/=j;
                cnt++;
            }
            result[j]=max(result[j],cnt);
        }
        if(res!=1){
            result[res]=max(result[res],1LL);
        }
    }
    ll ans=0;
    ll res=1;
    for(int j=2;j*j<=max_n;j++){
        res*=mod_pow(j,result[j]);
        res%=MOD;
    }
    for(int i=0;i<N;i++){
        ll now=res;
        now*=mod_pow(a[i],MOD-2);
        now%=MOD;
        ans+=now;
        ans%=MOD;
    }
    cout << ans << endl;
}