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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader((new InputStreamReader(System.in)));
        String[] l = reader.readLine().split(" ");
        int N = Integer.parseInt(l[0]);
        String[] list = reader.readLine().split(" ");
        int[] arr = new int[N];
        for(int i= 0;i<N;i++){
            arr[i] =Integer.parseInt(list[i]);
        }

        long sum = 0;
        long lcm = LCM(arr);
        for(int i1 = 0 ;i1<N;i1++){
            sum=sum+ lcm/(arr[i1]);
            if(sum>=1000000007) sum%=1000000007;
        }
        System.out.println(sum);
    }
    public static long LCM(int[] arr){
        long res = lcm(arr[0],arr[1]);
        for(int j = 2;j<arr.length;j++){
            res=lcm(res,arr[j]);
        }
        return res;
    }
    public static long lcm(long a, long b){
        long res = a*b/gcd(a,b);
        return res;
    }
    public static long gcd(long a, long b){
        while(b>0){
            long emp =b;
            b=a%b;
            a=emp;
        }
        return a;
    }

}