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: Time Limit Exceeded)

import java.math.BigInteger;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        BigInteger lcm = BigInteger.ONE;
        BigInteger[] a = new BigInteger[n];
        BigInteger c = new BigInteger("1000000007");
        for(int i=0; i<n; i++) {
            a[i] = new BigInteger(in.next());
            BigInteger gcd = gcd(lcm, a[i]);
            lcm =  lcm.multiply(a[i]).divide(gcd);
        }
        long result = 0;
        for(int i=0; i<n; i++) {
            result += lcm.divide(a[i]).remainder(c).longValue();
        }
        result = result % 1000000007;
        System.out.println(result);
    }
    private static BigInteger gcd(BigInteger a, BigInteger b) {
        if(b.equals(BigInteger.ZERO)) {
            return a;
        }
        return gcd(b, a.remainder(b));
    }
}