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: Accepted)

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

public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		String str = scan.nextLine();

		int n = Integer.parseInt(str);

		str = scan.nextLine();
		String[] substr = str.split(" ", 0);

		BigInteger[] array = new BigInteger[10000];
		for (int i=0; i<n; i++) {
			array[i] = BigInteger.valueOf(Integer.parseInt(substr[i]));
		}

		BigInteger l = array[0];
		for (int i=1; i<n; i++) {
			l = array[i].multiply(l).divide(array[i].gcd(l));
		}
		BigInteger ans = BigInteger.ZERO;
		BigInteger mod = BigInteger.valueOf(1000000007);
		l = l.mod(mod);
		for (int i=0; i<n; i++) {
			ans = ans.add(l.multiply(array[i].modInverse(mod)));
			ans = ans.mod(mod);
		}
		System.out.println(ans);

	}

    static BigInteger gcd(BigInteger a, BigInteger b){
        return a.gcd(b);
    }
    static BigInteger lcm(BigInteger a, BigInteger b){
        return a.multiply(b).divide(gcd(a,b));
    }
}