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 Java7 (OpenJDK 1.7.0) (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[] a = new BigInteger[10007];
		for(int i = 0;i < n;i++) {
			a[i] = in.nextBigInteger();
		}
		in.close();
		BigInteger x = a[0];
		BigInteger gcd = x;
		for(int i = 1;i < n;i++) {
			gcd = Quick_GCD(gcd,a[i]);
			x = x.multiply(a[i].divide(gcd));
			gcd = x;
		}
		BigInteger ans = BigInteger.ZERO;
		for(int i = 0;i < n;i++) {
			ans = ans.add(x.divide(a[i]));
		}
		System.out.print(ans.mod(BigInteger.valueOf(1000000007)));
	}
	
	public static BigInteger Quick_GCD(BigInteger a,BigInteger b)
    {
	        BigInteger r;
	        while(b.compareTo(BigInteger.ZERO)==1)
	        {
	             r=a.mod(b);
	             a=b;
	             b=r;
	        }
	        return a;
    }
}