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: Wrong Answer)

import java.util.*;
public class Main {
	
	public static long gcd(long m, long n) {
        return n == 0 ? m : gcd(n, m % n);
    }
	public static long lcm(long m, long n) {
		return m * n / gcd(m, n);
	}
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long[] x=new long[n];
		long[] y=new long[n];
		long c = 0;
		for(int i=0;i<n;i++) {
			x[i] = sc.nextInt();
			y[i] = x[i];
		}
		long t = 0;
		for(int i=0;i<n-1;i++) {
			t = lcm(x[i],x[i+1]);
			x[i+1] = t;
		}
		for(int i=0;i<n;i++) {
			c+=t/y[i];
			c%=(int)1e9+7;
		}
		System.out.print(c);
	}
}