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 final int MAX = (int)1e5*2+9;
    public static final int MOD = (int)1e9+7;
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        int[] a = new int[n];
        for(int i=0; i<n; i++){
            a[i] = Integer.parseInt(sc.next());
        }
        
        long lcm = 1;
        for(int i=0; i<n; i++){
            lcm = lcm(lcm, a[i]);
        }
        
        long ans = 0;
        for(int i=0; i<n; i++){
            long tmp = lcm / a[i];
            ans += tmp;
            ans %= MOD;
        }
        
        System.out.println(ans);
        
    }
    
    private static long lcm(long num1, long num2) {
        return num1 * num2 / gcd(num1, num2);
    }
    
    public static long gcd(long num1,long num2) {
        if(num2==0){
            return num1;
        }
        return gcd(num2,num1%num2);
    }
}