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: Runtime Error)

import java.util.*;
 
public class Main {
public static final long MOD = 1000000007;

    public static long gcd(long a, long b){
        if(b > a) return gcd(b, a);
        if(b == 0) return a;

        return gcd(b, a % b);
    }

    public static long lcm(long a, long b){
        return (a / gcd(a, b)) * b;
    }

    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        long N = Long.parseLong(sc.next());
        long[] a = new long[(int)N];
        for(int i = 0; i < N; i++){
            a[i] = Long.parseLong(sc.next());
        }
        sc.close();

        Long commonLcm = 1L, ans = 0L;
        for(int i = 0; i < N; i++){
            commonLcm = lcm(commonLcm, a[i]);
        }

        for(long c : a){
            ans += (commonLcm / c) % MOD;
            ans %= MOD;
        }
        System.out.println(ans);
    }
}