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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;

namespace solve
{
    class Program
    {
        static long  Gcd(long x, long y)
        {
            if (y == 0) return x;
            return Gcd(y, x % y);
        }

        static long  Lcm(long x, long y)
        {
            return x * y / Gcd(x, y);
        }

        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            long[] A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            long lc = A[0];
            long mod = 1000000007;
            for (int i = 1; i < N; i++)
            {
                lc = Lcm(lc, A[i]);
            }
            long s = 0;
            for (int i = 0; i < N; i++)
            {
                s += lc / A[i];
                s %= mod;
            }
            Console.WriteLine(s);
        }
    }
}