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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        var N = int.Parse(ReadLine());
        var A = ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

        BigInteger LCM(BigInteger x, BigInteger y) => x * y / BigInteger.GreatestCommonDivisor(x, y);
        
        var lcm = new BigInteger(A[0]);

        for (int i = 1; i < N; i++)
        {
            lcm = LCM(lcm, A[i]);
        }

        var BSum = new BigInteger();

        for (int i = 0; i < N; i++)
        {
            BSum = (BSum + lcm / A[i]) % 1000000007;
        }

        WriteLine(BSum);
    }
}