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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static Reader;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split().Select(Parse).ToArray();
        var lcm = new ModInt((long)(a.Aggregate(LCM) % 1000000007));
        var res = a.Select(x => lcm / ((long)x)).Aggregate(new ModInt(0), (x, y) => x + y);
        Console.WriteLine(res);
    }

    static BigInteger Parse(string s)
    {
        BigInteger res = 0;
        for (int i = 0; i < s.Length; i++)
        {
            res *= 10;
            res += s[i] - '0';
        }
        return res;
    }

    static BigInteger LCM(BigInteger a, BigInteger b) { return a / BigInteger.GreatestCommonDivisor(a, b) * b; }
}


struct ModInt
{
    const int MOD = 1000000007;
    const long POSITIVIZER = ((long)MOD) << 31;
    long Data;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt(long data) { if ((Data = data % MOD) < 0) Data += MOD; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator long(ModInt modInt) => modInt.Data;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator ModInt(long val) => new ModInt(val);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, int b) => new ModInt() { Data = (a.Data + b + POSITIVIZER) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, long b) => new ModInt(a.Data + b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, ModInt b) { long res = a.Data + b.Data; return new ModInt() { Data = res >= MOD ? res - MOD : res }; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, int b) => new ModInt() { Data = (a.Data - b + POSITIVIZER) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, long b) => new ModInt(a.Data - b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, ModInt b) { long res = a.Data - b.Data; return new ModInt() { Data = res < 0 ? res + MOD : res }; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, int b) => new ModInt(a.Data * b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, long b) => a * new ModInt(b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator /(ModInt a, ModInt b) => new ModInt() { Data = a.Data * GetInverse(b) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public override string ToString() => Data.ToString();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static long GetInverse(long a)
    {
        long div, p = MOD, x1 = 1, y1 = 0, x2 = 0, y2 = 1;
        while (true)
        {
            if (p == 1) return x2 + MOD; div = a / p; x1 -= x2 * div; y1 -= y2 * div; a %= p;
            if (a == 1) return x1 + MOD; div = p / a; x2 -= x1 * div; y2 -= y1 * div; p %= a;
        }
    }
}

static class Reader
{
    const int BUF_SIZE = 1 << 12;
    static Stream Stream = Console.OpenStandardInput();
    static byte[] Buffer = new byte[BUF_SIZE];
    static int ptr = BUF_SIZE - 1;
    static void Move() { if (++ptr >= Buffer.Length) { Stream.Read(Buffer, 0, BUF_SIZE); ptr = 0; } }


    public static int NextInt
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        get
        {
            int res = 0; while (Buffer[ptr] < 48) Move();
            do { res = res * 10 + (int)(Buffer[ptr] ^ 48); Move(); } while (48 <= Buffer[ptr]);
            return res;
        }
    }
}