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: Time Limit Exceeded)

#region いつもの
#pragma warning disable
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using static AtCoderProject.Global;

namespace AtCoderProject
{
    static class Global
    {
        private class ComparerReverseImpl<T> : Comparer<T> where T : IComparable<T> { public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); }
        public static IComparer<T> ComparerReverse<T>() where T : IComparable<T> => new ComparerReverseImpl<T>();
        public static BigInteger ParseBigInteger(string s)
        {
            // MonoのBigInteger.Parseが遅いので自前実装
            var res = BigInteger.Zero;
            var splited = new string[(s.Length + 7) / 8];
            for (var i = 0; i < splited.Length - 1; i++)
            {
                splited[i] = s.Substring(8 * i, 8);
            }
            splited[splited.Length - 1] = s.Substring(8 * (splited.Length - 1));
            foreach (var sp in splited)
            {
                res *= (int)Math.Pow(10, sp.Length);
                res += int.Parse(sp);
            }
            return res;
        }
        public static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        public static string AllJoin<T>(IEnumerable<T> source) => string.Join(" ", source);
    }
    static class Ext
    {
        public static T[] Sort<T>(this T[] arr)
        {
            Array.Sort(arr);
            return arr;
        }
        public static T[] Reverse<T>(this T[] arr)
        {
            Array.Reverse(arr);
            return arr;
        }
        public static T[][] Chunk<T>(this T[,] source)
        {
            var len0 = source.GetLength(0);
            var len1 = source.GetLength(1);
            var res = new T[len0][];
            for (var i = 0; i < len0; i++)
            {
                res[i] = new T[len1];
                for (var j = 0; j < len1; j++)
                {
                    res[i][j] = source[i, j];
                }
            }
            return res;
        }

        public static Tuple<TSource, TMax> MaxBy<TSource, TMax>
            (this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector)
            where TMax : IComparable<TMax>
        {
            TMax max;
            TSource maxByItem;

            var e = source.GetEnumerator();
            e.MoveNext();
            maxByItem = e.Current;
            max = maxBySelector(maxByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = maxBySelector(item);
                if (max.CompareTo(next) < 0)
                {
                    max = next;
                    maxByItem = item;
                }
            }
            return Tuple.Create(maxByItem, max);
        }
        public static Tuple<TSource, TMin> MinBy<TSource, TMin>
            (this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector)
            where TMin : IComparable<TMin>
        {
            TMin min;
            TSource minByItem;

            var e = source.GetEnumerator();
            e.MoveNext();
            minByItem = e.Current;
            min = minBySelector(minByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = minBySelector(item);
                if (min.CompareTo(next) > 0)
                {
                    min = next;
                    minByItem = item;
                }
            }
            return Tuple.Create(minByItem, min);
        }
        public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public int Int0 => Int - 1; public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public string[] String => this.Select(cr => cr.String).ToArray(); public int[] Int => this.Select(cr => cr.Int).ToArray(); public int[] Int0 => this.Select(cr => cr.Int - 1).ToArray(); public long[] Long => this.Select(cr => cr.Long).ToArray(); public double[] Double => this.Select(cr => cr.Double).ToArray(); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    public class Program
    {
        [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader cr;
        public Program(ConsoleReader consoleReader) { this.cr = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc());

        #endregion
        public object Calc()
        {
            var N = cr.Int;
            var a = cr.Split.Int;
            var lcm = Lcm(a.Select(i => (BigInteger)i).ToArray());

            Mod b = 0;
            foreach (var item in a)
            {
                b += (long)(lcm / item % Mod.mod);
            }

            return b;
        }

        BigInteger Gcd(BigInteger a, BigInteger b) => b > a ? Gcd(b, a) : (b == 0 ? a : Gcd(b, a % b));
        BigInteger Lcm(BigInteger a, BigInteger b) => a / Gcd(a, b) * b;

        BigInteger Lcm(params BigInteger[] nums)
        {
            var lcm = nums[0];
            for (var i = 1; i < nums.Length; i++)
                lcm = Lcm(lcm, nums[i]);
            return lcm;
        }
        struct Mod : IEquatable<Mod>
        {
            public const long mod = 1000000007;
            public readonly long val;
            public Mod(long val, bool isValid) : this(isValid ? val % mod : val) { }
            public Mod(long val) { this.val = val; }
            public override bool Equals(object obj) => (obj is Mod) ? this == ((Mod)obj) : false;
            public bool Equals(Mod obj) => this == obj;
            public override int GetHashCode() => val.GetHashCode();
            public override string ToString() => val.ToString();
            public static implicit operator Mod(long x) => new Mod(x);
            public static Mod operator +(Mod x, Mod y) => (x.val + y.val) % mod;
            public static Mod operator -(Mod x, Mod y) => x.val >= y.val ? (x.val - y.val) % mod : (x.val - y.val) % mod + mod;
            public static Mod operator *(Mod x, Mod y) => (x.val * y.val) % mod;
            public static Mod operator /(Mod x, Mod y) => x * y.Inverse();
            public static bool operator ==(Mod x, Mod y) => x.val == y.val;
            public static bool operator !=(Mod x, Mod y) => x.val != y.val;
            public Mod Inverse()
            {
                long a = val, b = mod, u = 1, v = 0;
                while (b > 0)
                {
                    long t = a / b;
                    var b2 = a - t * b;
                    a = b; b = b2;
                    var v2 = u - t * v;
                    u = v; v = v2;
                }
                u %= mod;
                if (u < 0) u += mod;
                return u;
            }
            public static Mod Pow(Mod x, int y)
            {
                Mod res = 1;
                for (; y > 0; y >>= 1)
                {
                    if ((y & 1) == 1) res *= x;
                    x *= x;
                }
                return res;
            }

            public static Factor CreateFactor(int max) => new Factor(max);
            public class Factor
            {
                private readonly Mod[] fac, finv;
                public Factor(int max)
                {
                    ++max;
                    var inv = new Mod[max];
                    fac = new Mod[max]; finv = new Mod[max];
                    fac[0] = fac[1] = 1;
                    finv[0] = finv[1] = 1;
                    inv[1] = 1;
                    for (var i = 2; i < max; i++)
                    {
                        fac[i] = fac[i - 1] * i;
                        inv[i] = mod - inv[mod % i].val * (mod / i) % mod;
                        finv[i] = finv[i - 1] * inv[i];
                    }
                }

                // 二項係数計算
                public Mod Combine(int n, int k)
                {
                    if (n < k) return 0;
                    if (n < 0 || k < 0) return 0;
                    return fac[n] * finv[k] * finv[n - k];
                }

                public Mod Factorial(int n) => fac[n];
                public Mod FactorialInvers(int n) => finv[n];
            }
        }

    }
}