Problem:
Score : 600 points

Problem Statement

There are N slimes standing on a number line.
The i-th slime from the left is at position x_i.

It is guaruanteed that 1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}.

Niwango will perform N-1 operations. The i-th operation consists of the following procedures:

Choose an integer k between 1 and N-i (inclusive) with equal probability.

Move the k-th slime from the left, to the position of the neighboring slime to the right.

Fuse the two slimes at the same position into one slime.

Find the total distance traveled by the slimes multiplied by (N-1)! (we can show that this value is an integer), modulo (10^{9}+7). If a slime is born by a fuse and that slime moves, we count it as just one slime.

Constraints

2 \leq N \leq 10^{5}

1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}

x_i is an integer.

Subtasks

400 points will be awarded for passing the test cases satisfying N \leq 2000.

Input

Input is given from Standard Input in the following format:

N
x_1 x_2 \ldots x_N

Output

Print the answer.

Sample Input 1

3
1 2 3

Sample Output 1

5

With probability \frac{1}{2}, the leftmost slime is chosen in the first operation, in which case the total distance traveled is 2.

With probability \frac{1}{2}, the middle slime is chosen in the first operation, in which case the total distance traveled is 3.

The answer is the expected total distance traveled, 2.5, multiplied by 2!, which is 5.

Sample Input 2

12
161735902 211047202 430302156 450968417 628894325 707723857 731963982 822804784 880895728 923078537 971407775 982631932

Sample Output 2

750927044

Find the expected value multiplied by (N-1)!, modulo (10^9+7).

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

#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 x = cr.Split.Int;
            var xDiff = new int[N - 1];
            for (int i = 0; i < N - 1; i++)
            {
                xDiff[i] = x[i + 1] - x[i];
            }
            Mod res = 0;
            Mod cur = 0;
            Mod fr = Mod.CreateFactor(N).Factorial(N-1);

            for (int i = 0; i < xDiff.Length; i++)
            {
                cur += fr / (i + 1);
                res += xDiff[i] * cur;
            }
            return res;
        }
        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];
            }
        }

    }
}