Problem:
Score : 300 points

Problem Statement

We have a sequence of N integers A~=~A_0,~A_1,~...,~A_{N - 1}.

Let B be a sequence of K \times N integers obtained by concatenating K copies of A. For example, if A~=~1,~3,~2 and K~=~2, B~=~1,~3,~2,~1,~3,~2.

Find the inversion number of B, modulo 10^9 + 7.

Here the inversion number of B is defined as the number of ordered pairs of integers (i,~j)~(0 \leq i < j \leq K \times N - 1) such that B_i > B_j.

Constraints

All values in input are integers.

1 \leq N \leq 2000

1 \leq K \leq 10^9

1 \leq A_i \leq 2000

Input

Input is given from Standard Input in the following format:

N K
A_0 A_1 ... A_{N - 1}

Output

Print the inversion number of B, modulo 10^9 + 7.

Sample Input 1

2 2
2 1

Sample Output 1

3

In this case, B~=~2,~1,~2,~1. We have:

B_0 > B_1

B_0 > B_3

B_2 > B_3

Thus, the inversion number of B is 3.

Sample Input 2

3 5
1 1 1

Sample Output 2

0

A may contain multiple occurrences of the same number.

Sample Input 3

10 998244353
10 9 8 7 5 6 3 4 2 1

Sample Output 3

185297239

Be sure to print the output modulo 10^9 + 7.

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

using System;
using System.Collections.Generic;
using System.Linq;
using System.Net.NetworkInformation;
using System.Security.Cryptography;
using System.Text;
using System.Threading;
using Extensions;
using static System.Math;
using static Extensions.MathExtension;
using static Extensions.ConsoleInputExtension;
using static Extensions.ConsoleOutputExtension;

class Solver
{
    public void Solve()
    {
        //Solve Code Here
        ModInt.Mod = 1000000000 + 7;
        int N = Cin;
        long K = Cin;
        var A = new int[N];
        for (int i = 0; i < N; i++) A[i] = Cin;
        var LLarge = new int[N];
        var RLarge = new int[N];
        var LSmall = new int[N];
        var RSmall = new int[N];
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < i; j++)
            {
                if (A[j] < A[i]) LSmall[i]++;
                if (A[j] > A[i]) LLarge[i]++;
            }

            for (int j = i + 1; j < N; j++)
            {
                if (A[j] < A[i]) RSmall[i]++;
                if (A[j] > A[i]) RLarge[i]++;
            }
        }

        var ans = new ModInt(0);
        var k = (ModInt) K;
        for (int i = 0; i < N; i++)
        {
            ans += ((ModInt) RSmall[i] * k * (k + (ModInt) 1) +
                     (ModInt) LSmall[i] * k * (k - (ModInt) 1)) /
                    (ModInt) 2;
        }

        Coutln(ans);
    }

    //Other Functions Here
}
//Other Classes Here

#if !DEBUG
class EntryPoint
{
    static void Main(string[] args)
    {
        new Solver().Solve();
        Flush();
    }
}
#endif

class PriorityQueue<T>
{
    private readonly List<Tuple<int, T>> _list = new List<Tuple<int, T>>();
    public int Count { get; private set; } = 0;

    public PriorityQueue()
    {
        _list.Add(null);
        _list.Add(null);
        _list.Add(null);
    }

    public void Push(T item, int priority)
    {
        var itemIndex = Count++;
        _list[itemIndex] = Tuple.Create(priority, item);
        while (_list.Count < Count + 2) _list.Add(null);

        int parentIndex;
        while ((parentIndex = GetParentIndex(itemIndex)) != -1 &&
               priority > (_list[parentIndex]?.Item1 ?? int.MaxValue))
        {
            Swap(itemIndex, parentIndex);
            itemIndex = parentIndex;
        }
    }

    private int GetParentIndex(int index)
    {
        if (index == 0) return -1;
        return ((index + 1) >> 1) - 1;
    }

    private Tuple<int, int> GetChildrenIndex(int index)
    {
        var item2 = (index + 1) << 1;
        var item1 = item2 - 1;
        return item2 >= _list.Count ? null : Tuple.Create(item1, item2);
    }

    public T Pop()
    {
        if (_list.Count <= 0 || _list[0] == null) throw new IndexOutOfRangeException();
        var item = _list[0].Item2;
        _list[0] = null;
        Tuple<int, int> childrenIndex;
        int index = 0;
        while ((childrenIndex = GetChildrenIndex(index)) != null &&
               (_list[childrenIndex.Item1] != null || _list[childrenIndex.Item2] != null))
        {
            if ((_list[childrenIndex.Item1]?.Item1 ?? int.MaxValue) >
                (_list[childrenIndex.Item2]?.Item1 ?? int.MinValue))
            {
                _list[index] = _list[childrenIndex.Item1];
                _list[childrenIndex.Item1] = null;
                index = childrenIndex.Item1;
            }
            else
            {
                _list[index] = _list[childrenIndex.Item2];
                _list[childrenIndex.Item2] = null;
                index = childrenIndex.Item2;
            }
        }

        Count--;
        return item;
    }

    public T Peek()
    {
        return _list[0].Item2;
    }

    private void Swap(int index1, int index2)
    {
        var tmp = _list[index1];
        _list[index1] = _list[index2];
        _list[index2] = tmp;
    }
}

struct Rational
{
    private long _numerator;
    private long _denominator;
    public long Numerator => _numerator;
    public long Denominator => _denominator;

    public Rational(long numerator, long denominator)
    {
        var gcd = GCD(numerator, denominator);
        _numerator = numerator / gcd;
        _denominator = denominator / gcd;
    }

    public static Rational operator +(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator + b._numerator * a._denominator,
            a._denominator * b._denominator);
    }

    public static Rational operator -(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator - b._numerator * a._denominator,
            a._denominator * b._denominator);
    }

    public static Rational operator *(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._numerator, a._denominator * b._denominator);
    }

    public static Rational operator /(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator, a._denominator * b._numerator);
    }

    public static explicit operator Rational(int i)
    {
        return new Rational(i, 1);
    }

    public static explicit operator Rational(long l)
    {
        return new Rational(l, 1);
    }

    public static explicit operator Rational(double d)
    {
        long denominator = 1;
        while (d % 1 != 0)
        {
            denominator *= 2;
            d *= 2;
        }

        return new Rational((long) d, denominator);
    }

    public static explicit operator Rational(float f)
    {
        long denominator = 1;
        while (f % 1 != 0)
        {
            denominator *= 2;
            f *= 2;
        }

        return new Rational((long) f, denominator);
    }
}

struct ModInt
{
    public long Value { get; }
    public static long Mod { get; set; } = 1000000000L + 7;

    public ModInt(long l)
    {
        long value = l % Mod;
        while (value < 0) value += Mod;
        Value = value % Mod;
    }

    public static implicit operator long(ModInt m)
    {
        return m.Value;
    }

    public static explicit operator ModInt(long l)
    {
        return new ModInt(l);
    }

    public static ModInt operator +(ModInt a, ModInt b)
    {
        return new ModInt(a.Value + b.Value);
    }

    public static ModInt operator -(ModInt a, ModInt b)
    {
        return new ModInt(a.Value - b.Value);
    }

    public static ModInt operator *(ModInt a, ModInt b)
    {
        return new ModInt(a.Value * b.Value);
    }

    public static ModInt operator /(ModInt a, ModInt b)
    {
        return new ModInt(a * b.Inverse());
    }

    public override string ToString()
    {
        return Value.ToString();
    }
}

static class ModIntMath
{
    public static ModInt Pow(this ModInt a, ModInt b)
    {
        var pow = b.Value;
        var m = a;
        ModInt ans = new ModInt(1);
        while (pow != 0)
        {
            if ((pow & 1) == 1)
            {
                ans *= m;
            }

            pow >>= 1;
            m *= m;
        }

        return ans;
    }

    public static ModInt Inverse(this ModInt m)
    {
        return m.Pow((ModInt) (ModInt.Mod - 2));
    }
}

class UnionFind
{
    private readonly int[] _array;

    public UnionFind(int N)
    {
        _array = new int[N];
        for (int i = 0; i < N; i++)
        {
            _array[i] = i;
        }
    }

    public int GetRootNode(int n)
    {
        if (_array[n] == n) return n;
        return _array[n] = GetRootNode(_array[n]);
    }

    public void UnionGroup(int a, int b)
    {
        var rootA = GetRootNode(a);
        var rootB = GetRootNode(b);
        if (rootA == rootB) return;
        _array[rootA] = rootB;
    }

    public bool IsSameGroup(int a, int b) => GetRootNode(a) == GetRootNode(b);

    public bool IsRoot(int n) => _array[n] == n;
}


namespace Extensions
{
    public class ConsoleInputExtension
    {
        private static readonly ConsoleInputExtension _cin = new ConsoleInputExtension();

        public static ConsoleInputExtension Cin => _cin;

        private static readonly Queue<string> _inputQueue = new Queue<string>();

        private ConsoleInputExtension()
        {
        }

        public static implicit operator string(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return _inputQueue.Dequeue();
        }

        public static implicit operator int(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return int.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator long(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return long.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator float(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return float.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator double(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return double.Parse(_inputQueue.Dequeue());
        }
    }

    public static class ConsoleOutputExtension
    {
        private static StringBuilder _builder = new StringBuilder();

        public static void Cout(object o)
        {
            _builder.Append(o);
        }

        public static void CoutF(object o)
        {
            _builder.Append(o);
            Flush();
        }

        public static void Coutln(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
        }

        public static void Coutln()
        {
            _builder.Append('\n');
        }

        public static void CoutlnF(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
            Flush();
        }

        public static void Flush()
        {
            Console.Write(_builder.ToString());
            _builder.Clear();
        }
    }

    public static class MathExtension
    {
        //最小公倍数
        public static int LCM(int num1, int num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        public static long LCM(long num1, long num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        //最大公約数
        public static int GCD(int num1, int num2)
        {
            int a = Math.Max(num1, num2);
            int b = Math.Min(num1, num2);
            int mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }

        public static long GCD(long num1, long num2)
        {
            long a = Math.Max(num1, num2);
            long b = Math.Min(num1, num2);
            long mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }
    }

    public static class EnumerableExtension
    {
        public delegate void Function<in T>(T val);

        public static void ForEach<T>(this IEnumerable<T> enumerable, Function<T> function)
        {
            foreach (var x in enumerable)
            {
                function(x);
            }
        }
    }
}