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: Wrong Answer)

using System;
using System.Collections.Generic;//list用
using System.Text.RegularExpressions;//正規表現用
using System.Text;//StringBuilder用
using System.Collections;//ハッシュテーブル用
using System.Linq;


class Program
{
    Hashtable ht = new Hashtable();
    static List<long> s = new List<long>();
    static long result;
    static long K,N;
    StringBuilder strresult= new StringBuilder("");//Append(str ○○)関数で文字を追加していく



    static void Main()
    {
        Modular mo = new Modular(0);//素数で割った余りを出せで使う★使い方：Modular型で宣言すると、その時点でのその素数で割った余りを保持する変数になる（powべき乗、Fac累乗、nCr組み合わせも関数として存在）カッコ内が初期値
        //Node no = new Node<>();//UnionFind★Find関数で根っこの値を返す（根っこの値が一緒なら同グループ）、Unite関数で二つの木をくっつける
        //Permutation pe = new Permutation<>();//配列＆リストを並べ替えた場合の全ケースを出力★All関数でリスト形式で返す。
        //Treap tr = new Treap<>();//平衡二分木★Insert()関数で挿入、FindIndex()関数で該当する大きさの物が入るべき配列番号を返す。
        // delegate int CFunc();//下関数に使うデリゲータ。コイツと同じ引数と戻り値で関数作って、下の評価式の部分に関数名を入れる。
        //PriorityQueue pr = new PriorityQueue<>(評価式);//優先度付キュー★Enqueue()で格納、Dequeue()で取りだし。引数は評価式（大と小のどちらが優先か）。
        Read1();
        Read2(N);
        long[] check2 = new long[N];
        for (int i = 0; i < N-1; i++) { for (int j = i + 1; j < N; j++) { if (s[i] > s[j]) { check2[i]++; } } }
        for (int i = 0; i < N; i++) { mo +=  check2[i] * K; }

      long[] check=new long[N];
       for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { if (s[i]>s[j]) { check[i]++; } } }//ワンセットの中に何個自分以上がある？
        for (int i = 0; i < N; i++) { mo += (long)(check[i]*K*(K-1))/(long)2; }

        result=(long)mo;
        Console.WriteLine(result.ToString());
    }


    static void Read1()
    {
        string[] tmp = Console.ReadLine().Split(' ');
        N = long.Parse(tmp[0]);
        K = long.Parse(tmp[1]);
    }

    static void Read2(long kosuu)
    {
        string[] tmp = Console.ReadLine().Split(' ');
        for (long i = 0; i < kosuu; i++) { s.Add(long.Parse(tmp[i])); }
    }


    static long Gcd(long a, long b)
    {
        var v = new[] { a, b };
        while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
        return v[0];
    }

    static long Lcm(long a, long b)
    {
        return a / Gcd(a, b) * b;
    }


}

class Modular
{
    private const int M = 1000000007;//素数
    private long value;
    public Modular(long value) { this.value = value; }
    public static implicit operator Modular(long a)
    {
        var m = a % M;
        return new Modular((m < 0) ? m + M : m);
    }
    public static Modular operator +(Modular a, Modular b)
    {
        return a.value + b.value;
    }
    public static Modular operator -(Modular a, Modular b)
    {
        return a.value - b.value;
    }
    public static Modular operator *(Modular a, Modular b)
    {
        return a.value * b.value;
    }
    private static Modular Pow(Modular a, int n)
    {
        switch (n)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                var p = Pow(a, n / 2);
                return p * p * Pow(a, n % 2);
        }
    }
    public static Modular operator /(Modular a, Modular b)
    {
        return a * Pow(b, M - 2);
    }
    private static readonly List<int> facs = new List<int> { 1 };
    private static Modular Fac(int n)
    {
        for (int i = facs.Count; i <= n; ++i)
        {
            facs.Add((int)(Math.BigMul(facs.Last(), i) % M));
        }
        return facs[n];
    }
    public static Modular Ncr(int n, int r)
    {
        return (n < r) ? 0
        : (n == r) ? 1
        : Fac(n) / (Fac(r) * Fac(n - r));
    }
    public static explicit operator int(Modular a)
    {
        return (int)a.value;
    }
}