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;

public class Hello
{
    public static int MOD = 1000000007;
    static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var k = int.Parse(line[1]);
        var s = Console.ReadLine().Trim();
        line = s.Split(' ');
        var a = Array.ConvertAll(line, int.Parse);
        var count = 0;
        for (int i = 0; i < n - 1; i++)
            for (int j = i + 1; j < n; j++)
                if (a[i] > a[j]) count++;
        line = (s + " " + s).Split(' ');
        var b = Array.ConvertAll(line, int.Parse);
        var count2 = 0;
        for (int i = 0; i < n; i++)
            for (int j = n; j < 2 * n; j++)
                if (b[i] > b[j]) count2++;
        var ans = count * (long)k % MOD;
        var ans2 = count2 * (long)k % MOD;
        ans2 *= k - 1;
        ans2 %= MOD;
        var Inv2 = getInv(2, MOD);
        ans2 = ans2 * Inv2 % MOD;
        ans += ans2;
        ans %= MOD;
        Console.WriteLine(ans);
    }
    public static long getInv(int a, int m)
    {
        var x = 0L; var y = 1L; var gcd = (long)m;
        var px = 1L; var py = 0L; var pgcd = (long)a;
        var temp = 0L;

        while (gcd > 0)
        {
            var quotient = pgcd / gcd;

            temp = x;
            x = px - quotient * temp;
            px = temp;

            temp = y;
            y = py - quotient * temp;
            py = temp;

            temp = gcd;
            gcd = pgcd - quotient * temp;
            pgcd = temp;
        }

        return px < 0 ? px + m : px;
    }

}