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;

class Modulo
{
    private const int MOD = 1000000007;
    private readonly int[] m_facs;
    public int Mul(int a, int b) => (int)(Math.BigMul(a, b) % MOD);
    public Modulo(int n)
    {
        m_facs = new int[n + 1];
        m_facs[0] = 1;
        for (int i = 1; i <= n; ++i)
            m_facs[i] = Mul(m_facs[i - 1], i);
    }
    public int Fac(int n) => m_facs[n];
    public int Pow(int a, int m)
    {
        switch (m)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                int p1 = Pow(a, m / 2);
                int p2 = Mul(p1, p1);
                return ((m % 2) == 0) ? p2 : Mul(p2, a);
        }
    }
    public int Div(int a, int b) => Mul(a, Pow(b, MOD - 2));
    public int Ncr(int n, int r)
    {
        if (n < r) return 0;
        if (n == r) return 1;
        int res = Fac(n);
        res = Div(res, Fac(r));
        res = Div(res, Fac(n - r));
        return res;
    }
}


public class Hello
{
    public static void Main()
    {
        var MOD = 1000000007;
        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;
        ans %= MOD;
        var md = new Modulo(2);
        var ans2 = (long)k * (k - 1);
        ans2 %= MOD;
        ans2 = md.Div((int)ans2, 2);
        ans2 *= count2;
        ans2 %= MOD;
        ans += ans2;
        ans %= MOD;
        Console.WriteLine(ans);
    }
}