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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using E = System.Linq.Enumerable;
using System.IO.Pipes;
using System.Threading;

class Program
{
    static char[] abc = "abcdefghijklmnopqrstuvwxyz".ToCharArray();
    static long mod = 1000000007;
    static void Main(string[] args)
    {
        //var N = long.Parse(Console.ReadLine());
        var NK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var N = NK[0];
        var K = NK[1];
        var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        long ans1 = 0;
        long ans2 = 0;
        for (int i = 0; i < N; i++)
        {
            var tentou = 0;
            var all = 0;
            for (int j = 0; j < N; j++)
            {
                if(A[j] < A[i])
                {
                    if(i < j)
                    {
                        tentou++;
                    }
                    all++;
                }
            }
            ans1 += tentou;
            ans2 += all;
        }
        ans1 *= K;
        ans1 %= mod;
        ans2 *= (K * (K - 1) / 2)%mod;
        ans2 %= mod;
        Console.WriteLine((ans1 + ans2)%mod);

    }

}