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.Text;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] p2 = Console.ReadLine().Split(' ');
            int N = int.Parse(p2[0]);
            int K = int.Parse(p2[1]);
            string[] As = Console.ReadLine().Split(' ');
            int[] A = new int[N];
            int[] T = new int[N];
            int[] L = new int[N];
            for (var i = 0; i < N; i++)
            {
                A[i] = int.Parse(As[i]);
            }
            for (var i = 0; i < N; i++)
            {
                for (var j = 0; j < N; j++)
                {
                    if (A[j] < A[i])
                    {
                        if (j < i) L[i]++;
                        T[i]++;
                    }
                }
            }
            long ans = 0;
            long it = (long)(K + 1) * K / 2;
            it = it % 1000000007;
            for (var i = 0; i < N; i++)
            {
                long add = ((it * T[i]) % 1000000007 + 1000000007) - ((long)K * L[i]) % 1000000007;
                ans += add%1000000007;
                ans = ans%1000000007;
            }
            Console.WriteLine(ans);
        }
    }
}