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;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Runtime.ExceptionServices;
using System.Security;
using System.Threading;
using System.Xml.Serialization;

namespace AtCoderCs
{

    class Program
    {

        const int mod = 1000000007;

        static void Main()
        {

            var args = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var num = args[0];
            var roop = args[1];
            var data = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            var inner = 0L;
            var outer = 0L;
            var list = new int[2000];

            for (int i = 0; i + 1 < num; i++)
            {
                for (int j = i; j < num; j++)
                {
                    if (data[i] > data[j]) inner++;

                }
                list[data[i] - 1]++;
            }

            list[data[num - 1] - 1]++;

            inner %= mod;
            inner = (inner * roop) % mod;

            outer = ((num * (num - 1)) >> 1) -
                list.Sum(x => (x < 2 ? 0 : ((x * (x - 1)) >> 1)));

            outer %= mod;
            outer *= ((roop * (roop - 1)) >> 1) % mod;

            Console.WriteLine((outer + inner) % mod);

        }



    }
}