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 AtCoder1
{
    class Program2
    {
        static void Main()
        {
            // A の中の転倒数*K + 別のAに存在する転倒数を Σ(K-1) * それぞれの値

            var input = Console.ReadLine().Split(' ').Select(long.Parse);
            var N = input.First();
            var K = input.Skip(1).First();
            var A = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var m = (long)Math.Pow(10, 9) + 7;

            decimal ans = 0;
            for (int i = 1; i < N; i++)
            {
                var tmp = 0L;
                for (int j = 0; j < i; j++)
                {
                    if (A[j] > A[i]) tmp++;
                }

                ans += (tmp % m) * K % m;
                ans %= m;
            }

            decimal sigma = K * (K - 1) / 2;

            for (int i = 0; i < N; i++)
            {
                var tmp = 0L;
                for (int j = 0; j < N; j++)
                {
                    if (A[j] > A[i]) tmp++;
                }

                ans += sigma * tmp % m;
                ans %= m;
            }

            Console.WriteLine(ans);
        }
    }
}