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.Linq;
using System.Numerics;

class B
{
	static void Main()
	{
		var M = 1000000007;
		var h = Console.ReadLine().Split().Select(int.Parse).ToArray();
		var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
		int n = h[0];
		BigInteger k = h[1];

		var m1 = new int[n];
		var m2 = new int[n];
		for (int i = 0; i < h[0]; i++)
		{
			for (int j = 0; j < i; j++) if (a[j] < a[i]) m1[i]++;
			for (int j = i + 1; j < n; j++) if (a[j] < a[i]) m2[i]++;
		}
		Console.WriteLine((k * (k - 1) / 2 * m1.Aggregate((x, y) => (x + y) % M) + k * (k + 1) / 2 * m2.Aggregate((x, y) => (x + y) % M)) % M);
	}
}