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;
class Program
{
	static void Main(string[] args)
	{
		long ans = 0;
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		long K = long.Parse(str[1]);
		long[]A = new long[N];
		string[] str2 = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			A[i] = long.Parse(str2[i]);
		}
		long mod = 1000000007;
		long a = 0;
		for(var i=N-1;i>=0;i--){
			for(var j=i-1;j>=0;j--){
				if(A[j]>A[i]){
					a++;
				}
			}
		}
		long a2 = 0;
		for(var i=N-1;i>=0;i--){
			for(var j=N-1;j>=0;j--){
				if(A[j]>A[i]){
					a2++;
				}
			}
		}
		long b = (K-1)*K/2 % mod;
		ans = a * K % mod + a2 * b % mod;
		Console.WriteLine(ans%mod);
	}
}