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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	static int MOD=1000000007;
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String[] s=br.readLine().split(" ");
		int N=Integer.parseInt(s[0]);
		int k=Integer.parseInt(s[1]);
		s=br.readLine().split(" ");
		int[] A=new int[N];
		for(int i=0;i<N;i++){
			A[i]=Integer.parseInt(s[i]);
		}
		HashMap<Integer,Integer> hm=new HashMap<>();
		for(int i=0;i<N;i++){
			int count=0;
			for(int j=0;j<N;j++){
				if(A[j]<A[i])
					count++;
			}
			hm.put(i,count);
		}
		//System.out.println(hm);
		long total=0;
		long factor=((long)k*((long)k-1));
		factor>>=1;
		factor%=MOD;
		for(int i=0;i<N;i++){
			total=(total+((hm.get(i)%MOD)*(factor)%MOD)%MOD);
		}
		int sum=0;
		int[] small=new int[N];
		for(int i=0;i+1<N;i++){
			for(int j=i+1;j<N;j++){
				if(A[i]>A[j]){
					small[i]++;
				}
			}
		}
		//System.out.println();
		for(int i=0;i<N;i++){
			sum=sum+small[i];
		}
		total=(total+((sum%MOD)*(k%MOD))%MOD)%MOD;
		System.out.println(total);
	}
}