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: Accepted)

import java.util.*;
public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    long k = sc.nextLong();
    int[] a = new int[n];
    long mod = 1000000007;
    long sum = 0;
    long cnt1 = 0;
    long cnt2 = 0;
    for(int i = 0;i < n;i++)a[i]=sc.nextInt();
    for(int i = 0;i < n;i++){
      for(int j = i+1;j < n;j++)if(a[i]>a[j])cnt1++;
    }
    sum = (sum+cnt1*k)%mod;
    for(int i = 0;i < n;i++){
      for(int j = 0;j < n;j++)
        if(a[i]>a[j])cnt2++;
    }
    long kk = (k*(k-1)/2)%mod;
    long s = (cnt2*kk)%mod;
    sum=(sum+s)%mod;
    System.out.println(sum);
  }
}