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.Arrays;
import java.util.Scanner;

public class Main {

    void run() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long k = sc.nextInt();

        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }

        int[] b = new int[n], c = new int[n];
        for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {
            if (i < j && a[i] > a[j]) {
                b[j]++;
            }
            if (a[i] > a[j]) {
                c[j]++;
            }
        }


        long MOD = (long)(1e9) + 7;
        long INV2 = (MOD + 1) / 2;
        long cnt = 0;
        for (int i = 0; i < n; i++) {
            cnt = (cnt + k * b[i]) % MOD;
            long mult = k * c[i] % MOD * (k - 1) % MOD * INV2 % MOD;
            cnt = (cnt + mult) % MOD;
        }
        System.out.println(cnt);
    }

    void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}