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: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

namespace ConsoleApp1 {
    public class Class1 {
        static void Main(string[] args) {
            var RL = Console.ReadLine().Trim().Split().Select(long.Parse).ToArray();
            var N = RL[0];
            var K = RL[1];
            var A = Console.ReadLine().Trim().Split().Select(long.Parse).ToArray();
            var mod = 1000000007;

            var a1 = new long[N];
            var a2 = new long[N];
            for(var i = 0;i < N; i++) {
                a1[i] = A.Skip(i).Take((int)N - i).Count(x => x < A[i]);
                a2[i] = A.Count(x => x < A[i]);
            }
            var t1 = ((a1.Sum() * K)) % mod;
            var t2 = (a2.Sum() * (((K - 1) * K) % mod) / 2 )% mod;
            var ans = (t1+ t2) % mod;
            Console.Write(ans);
        }
    }
}