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 PHP (5.6.30) (judge verdict: Runtime Error)

<?php


$input=explode(' ',trim(fgets(STDIN))) ;
$n = $input[0];
$k = $input[1];
$counter = 0 ;

$str=explode(' ',trim(fgets(STDIN))) ;
for($i=0;$i<$k;$i++){
for($ii=$i;$ii<$k;$ii+){
  if($str[$ii]<$str[$i]){
  $counter += $k-1 ;
  }
}}

for($j=0;$j<$k;$j++){
for($jj=0;$jj<$j;$jj+){
  if($str[$jj]<$str[$j]){
  $counter += $k ;
  }
}}

if(strlen($counter)>9){
  $ans_1=substr($counter,0,-9) ;
  $ans_2=substr($counter,strlen($counter)-9) ;
    echo $ans_1*7+$ans_2;
}else{
echo $counter ;
}