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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

{-# LANGUAGE OverloadedStrings #-}
import Data.Maybe
import Data.Char
import Data.List
import qualified Data.ByteString.Char8 as BS
import qualified Data.Vector.Unboxed as VU

modInt = 10^9+7

main = do
  [n, k] <- getIntList
  ns <- getIntList
  let ms = mkpair [] ns
  print . foldr (((`mod` modInt).).(+)) 0 . map (f k) $ ms
    where
      both f (a, b) = (f a, f b)
      mkpair _ [] = []
      mkpair ps (q:qs) = both (length . filter (<q)) (ps, qs) : mkpair (q:ps) qs
      f k (p, q) = k * ((p + q) * k + (q - p)) `div` 2

-- IO
readInt :: BS.ByteString -> Int
readInt = fst . fromJust . BS.readInt

getInt :: IO Int
getInt = readInt <$> BS.getLine

getIntList :: IO [Int]
getIntList = unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

getIntVec :: Int -> IO (VU.Vector Int)
getIntVec n = VU.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine