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: Accepted)

base = 10^9 + 7

-- O(N^2)で十分と解説にあったので比較
doCount :: [Int] -> [(Integer,Integer)]
doCount as = loop [] as
  where
    cnt v xs = fromIntegral $ length $ filter (v >) xs
    loop as (b:bs) = (cnt b as, cnt b bs) : loop (b:as) bs
    loop _ [] = []
  
compute :: Integer -> Integer -> [Int] -> Integer
compute n k as = foldl1 add $ map f $ doCount as
  where
    f (x, y) = k * y + k * (k-1) * (x+y) `div` 2
    add x y = (x+y) `mod` base

main = do
  li <- getLine
  let [n,k] = map read $ words li
  li <- getLine
  let as = map read $ words li
  let ans = compute n k as
  print ans