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 Ruby (2.7.1) (judge verdict: Accepted)

MOD = 10**9+7
n,k = gets.chomp.split(" ").map(&:to_i)
a = gets.chomp.split(" ").map(&:to_i)
b = Array.new(n,0)
n.times do |i|
  x = a[i]
  (n-1).times do |j|
    if x > a[(i+j+1)%n]
      b[i] += 1
    end
  end
end
ans = 0
n.times do |i|
  ans += (b[i] * (k-1) * k / 2) % MOD
  ans %= MOD
end
for i in 0..n-2
  for j in (i+1)..n-1
    if a[i] > a[j]
      ans += k
      ans %= MOD
    end
  end
end
puts ans