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 Python (3.4.3) (judge verdict: Accepted)

# jsc2019-qualB - Kleene Inversion
from collections import Counter
from itertools import accumulate


def main():
    N, K = tuple(map(int, input().split()))
    A = tuple(map(int, input().split()))
    MOD = 10 ** 9 + 7
    C = list(Counter(A).values())
    ac = list(accumulate(C[:-1]))
    x = sum(i * j for i, j in zip(C[1:], ac)) % MOD
    y = 0
    for i, a in enumerate(A[:-1]):
        y += sum(b > a for b in A[i + 1 :])
    ans = (x * (1 + K) * K // 2) % MOD
    ans = (ans - y * K) % MOD
    print(ans)


if __name__ == "__main__":
    main()