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: Wrong Answer)

import sys
import numpy as np
input = sys.stdin.readline

def main():
    N, K = map(int, input().split())
    a = list(map(int, input().split()))

    MOD = int(1e9) + 7

    count = np.zeros((N, 2001), dtype=int)

    count[0][a[0]] += 1
    for i in range(1, N):
        count[i] = count[i-1]
        count[i][a[i]] += 1
    
    for i in range(1, 2001):
        count[:, i] += count[:, i-1]
    # print(count)
    ans = 0
    for i in range(N-1):
        left = count[i][a[i]-1]
        right = count[-1][a[i]-1] - left
        if left + right == 0:
            continue
        start = (left + right) * (K - 1) + right
        end = right
        num = (start - end) // (left + right) + 1
        # print(left, right, start, end, num)
        ans += (num * (start + end)) // 2
        ans %= MOD
        # print((num * (start + end)) // 2)
    print(ans)


if __name__ == "__main__":
    main()