Score : $300$ points

Problem Statement

We have a sequence of $N$ integers $A \sim = \sim A_0, \sim A_1, \sim ..., \sim A_{N - 1}$.

Let $B$ be a sequence of $K \times N$ integers obtained by concatenating $K$ copies of $A$. For example, if $A \sim = \sim 1, \sim 3, \sim 2$ and $K \sim = \sim 2$, $B \sim = \sim 1, \sim 3, \sim 2, \sim 1, \sim 3, \sim 2$.

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 $(i, \sim j) \sim (0 \leq i < j \leq K \times N - 1)$ 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 $10^9 + 7$.

2 2
2 1

3

In this case, $B \sim = \sim 2, \sim 1, \sim 2, \sim 1$. We have:

• $B_0 > B_1$
• $B_0 > B_3$
• $B_2 > B_3$

Thus, the inversion number of $B$ is $3$.

3 5
1 1 1

0

$A$ may contain multiple occurrences of the same number.

10 998244353
10 9 8 7 5 6 3 4 2 1

185297239

Be sure to print the output modulo $10^9 + 7$.