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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::{BufRead, BufWriter, Write};

const P: usize = 1000000007;

fn main() {
    let stdin = std::io::stdin();
    let stdout = std::io::stdout();
    solve(&mut stdin.lock(), &mut BufWriter::new(stdout.lock()));
}

fn solve<R: BufRead, W: Write>(stdin: &mut R, stdout: &mut BufWriter<W>) {
    let (n, k): (usize, usize) = stdin.gets().split(' ').values();
    let alist = stdin.gets().split(' ').map(|x| x.parse().unwrap()).collect::<Vec<u32>>();

    let mut x = 0;
    for i in 0..n {
        for j in i + 1..n {
            if alist[i] > alist[j] {
                x += 1;
            }
        }
    }
    let mut ans = k * x;
    x = 0;
    for i in 0..n {
        for j in 0..n {
            if i != j && alist[i] > alist[j] {
                x += 1;
            }
        }
    }
    ans = (k * (k - 1) / 2 % P * x + ans) % P;
    writeln!(stdout, "{}", ans).unwrap();
}

trait Gets { fn gets(&mut self) -> String; }
impl<T: std::io::BufRead> Gets for T {
    fn gets(&mut self) -> String { self.lines().next().unwrap().unwrap() } }

trait Values<T> { fn values(&mut self) -> T; }
impl<'a, I, T1, T2> Values<(T1, T2)> for I
    where I: Iterator<Item=&'a str>,
          T1: std::str::FromStr, T1::Err: std::fmt::Debug,
          T2: std::str::FromStr, T2::Err: std::fmt::Debug {
    fn values(&mut self) -> (T1, T2) {
        (self.next().unwrap().parse().unwrap(),
         self.next().unwrap().parse().unwrap())
    }
}