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)

#[allow(unused_imports)]
use std::char::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::*;
use std::str::FromStr;

#[allow(unused_macros)]
macro_rules! debug {($($a:expr),*) => {println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);}}
#[allow(unused_macros)]
macro_rules! input {(source=$s:expr,$($r:tt)*) => {let mut iter=$s.split_whitespace(); let mut next=||{iter.next().unwrap()}; input_inner! {next,$($r)*}};($($r:tt)*) => {let stdin=std::io::stdin();let mut bytes=std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next=move||->String{bytes.by_ref().map(|r|r.unwrap() as char).skip_while(|c|c.is_whitespace()).take_while(|c|!c.is_whitespace()).collect()}; input_inner! {next,$($r)*}};}
#[allow(unused_macros)]
macro_rules! input_inner {($next:expr) => {}; ($next:expr,) => {}; ($next:expr,$var:ident:$t:tt$($r:tt)*) => {let $var=read_value!($next,$t); input_inner! {$next$($r)*}};}
#[allow(unused_macros)]
macro_rules! read_value {($next:expr,($($t:tt),*)) => {($(read_value! ($next,$t)),*)}; ($next:expr, [$t:tt; $len:expr]) => {(0..$len).map(|_|read_value! ($next,$t)).collect::<Vec<_>>()}; ($next:expr,chars) => {read_value! ($next,String).chars().collect::<Vec<char>>()}; ($next:expr,usize1) => {read_value! ($next,usize)-1}; ($next:expr,$t:ty) => {$next().parse::<$t>().expect("Parse error")};}

#[derive(PartialEq, PartialOrd)]
pub struct Total<T>(pub T);
impl<T: PartialEq> Eq for Total<T> {}
impl<T: PartialOrd> Ord for Total<T> {
    fn cmp(&self, other: &Total<T>) -> std::cmp::Ordering {
        self.0.partial_cmp(&other.0).unwrap()
    }
}

#[allow(dead_code)]
const MAX: usize = 100006;
#[allow(dead_code)]
const INF_U32: u32 = 1 << 31;
#[allow(dead_code)]
const INF_I32: i32 = 1 << 30;
#[allow(dead_code)]
const INF_U64: u64 = 1 << 63;
#[allow(dead_code)]
const INF_I64: i64 = 1 << 62;
#[allow(dead_code)]
const MOD: i64 = 1e9 as i64 + 7;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[allow(unused_imports)]
use std::f64;

fn main() {
    input!{n:usize, k:i64, a:[i64;n]};

    let mut cnt1 = vec![0;n];
    let mut cnt2 = vec![0;n];

    for i in 0..n {
        for j in 0..n {
            if a[i] > a[j] {
                cnt1[i] += 1;
                if i < j { cnt2[i]+=1; }
            }
        }
    }
    //debug!(cnt1);
    //debug!(cnt2);
    let mut ans = 0i64;
    for i in 0..n {
        ans += (cnt2[i]*k)%MOD;
        let mut kk = k*(k-1)/2;
        kk %= MOD;
        ans += (cnt1[i]*kk)%MOD;
        ans %= MOD;
    }
    println!("{}", ans);
}