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(non_snake_case)]
#[allow(unused_imports)]
use std::io::{self, Write};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
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)*}
    };
}
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)*}
    };
}
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, char) => {
        read_value!($next, String).chars().collect::<Vec<char>>()[0]
     };
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
     };
    ($next:expr, isize1) => {
        read_value!($next, isize) - 1
    };
     ($next:expr, $t:ty) => {
         $next().parse::<$t>().expect("Parse error")
    };
}
macro_rules! printvec {
    ( $item:expr ) => {
        for &i in &$item {
            print!("{} ", i);
        }
        println!("");
    }
}
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}
#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);
impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}
#[derive(PartialEq, PartialOrd, Clone, Debug)]
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>) -> Ordering {
        self.0.partial_cmp(&other.0).unwrap()
    }
}
#[allow(dead_code)]
const MOD: usize = 1000000007;
#[allow(dead_code)]
fn factorial(n: usize) -> usize {
    (1..n+1).into_iter().fold(1, |acc, i| acc * i)
}
#[allow(dead_code)]
fn comb(n: usize, r: usize) -> usize {
    if n - r < r {
        comb(n, n - r)
    } else {
        (1..r+1).into_iter().fold(1, |acc, i| acc * (n - r + i) / i)
    }
}


fn main() {
    input!{
        N: usize, K: usize,
        A: [usize; N],
    }

    let mut inner = vec![0; N];

    for i in 0..N {
        for j in 0..N {
            if A[i] > A[j] {
                inner[i] += 1;
            }
        }
    }

    let mut right = vec![0; N];

    for i in 0..N {
        for j in i..N {
            if A[i] > A[j] {
                right[i] += 1;
            }
        }
    }

    let mut ans = 0;

    for i in 0..N {
        ans += (((K * (K - 1) / 2 ) % MOD) * inner[i] + K * right[i]) % MOD;
        ans %= MOD;
    }

    println!("{}", ans);
}