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::*;

const SP: u8 = b' ';
const LF: u8 = b'\n';

struct CharacterInput<'a> {
    locked_stdin: StdinLock<'a>,
    bytes_buffer: Vec<u8>,
}

impl<'a> CharacterInput<'a> {
    fn read(&mut self, delimiter: u8) -> &[u8] {
        self.bytes_buffer.clear();

        let len = self
            .locked_stdin
            .read_until(delimiter, &mut self.bytes_buffer)
            .unwrap();

        let end_index = match self.bytes_buffer.last() {
            Some(byte) => {
                if *byte == delimiter {
                    len - 1
                } else {
                    len
                }
            }
            None => len,
        };

        &self.bytes_buffer[0..end_index]
    }

    fn scan_u(&mut self, delimiter: u8) -> u32 {
        self.read(delimiter)
            .into_iter()
            .fold(0, |accumulator, byte| {
                (byte - b'0') as u32 + accumulator * 10
            })
    }

    fn scan_u_vec(&mut self, n: usize, separator: u8, delimiter: u8) -> Vec<u32> {
        let mut vector = Vec::with_capacity(n as usize);
        for _i in 0..n - 1 {
            vector.push(self.scan_u(separator));
        }
        vector.push(self.scan_u(delimiter));
        vector
    }
}

fn create_cin<'a>(input: StdinLock<'a>, buffer_capacity: usize) -> CharacterInput {
    CharacterInput {
        locked_stdin: input,
        bytes_buffer: Vec::with_capacity(buffer_capacity),
    }
}

fn println<T: std::string::ToString>(s: T) {
    println!("{}", s.to_string());
}

// ------------------------------------------------------------------------

fn main() {
    let cin = stdin();
    let cin = &mut create_cin(cin.lock(), 64);

    let n = cin.scan_u(SP) as usize;
    let k = cin.scan_u(LF) as usize;
    let a = cin.scan_u_vec(n, SP, LF);

    let mut count: usize = 0;
    let k_tri = k * (k + 1) / 2;
    let k_minus_one_tri = (k - 1) * k / 2;

    for i in 0..n {
        let a_1 = a[i];
        let mut former_count = 0;
        if i > 0 {
            for m in 0..i {
                let a_2 = a[m];
                if a_1 > a_2 {
                    former_count += 1;
                }
            }
        }
        let mut latter_count = 0;
        for m in i + 1..n {
            let a_2 = a[m];
            if a_1 > a_2 {
                latter_count += 1;
            }
        }
        // count = (count + former_count * k_minus_one_tri) % 1000000007;
        // count = (count + latter_count * k_tri) % 1000000007;
        count = (0..former_count).fold(count, |acc, _cur| (acc + k_minus_one_tri) % 1000000007);
        count = (0..latter_count).fold(count, |acc, _cur| (acc + k_tri) % 1000000007);
    }

    println(count);
}