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_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]



#[allow(unused_macros)]
macro_rules! invec {
    ( $ t : ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s
                .trim()
                .split_whitespace()
                .map(|s| s.parse::<$t>().unwrap())
                .collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }};
}

#[allow(unused_macros)]
macro_rules! get {
      ($t:ty) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.trim().parse::<$t>().unwrap()
          }
      };
      ($($t:ty),*) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              let mut iter = line.split_whitespace();
              (
                  $(iter.next().unwrap().parse::<$t>().unwrap(),)*
              )
          }
      };
      ($t:ty; $n:expr) => {
          (0..$n).map(|_|
              get!($t)
          ).collect::<Vec<_>>()
      };
      ($($t:ty),*; $n:expr) => {
          (0..$n).map(|_|
              get!($($t),*)
          ).collect::<Vec<_>>()
      };
      ($t:ty ;;) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.split_whitespace()
                  .map(|t| t.parse::<$t>().unwrap())
                  .collect::<Vec<_>>()
          }
      };
      ($t:ty ;; $n:expr) => {
          (0..$n).map(|_| get!($t ;;)).collect::<Vec<_>>()
      };
}

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [$t:tt]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}


#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    ($arg:expr) => (println!("{:?}",$arg));
}


#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}


use std::cmp;
use std::collections::HashMap;


#[allow(dead_code)]
static INF_I64 :i64 = 9223372036854775807;
#[allow(dead_code)]
static INF_I32 : i32 = 2147483647;
#[allow(dead_code)]
static INF_USIZE : usize = 18446744073709551615;

use std::ops::{ Add, Sub , Div , Mul };

#[derive(Debug,Copy,Clone)]
pub struct ModInt {
    x : i64,
    global_mod: i64
}


impl ModInt{
    pub fn  new (p:i64) -> Self {
        let gm =1000000007;
        let a = (p % gm + gm)% gm;     
        return ModInt{x:a,global_mod:gm};
    }

    pub fn inv (self) -> Self{
        return self.pow(self.global_mod-2);

    }

    pub fn pow (self , t:i64) -> Self{
        if(t==0 ) {return ModInt::new(1)};
        let mut a = self.pow(t>>1);
        a = a*a;
        if(t&1 != 0) {a = a* self};
        return a;
    }
}


impl Add for ModInt {
    type Output = ModInt;
    fn add(self,other : ModInt) -> ModInt{
        let ret  = self.x + other.x ;
        return ModInt::new(ret);
    }
}


impl Sub for ModInt {
    type Output = ModInt;
    fn sub(self,other : ModInt) -> ModInt{
        let ret  = self.x - other.x;
        return ModInt::new(ret);
    }
}


impl Mul for ModInt {
    type Output = ModInt;
    fn mul(self,other : ModInt) -> ModInt{
        let ret  = self.x * other.x ;
        return ModInt::new(ret);
    }
}


impl Div for ModInt {
    type Output = ModInt;
    fn div(self,other : ModInt) -> ModInt{
        let ret  = self.x * other.inv().x;
       return ModInt::new(ret);
    }
}


impl std::string::ToString for ModInt{
    fn to_string(&self) -> String{
        return self.x.to_string();
    }
}



fn main() {

    input! { 
       n: usize,
       k : usize,
       a: [usize;n],
    }

    let mut ans = 0_usize;
    let mut tmp = 0_usize;
    let mut tmp2 = 0_usize;
    for i in 0..n-1{
        for j in i+1..n{
            if a[i] > a[j] {
                tmp+=1;
            }
        }
    }

    for i in 0..n{
        for j in 0..n{
            if a[i] > a[j] {
                tmp2 +=1;
            }
        }
    }

    let mut ans2 = tmp * k;
    let ans3 =  ModInt::new(ans2 as i64) + ModInt::new(tmp2 as i64) * ModInt::new((k as i64)-1) * ModInt::new(k as i64) / ModInt::new(2);
    
    
    
    
    println!("{}", ans3.to_string());
    


}