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 C++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include<iostream>
#include<cstdio>
#include<stack>
#include<queue>
#include<algorithm>
#include<string>
#include<set>
#include<map>
#include<vector>
#include<math.h>
#include<tuple>
#include<string.h>
#include <numeric> 
#include<unordered_map>
using namespace std; 
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
  enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (auto it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define pp(...) "\033[94m [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "]\033[0m"
#define pp1(...) "\033[1;47;35m" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "]\033[0m"
#define dg(x) debug() << pp1(x)
#define dg1(x) debug() << pp(x)
#define dg2(x,y) debug() << pp(x) pp(y)
#define dg3(x,y,z) debug() << pp(x) pp(y) pp(z)
#define dg4(w,x,y,z) debug() << pp(w) pp(x) pp(y) pp(z)
#define int long long
#define all(x) x.begin() , x.end()
#define clr(x) memset(x , 0 , sizeof x);
#define sz(x) (int)x.size()
template<typename T> void db(T x ){ debug() <<">>> " <<  x; }
template<typename T> void db(T x , T y){ debug() <<">>> " <<  x <<" , "<< y; }
template<typename T> void db(T x , T y , T z){ debug() <<">>> "<< x <<" , "<< y <<" , "<< z; }
template<typename T> void db(T x , T y , T z , T a){ debug() <<">>> "<< x <<" , " << y <<" , "<< z <<" , "<< a; }
const int xx = 2e5;
const int Mod = 1e9 + 7;
const int inf = 1e18;
const int Maxn = 20010;
auto in = [](auto &&... args) { (cin >> ... >> args); };


signed main(){
  ios::sync_with_stdio(false);
  cin.tie(0);
  
  int n , k;
  cin >> n >> k;
  vector<int> a(n);
  for(int i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<int>inversion(n) , Cnt(n);

  for(int i = 0; i < n ; i++) {
    int c = 0;
    for(int j = i + 1; j < n; j++) {
      if(a[j] < a[i]) c++;
    }
    inversion[i] = c;

    c = 0;
    for(int j = 0; j < n; j++) {
      if(i == j) continue;
      if(a[j] < a[i]) c++;
    }
    Cnt[i] = c;
  }
  dg(inversion);dg(Cnt);
  int ans = 0;
  int K = (k * (k - 1) / 2);
  for(int i = 0; i < n; i++) {
    int x = (inversion[i] * k) % Mod;
    int y = ( K * Cnt[i]) % Mod;
    ans += (x + y) % Mod;
    ans = ans % Mod; 
  }
  cout << ans << '\n';
}