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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdint.h>

int main(){
    long long int N,K,A[2000];
    long long int i,j;
    long long int inv=0,temp;
    scanf("%lld %lld",&N,&K);
    for(i = 0 ; i < N ; i++){
        scanf("%lld",&A[i]);
    }
    for(i = 0 ; i < N  ; i++){
        for(j = i+1 ; j < N ; j++){
            if(A[i] > A[j]){
                inv += K;
            }
        }
    }

    for(i = 0 ; i < N ; i++){
        for(j = 0 ; j < N ; j++){
            if(A[i] > A[j]){
                inv += (K - 1)*K/2;
            }
        }
    }
    printf("%lld",inv % 1000000007);
    return 0;
}