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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program kadai
   implicit none
    integer  ::  n,k
    integer,allocatable  ::  a(:)
    integer  ::  i,j
    integer(8)  ::  big
    integer(8)  ::  num1,num2,num
    integer(8)  ::  small
    integer(8)  ::  kari

    read(*,*) n,k
    allocate(a(n))
    read(*,*) a

    num=0
    big=0
    small=0
    kari=0

    do i=1,n-1
        do j=i+1,n
            if (a(i)>a(j)) then
                big=big+1
            end if
            if (a(i)<a(j)) then
                small=small+1
            end if
        end do
    end do

    !write(*,*) big,small
    big=mod(big,1000000007)
    small=mod(small,1000000007)

    kari=dble(k-1)*dble(k)/2
    kari=mod(kari,1000000007)
    !write(*,*) kari

    num1=dble(kari)*dble(small)
    num1=mod(num1,1000000007)
    kari=mod(kari+k,1000000007)
    num2=dble(kari)*dble(big)
   ! write(*,*) num1,num2
    num2=mod(num2,1000000007)
   ! write(*,*) num2
    num=mod(num1+num2,1000000007)

    write(*,*) num

stop
contains

end program kadai