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 Python (3.4.3) (judge verdict: Wrong Answer)

from sys import stdin
from collections import defaultdict, deque, Counter
import sys
from bisect import bisect_left
import heapq
import math

sys.setrecursionlimit(1000000000)
MIN = -10 ** 9
MOD = 10 ** 9 + 7
INF = float("inf")
IINF = 10 ** 18

#n = int(stdin.readline().rstrip())
#l = list(map(int, stdin.readline().rstrip().split()))
n,k = map(int, stdin.readline().rstrip().split())
#S = [list(stdin.buffer.readline().decode().rstrip()) for _ in range(h)]
A = list(map(int, stdin.readline().rstrip().split()))

a_tento = 0
for i in range(n-1):
    for j in range(i+1,n):
        if A[i] > A[j]:
            a_tento += 1

a_inten = 0
for i in range(n):
    for j in range(n):
        if A[i] > A[j]:
            a_inten += 1

a_inten = a_inten - a_tento

print(int((a_tento*(k*(k+1)/2)+ a_inten*((k*(k-1)/2)))  %MOD))