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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# coding: utf-8

import sys
import math
import collections
import itertools
def input(): return sys.stdin.readline().strip()
def gcd(x, y): return y if x % y == 0 else gcd(y, x % y)
def lcm(x, y): return (x * y) // gcd(x, y)
MOD = 10 **9 + 7

# N = int(input())
# S = input()
N, K = map(int, input().split())
# 横
A = [int(x) for x in input().split()]
# 縦
# A = [int(input()) for _ in range(N)]
# 多次元
# L = [[int(x) for x in input().split()] for _ in range(N)]

ans = 0
tmp = 0

for i, a in enumerate(A) :
    for aa in range(i, N) :
        if a > A[aa] :
            ans += 1

for a in A :
    for aa in A :
        if a > aa :
            tmp += 1

ans = (ans * K) % MOD
ans %= MOD
ans += int(((tmp * ((K * (K - 1) % MOD) % MOD) / 2)))
ans %= MOD

print(ans)