Description

Input

The first line contains two integers $n$ and $k$ ($1 \le n \le 5000$, $1 \le k \le 8$).

The second line contains $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \le p_i \le n$).

Output

Print the minimum possible number of inversions in the permutation $q$.

1 1
1

0

3 1
2 3 1

1

5 2
5 4 3 2 1

6

10 3
5 8 6 10 2 7 4 1 9 3

18

Note

In the first example, the only permutation is $q = [1]$ ($0$ inversions). Then $p_{q_1} = 1$.

In the second example, the only permutation with $1$ inversion is $q = [1, 3, 2]$. Then $p_{q_1} = 2$, $p_{q_2} = 1$, $p_{q_3} = 3$.

In the third example, one of the possible permutations with $6$ inversions is $q = [3, 4, 5, 1, 2]$. Then $p_{q_1} = 3$, $p_{q_2} = 2$, $p_{q_3} = 1$, $p_{q_4} = 5$, $p_{q_5} = 4$.