Chef has an array with $N$ elements. He wants you to remove exactly $K$ elements from the array such that number of pairs $(i,j)$ where $i$ $<$ $j$ and $A[i]$ $\geq$ $A[j]$ are maximum.

Can you help him with this?

INPUT

First line contains two space separated integers $N$ and $K$.

Next line contains $N$ space separated integers.
 

OUTPUT

Print the maximum number of such pairs.

CONSTRAINTS

1 $\leq$ $N$ $\leq$ 20

1 $\leq$ $K$ $\leq$ 10

1 $\leq$ $A[i]$ $\leq$ 10⁵