Non-aggression

Problem Source

SCOI2005

Problem Description

Place $k$ kings on an $n \times n$ chessboard so that they do not overlap and do not attack each other. Count the number of valid placements.

Each king attacks the $8$ squares around it.

Input Format

One line containing two integers $n, k$.

Output Format

Output one line containing a number: the number of placements.

Sample Input

3 2

Sample Output

16

Constraints

For all data, $1 \leq n \leq 9, 0 \leq k \leq n^2$.