Description

Original problem from: SGU 223

Place $k$ kings on an $n \times n$ chessboard such that no two kings attack each other. A king can attack all 8 adjacent squares. Find the total number of valid configurations.

Input Format

A single line containing two integers $n$ and $k$.

Output Format

Output the total number of valid configurations. If it's impossible to place the kings, output $0$.

Sample 1

3 2

16

Sample 2

4 4

79

Constraints & Notes

For all test cases, $1\le n\le 10$, $0\le k\le n^2$.