Place $K$ kings on an $N \times N$ chessboard such that no two kings attack each other. How many ways are there to place them? A king can attack the squares adjacent to it in all 8 directions: up, down, left, right, and the four diagonals (top-left, bottom-left, top-right, bottom-right).
Input
The input consists of a single line containing two integers $N$ and $K$ ($1 \le N \le 9$, $0 \le K \le N \times N$).
Output
The number of ways to place the kings.
Examples
Input 1
3 2
Output 1
16