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Time Limit: 1 s Memory Limit: 128 MB Total points: 100

#15151. No Kings

Statistics

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

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