A Queen Problem

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Points: 7
Time limit: 2.0s
Memory limit: 64M

Author:
Problem type

Yi is an avid chess player. He would like to know how many ways it is possible to place \(K\) queens on an \(N \times N\) chessboard such that no queen is in an attacking position.

The queen can move diagonally, horizontally and vertically, thus combining the properties of a bishop and a rook. Two queens are in the attacking positions if they are on the path of each other.

Input Specification

The first line will contain two integers \(N, K\ (1 \le N \le 10, 1 \le K \le N^2)\).

Output Specification

The number of ways to place \(K\) queens on an \(N \times N\) chessboard such that no queens are in an attacking position.

Sample Input 1

3 2

Sample Output 1

8

Sample Input 2

4 4

Sample Output 2

2

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