Little Bishops#2352
A bishop is a piece used in the game of chess played on a square board. A bishop can only move diagonally from its current position, and two bishops can attack each other if one is on the path of the other. In the following figure, the dark squares show the possible moves for bishop B1 from its current position. Bishops B1 and B2 attack each other, while B1 and B3 do not. B2 and B3 also do not attack each other.
Given two numbers and , determine the number of ways to place bishops on an n \times n chessboard so that no two bishops attack each other.
Each line is a separate test and contains two integers: (1 \leq n \leq 8) and (0 \leq k \leq n^2). The last test contains two zeros and should not be processed.
For each test, print on a separate line the number of ways to place the given number of bishops on an n \times n chessboard so that no two bishops attack each other. It is guaranteed that the answer will always be less than 10^{15}.
Example 1