Bishops#3058
A bishop is a chess piece played on a square board. A bishop moves only diagonally, and two bishops attack each other if one is on the path of the other. In the figure, the dark squares indicate the possible moves for bishop B1 from its current position. Bishops B1 and B2 attack each other, but B1 and B3 do not. B2 and B3 do not attack each other.
Given 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 contains a test case with two integers (1 \leq n \leq 30) and (0 \leq k \leq n^2). The last test case contains two zeros and should not be processed.
For each test case, output a line with the number of ways to place bishops on an n \times n chessboard so that no two bishops attack each other. The answer will always be less than 10^{15}.
Example 1