A bishop is a piece used in the game of chess which is played on a board of square grids. A bishop can only move diagonally from its current position. Two bishops attack each other if one is on the path of the other. In the following figure, the dark squares represent the reachable locations for bishop B1 from its current position. The figure also shows that the bishops B1 and B2 are in attacking positions, whereas B1 and B3 are not. B2 and B3 are also in non-attacking positions.
Given two numbers n and k, your job is to determine the number of ways that one can put k bishops on an n × n chessboard so that no two of them are in attacking positions.
The input file may contain multiple test cases. Each test case occupies a single line in the input file and contains two integers: n (1 ≤ n ≤ 8) and k (1 ≤ k ≤ n2).
A test case containing two zeros for n and k terminates the input. (You do not need to process this particular input.)
2 2 2 3 4 4 8 6 8 12 0 0
For each test case in the input, print a line containing the total number of ways that one can put the given number of bishops on a chessboard of the given size so that no two of them are in attacking positions. You may safely assume that this number will be less than 1015.
4 0 260 5599888 489536
To Rezaul Alam Chowdhury.