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 and 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 ** B_{1}** form its current
position. The figure also shows that the bishops

Now, given two numbers **n** and **k**, your job is to determine the
number of ways 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 ≤ 30)** and **k (0 ≤ k ≤ n ^{2})**.

A test case containing two zeros
for **n** and **k** terminates the input and you
won’t need to process this particular input.

For each test case in the input
print a line containing the total number of ways 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 **10 ^{15}**.

** **

8 6

4 4

20 40

30 5

0 0

** **

5599888

260

0

3127859642656

**(World Finals Warm-up Contest,
Problem setter: Rezaul Alam Chowdhury)**