Description

给定颜色种数和环上的珠子总数，问有多少种染色方案（通过旋转和翻转相同的算同一种）。

Format

Input

Every line of the input defines a test case and contains two integers: the number of available colors c followed by the length of the bracelets s. Input is terminated by c = s = 0. Otherwise, both are positive, and, due to technical difficulties in the bracelet-fabrication-machine, cs <= 32, i.e. their product does not exceed 32.

Output

For each test case output on a single line the number of unique bracelets. The figure below shows the 8 different bracelets that can be made with 2 colors and 5 beads.

Samples

1 1
2 1
2 2
5 1
2 5
2 6
6 2
0 0

1
2
3
5
8
13
21