Time Limit: Java: 2000 ms / Others: 2000 ms
Memory Limit: Java: 65536 KB / Others: 65536 KB
A bracelet is a ring-like sequence of s beads each of which can have one of c distinct colors. The ring is closed, i.e. has no beginning or end, and has no direction. Assume an unlimited supply of beads of each color. For different values of s and c, calculate the number of different bracelets that can be made.
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.
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.