A sequence S such that E(S)=S is called an eigensequence. For instance, S = 2,3,4,6,8,12,16,18,20 is an eigensequence.
Given integers a_{1} and a_{n}, how many eigensequences (of any length) start with a_{1} and end with a_{n}?
Input has many data lines, followed by a terminating line. Each line has two integers, a_{1} and a_{n}. If a_{1} < a_{n}, it's a data line. Otherwise it's a terminating line that should not be processed. On each line, 0 ≤ a_{1} ≤ a_{n} ≤ 44. This guarantees that each output fits into 32 bit integer.
For each data line, print a line with a_{1}, a_{n}, and x, where x is the number of eigensequences (of any length) that start with a_{1} and end with a_{n}.
0 3 5 7 2 8 0 0
0 3 3 5 7 1 2 8 12