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 a1 and an, how many eigensequences (of any length) start with a1 and end with an?
Input has many data lines, followed by a terminating line. Each line has two integers, a1 and an. If a1 < an, it's a data line. Otherwise it's a terminating line that should not be processed. On each line, 0 ≤ a1 ≤ an ≤ 44. This guarantees that each output fits into 32 bit integer.
For each data line, print a line with a1, an, and x, where x is the number of eigensequences (of any length) that start with a1 and end with an.
0 3 5 7 2 8 0 0
0 3 3 5 7 1 2 8 12