Problem E: Eigensequence

Given an increasing sequence of integers a1, a2, a3, ..., ak, the E-transform produces a sequence of the same length, b1, b2, b3, ..., bk such that For example, from S = 0, 1, 4, 9, 16, 25, 36, 49 one gets E(S) = 0, 1, 3, 5, 14, 18, 33, 39.

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.

Sample input

0 3
5 7
2 8
0 0

Output for sample input

0 3 3
5 7 1
2 8 12

Don Reble