# Eigensequence

Given an increasing sequence of integers a1, a2, a3, . . . , ak, the E-transform produces a sequence of the samelength,b1,b2,b3,...,bk suchthat • b1 = a1 • for j > 1, bj is the only integer aj−1 < bj ≤ aj, which is divisible byaj − aj−1. 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 Input has many data lines, followed by a terminating line. Each line has two integers, a1 and an. If a1 < n, 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. Output 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 03 57 28 00 Sample Output 033 571 2 8 12