Consider the problem of computing ord_b1 a, ord_b2 a, ..., ord_bk a,
given positive integers a, b1, ..., bk, with each bi prime. Here ord_q a
means the largest integer e such that a mod q^e = 0.

For example, if the input is 600, 2, 5, then the output is 3, 2. (The
complete factorization of 600 is 2^3 3^1 5^2.)

State an algorithm that solves this problem in time n^{1+o(1)}, where n
is the number of bits of input.