A virus infects a bacterium, and modifies a replication process in the bacterium by inserting:

at every A, a polyA of length 1 to 5;

at every C, a polyC of length 1 to 10;

at every G, a polyG of arbitrary length ≥ 1

at every T, a polyT of arbitrary length ≥ 1.

No gaps or other insertions are allowed in the virally modified DNA. For example, the sequence AAATAAAGGGGCCCCCTTTTTTTCC is an infected version of ATAGCTC. Given sequences v and w, describe an efficient algorithm that will determine if v could be an infected version of w.

In this case, W is any original sequene and v is the squence we're comparing to w to see if v is the infected version of it.