Little Elephant and Strings

A Little Elephant from the Zoo of Lviv likes lucky strings, i.e., the strings that consist only of the lucky digits 4 and 7. The Little Elephant has K favorite lucky strings A1, A2, ..., AK. He thinks that the lucky string S is good if either |S| ≥ 47 or for some j from 1 to K we have that Aj is a substring of S. The Little Elephant has found N lucky strings B1, B2, ..., BN under the pillow. Now