Suppose that A = {$\displaystyle a_1,a_2,...$} and B = {$\displaystyle b_1,b_2,...$} and that A contains arbitrarily large arithmetic progressions. Suppose there exists a K such that, for all n, $\displaystyle |b_n-a_n|\leq K$. Prove that B contains arbitrarily large arithmetic progressions.

I am having a hard time applying Van der Waerden's Theorem to the set B using only the information given. I know I am overlooking something, but I am not sure what. Thanks.