Show that for n,k$\displaystyle \in \mathbb{N}$, there exists W*=W*(n,k) such that if the interval {1, 2, ..., W*(n,k)} is k-colored, then there will be a monochromatic arithmetic progression of length n and the common difference of the arithmetic progression is of the same color.

I know that the first condition is simply Van der Waerden's Theorem. But I don't see how to incorporate the second condition in order to prove existence. Thanks.