Unequal vector multiplication

I have a 4 row vector (A) and a 2 row vector (B) and I want to multiply the 1st two row elements of (A) each by the first element of (B) and the 3rd & 4th row elements of (A) each by the 2nd row element of (B). I want to do this element by element to give me a 4 row vector at the end. It's made more complicated by the fact the numbers of rows in both vectors can change although (A) will always have twice the number of rows as (B). I thought of trying to match the number of rows in (B) to (A) so I can simply multiply the two but not sure how to go about this. 

Any help appreciated.