I could just start cutting them off

Algebra Level 4

$a = \dfrac{1^2}{1} + \dfrac{2^2}{3} + \dfrac{3^2}{5}+\ldots + \dfrac{1001^2}{2001}\\ b = \dfrac{1^2}{3} + \dfrac{2^2}{5} + \dfrac{3^2}{7}+\ldots+ \dfrac{1001^2}{2003}$

Define $a,b$ as above. What is the closest integer to $(a- b)$ ?