AMC 8 2007 Problem 13

Sets $A$ and $B$, shown in the Venn diagram, have the same number of elements. Their union has $2007$ elements and their intersection has $1001$ elements. Find the number of elements in $A$.

$\mathrm{(A)}\ 503 \mathrm{(B)}\ 1006 \mathrm{(C)}\ 1504 \mathrm{(D)}\ 1507 \mathrm{(E)}\ 1510$