Let \[ \begin{array}{ccccccccccc} A &=& 5 \cdot 6 &-& 6 \cdot 7 &+& 7 \cdot 8 &-& \cdots &+& 2003 \cdot 2004, \\ B &=& 1 \cdot 10 &-& 2 \cdot 11 &+& 3 \cdot 12 &-& \cdots &+& 1999 \cdot 2008. \end{array} \] 
Find the value of $A-B$.

Let's think step by step and output the final answer within \boxed{}.
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