AMC 12 2001 Problem 21

Four positive integers a, b, c, and d have a product of 8 ! and satisfy

\begin{aligned} a b+a+b=524 \\ b c+b+c=146, \text { and } \\ c d+c+d=104 \end{aligned}

What is a-d ?

Answer Choices
A. 4
B. 6
C. 8
D. 10
E. 12