Let a>0, and let P(x) be a polynomial with integer coefficients such that
\begin{aligned} P(1)=P(3)=P(5)=P(7)=a, \text { and } P(2)=P(4)=P(6)=P(8)=-a . \end{aligned}
What is the smallest possible value of a ?
Answer Choices
A. 105
B. 315
C. 945
D. 7 !
E. 8 !