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 !