For every positive even integer \(n,\) the function \(h(n)\) is defined to be the product of all the even integers from 2 to \(n,\) inclusive. If \(p\) is the smallest prime factor of \(h(100) +1,\) then \(p\) is?

A. Between 2 and 20
B. Between 10 and 20
C. Between 20 and 30
D. Between 30 and 40
E. Greater than 40

[spoiler]OA=E[/spoiler]

Source: GMAT Prep