Problem Solving

For every positive integer n, the function h(n) is defined to be the product of all 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 10
B) between 10 and 20
C) between 20 and 30
D) between 30 and 40
E) greater than 40

Please provide the answer with explanation.