# Problem 381: (prime-k) factorial
For a prime p let S(p) = (∑(p-k)!) mod(p) for 1 ≤ k ≤ 5. For example, if
p=7, (7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6! + 5! + 4! + 3! + 2!
= 720+120+24+6+2 = 872. As 872 mod(7) = 4, S(7) = 4. It can be verified
that ∑S(p) = 480 for 5 ≤ p < 100. Find ∑S(p) for 5 ≤ p < 108.