Fast way to calculate n! mod m where m is prime?

I was curious if there was a good way to do this. My current code is something like:

def factorialMod(n, modulus):
    ans=1
    for i in range(1,n+1):
        ans = ans * i % modulus    
    return ans % modulus

But it seems quite slow!

I also can't calculate n! and then apply the prime modulus because sometimes n is so large that n! is just not feasible to calculate explicitly.

I also came across http://en.wikipedia.org/wiki/Stirling%27s_approximation and wonder if this can be used at all here in some way?

Or, how might I create a recursive, memoized function in C++?