Calculating n! mod m when m is not prime

I have read a lot of good algos to calculate n! mod m but they were usually valid when m was prime . I wanted to know whether some good algo exists when m is not prime .I would be helpful if someone could write the basic function of the algo too.I have been using

long long factMOD(long long n,long long mod)
{
    long long res = 1; 
    while (n > 0)
    {
        for (long long i=2, m=n%mod; i<=m; i++)
        res = (res * i) % mod;
        if ((n/=mod)%2 > 0) 
        res = mod - res;
    }
    return res;
}

but getting wrong answer when I try to print factMOD(4,3) even. source of this algo is :
http://comeoncodeon.wordpress.com/category/algorithm/

This is what I've come up with:

#include <stdio.h>
#include <stdlib.h>

unsigned long long nfactmod(unsigned long long n, unsigned long long m)
{
    unsigned long long i, f;
    for (i = 1, f = 1; i <= n; i++) {
        f *= i;
        if (f > m) {
            f %= m;
        }
    }
    return f;
}

int main(int argc, char *argv[])
{
    unsigned long long n = strtoull(argv[1], NULL, 10);
    unsigned long long m = strtoull(argv[2], NULL, 10);

    printf("%llu\n", nfactmod(n, m));

    return 0;
}

and this:

h2co3-macbook:~ h2co3$ ./mod 1000000 1001001779
744950559
h2co3-macbook:~ h2co3$

runs in a fraction of a second.