k = [n/p]
m = n%p
n! mod p =  1      * 2     * ... * (p-1)  * p
      * (p+1)  * (p+2) * ... * (2p-1) * 2p
      * ...
      * (kp+1) * (kp+2) * ... * (kp+m)      mod p

     =  1 * 2 * ... * (p-1) * p
      * 1 * 2 * ... * (p-1) * 2p
      * ...
      * 1 * 2 * ... * m          mod p

     =  [(n%p)! * (p-1)!^(n/p)] * [(n/p)! * p^(n/p)]    mod p