/*  combUL.cpp by K.Tsuru  */ 
/**************************************
It provides a binomial coefficient nCk
 ulong version. When n < 30 does not overflow.
**************************************/
#include "typedef.h"

ulong combUL(ulong n, ulong k) {
//  k = min(n, n - k);
    if(n < k) return 0;
    k = (n < n - k) ? n : n-k; // if n==k, k becomes 0.
    ulong r;
    if(k == 0) r = 1; // includes the case n == k
    else {
        r = combUL(n-1, k-1);
        r *=n;  r/= k;
    }
    return r;
}