factorial(0, 1).
factorial(N, Fact) :-
    N > 0,
    PrevN is N - 1,
    factorial(PrevN, PrevFact),
    Fact is N * PrevFact.

binom_down(N, 0, 1) :- !.
binom_down(N, K, Res) :-
    K > 0, K < N,
    PrevK is K-1,
    PrevN is N-1,
    binom_down(PrevN, PrevK, PrevRes),
    binom_down(PrevN, K, CurRes),
    Res is CurRes + PrevRes.

binom_down(N, N, 1) :- !.
binom_down(N, K, Res) :-
    K =:= N,
    Res is 1, !.

binom_down(N, K, Res) :-
    K> N,
    Res is 0, !.