pb(T, R):-
    pbtNodes(T, T1),
    pbtCheck(T1, R).

pbtNodes(t(Key, nil, nil), t(Key, nil, nil, [1])).

pbtNodes(t(Key, nil, R), t(Key, nil, R, [0])).

pbtNodes(t(Key, L, nil), t(Key, L, nil, [0])).

pbtNodes(t(Key, L, R), t(Key, t(LKey, LL, LR, LRes), t(RKey, RL, RR, RRes), Res)):-
    pbtNodes(L, t(LKey, LL, LR, LRes)),
    pbtNodes(R, t(RKey, RL, RR, RRes)),
    append(LRes, RRes, Res).

pbtCheck(nil, []).

pbtCheck(t(_, nil, nil, _), []).

pbtCheck(t(_, nil, nil), []).

pbtCheck(t(Key, L, R, Kids), [Key|Res]):-
    findZero(Kids), !,
    pbtCheck(L, Res1),
    pbtCheck(R, Res2),
    append(Res1, Res2, Res).

pbtCheck(t(_, L, R, _), Res):-
    pbtCheck(L, Res1),
    pbtCheck(R, Res2),
    append(Res1, Res2, Res).

findZero([0|_]):-!, fail.

findZero([]).

findZero([_|T]):- !,
    findZero(T).