How to prune a tree at a given depth in Prolog?

Question

Prolog

I want to prune a tree at a given depth. Arguments: arbitrary binary tree; required depth; resulting tree.

first(M,N):-
N>0,M=..[H|T],((T==[],write(H));(T\=[],write(H),Q is N-1,second(T,Q))).
second(M,N):-
N>0,M=[H|T],first(H,N),((T==[]);(T\=[],second(T,N)) ).
second(_,0):-!.

I wrote a program that gives me this result.

?- first(s(f(b(m,k),a),t(a,g)),4).
sfbmkatag
True

But I need to get this result.

?- first(s(f(b(m,k),a),t(a,g)),2,X).
X = s(f,t)
True

?- first(s(f(b(m,k),a),t(a,g)),3,X).
X = s(f(b,a),t(a,g))
True

Please someone tell me how to do this. Not necessarily on Visual, you can on Turbo.