import cp.

%
% Reversible: find Degree and N given M
%
go2 =>
  Ms = [4,20,105], % The multifactorials to identify

  foreach(M in Ms)
    println(m=M),
    Degree :: 1..10, % limit of the degree
    N :: 1..100, % limit of N
    All = findall([N,Degree,M], (multifactorial_reversible(N,Degree,M),
                               solve([M,N,Degree]))),
    foreach([NN,DD,MM] in All.sort)
      printf("n=%d degree=%d m=%d\n",NN,DD,MM)
    end,
    nl
  end,
  nl.

% reversible variant (using CP)
multifactorial_reversible(N,_D,M) :-
 N #<= 0, M #= 1.
multifactorial_reversible(N,D,M) :-
 D #> 0,
 N #> 0,
 ND #= N-D,
 multifactorial_reversible(ND,D,M1),
 M #= N*M1.