% 2017 Round 2, Problem A, in Picat, by Afa Zhou
% https://code.google.com/codejam/contest/5314486/dashboard
% Fresh Chocolate

import util.

main =>
    T = read_line().to_int(),
    foreach (TC in 1..T)
        [_N,P] = [to_int(Token) : Token in read_line().split()],
        G = [to_int(Token) : Token in read_line().split()],
        dc(G,P,F),
        printf("Case #%w: %w\n", TC, F)
    end.

dc(G,P,F) =>
    Rs = [E mod P : E in G].sort(),
    Z = sum([1 : 0 in Rs]),
    Rs1 = delete_all(Rs,0),
    A = new_array(P-1),
    bind_vars(A,0),
    update_group(Rs1,A),
    schedule(0,A,P,F1),
    F = F1+Z.

update_group([],_A) => true.
update_group([R|Rs],A) =>
    A[R] := A[R]+1,
    update_group(Rs,A).

table (+,+,+,max)
schedule(_L,A,_P,F),
    foreach (I in 1..len(A))
        A[I] == 0
    end
=>
    F = 0.
schedule(L,A,P,F) =>
    between(1,len(A),I),
    A[I] !== 0,
    A1 = copy_term(A),
    A1[I] := A1[I] - 1,
    L1 = (L+I) mod P,
    schedule(L1,A1,P,F1),
    (L == 0 -> F = F1+1; F = F1).
     
    
  
  

picat-lang.org