% fair_warning.pi (in Picat)
% by N.F. Zhou, Jan. 2, 2016
% https://code.google.com/codejam/contest/433101/dashboard#s=p1&a=1
% Qualification Round 2010
% Problem B. Fair Warning
%
% to use: picat fair_warning < input_file > output_file
%
main =>
    T = read_int(),
    foreach (TC in 1..T)
        do_case(TC)
    end.

do_case(TC) =>
    N = read_int(),
    Ts = [read_int() : _ in 1..N],
    Ts = [T1|TsR],
    Ds = [abs(Ti-T1) : Ti in TsR],
    gcd_lst(Ds) = G,
    M = T1 div G,
    (M*G == T1 -> Y = 0; Y = (M+1)*G-T1),
    printf("Case #%w: %w\n",TC, Y).

gcd_lst([A]) = A.
gcd_lst([A,B]) = gcd(A,B).
gcd_lst([A,B|Lst]) = gcd_lst([gcd(A,B)|Lst]).

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