% snapper_chain.pi (in Picat)
% by M. Bionchik, July, 2015
% https://code.google.com/codejam/contest/433101/dashboard#s=p0
% Qualification Round 2010
% Problem A. Snapper Chain
%
% to use: picat snapper_chain < input_file > output_file
%

main =>
    T = read_int(stdin),
    foreach(I in 1..T)
        do_case(I)
    end.

do_case(Case) =>
    N = read_int(stdin),        % number of snapper devices
    K = read_int(stdin),        % number of snaps

    writef("Case #%w: %s%n", Case, cond(snapper(N,K),"ON","OFF")).

/*
snapper(1, K) => K mod 2 == 1.
snapper(N, K) => snapper(N-1, K), K mod 2**N >= 2**(N-1), K mod 2**N <= 2**N-1.
*/
snapper(N, K) => K mod 2**N == 2**N-1.

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