% 2017 Round 1C, Problem A, in Picat, by Alfredo Beaumont
% https://code.google.com/codejam/contest/3274486/dashboard
% Ample Syrup

import util, mip.

go(T, N, K, Xs) =>
    S1 = [0.000001 * P[1] * P[1] * pi : P in Xs],
    S2 = [0.000001 * P[1] * P[2] * 2 * pi : P in Xs],
    X = new_array(N),
    X :: 0..1,
    sum(X) #= K,
    Y = new_array(N),
    Y :: 0..1,
    sum(Y) #= 1,
    %sum([(X[I] * Y[I]) : I in 1..N]) #= 1,
    foreach(I in 1..N)
        (Y[I] #= 1) #=> (X[I] #= 1)
    end,
    S #= sum([(S2[I] * X[I] + S1[I] * Y[I]) : I in 1..N]),
    solve($[max(S)], [S, X, Y]),
    printf(stderr, "Case #%d: %f\n", T, S * 1000000).


main() =>
    [T] = [X.to_number() : X in readln().split()],
    foreach(I in 1..T)
        [N, K] = [X.to_number() : X in readln().split()],
        Xs = [[X.to_number() : X in readln().split()] : J in 1..N],
        go(I, N, K, Xs)
    end.

picat-lang.org