function [K_range, N_b, N_s] = get_phase_transition_curve(N, M, K_max)
    % This function give the phase transition curve of FAR
    % input: N, M: FAR parameters
    % output: N_b, N_s: the phase transition curve of FAR in block case and scalar case

    if nargin < 3
        K_max = 25;
    end

    tau_min = 0;
    tau_max = 15;
    tau_interval = 0.05;
    tau_range = tau_min:tau_interval:tau_max;

    K_range = 1:K_max;

    N_b = zeros(length(K_range), 1);
    N_s = zeros(length(K_range), 1);

    cache_filename_1 = ...
        "../data/PT_curve_data/" + ...
        "I_2.mat";

    cache_filename_2 = ...
        "../data/PT_curve_data/" + ...
        "I_" + "" + string(2 * M) + ...
        ".mat";

    I_2 = get_integral(cache_filename_1, "I_2", tau_range, 2);
    I_2M = get_integral(cache_filename_2, "I_2M", tau_range, 2 * M);

    for K_idx = 1:length(K_range)
        K = K_range(K_idx);
        f_set_1 = zeros(length(tau_range), 1);
        f_set_2 = zeros(length(tau_range), 1);

        for tau_idx = 1:length(tau_range)
            tau = tau_range(tau_idx);
            f_set_1(tau_idx) = 1/2 * (K * (2 * M + tau ^ 2) + (N - K) * I_2M(tau_idx));
            f_set_2(tau_idx) = M / 2 * (K * (2 + tau ^ 2) + (N - K) * I_2(tau_idx));
        end

        N_b(K_idx) = min(f_set_1);
        N_s(K_idx) = min(f_set_2);
    end

end