public static long inverseCdfFast(final double p, final double s, final double N) {
        if (p > 1d || p < 0d)
            throw new IllegalArgumentException("p must be between 0 and 1");

        final double tolerance = 0.01d;
        double x = N / 2;

        final double D = p * (12 * (Math.pow(N, 1 - s) - 1) / (1 - s) + 6 - 6 * Math.pow(N, -s) + s - Math.pow(N, -1 - s) * s);

        while (true) {
            final double m    = Math.pow(x, -2 - s);
            final double mx   = m   * x;
            final double mxx  = mx  * x;
            final double mxxx = mxx * x;

            final double a = 12 * (mxxx - 1) / (1 - s) + 6 * (1 - mxx) + (s - (mx * s)) - D;
            final double b = 12 * mxx + 6 * (s * mx) + (m * s * (s + 1));
            final double newx = Math.max(1, x - a / b);
            if (Math.abs(newx - x) <= tolerance)
                return (long) newx;
            x = newx;
        }
    }