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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def final_spin_from_f0_tau(f0, tau, l=2, m=2):
 """Returns the final spin based on the given frequency and damping time. .. note:: Currently, only l = m = 2 is supported. Any other indices will raise a ``KeyError``. Parameters f0 : float or array Frequency of the QNM (in Hz). tau : float or array Damping time of the QNM (in seconds). l : int, optional l-index of the harmonic. Default is 2. m : int, optional m-index of the harmonic. Default is 2. Returns ------- float or array The spin of the final black hole. If the combination of frequency and damping times give an unphysical result, ``numpy.nan`` will be returned. """

    f0, tau, input_is_array = ensurearray(f0, tau)
    # from Berti et al. 2006
    a, b, c = _berti_spin_constants[l,m]
    origshape = f0.shape
    # flatten inputs for storing results
    f0 = f0.ravel()
    tau = tau.ravel()
    spins = numpy.zeros(f0.size)
    for ii in range(spins.size):
        Q = f0[ii] * tau[ii] * numpy.pi
        try:
            s = 1. - ((Q-a)/b)**(1./c)
        except ValueError:
            s = numpy.nan
        spins[ii] = s
    spins = spins.reshape(origshape)
    return formatreturn(spins, input_is_array)