def partition_varied_cfg_list(cfg_list, default_cfg=None, recursive=False):
    r"""
    Separates varied from non-varied parameters in a list of configs

    TODO: partition nested configs

    CommandLine:
        python -m utool.util_gridsearch --exec-partition_varied_cfg_list:0

    Example:
        >>> # ENABLE_DOCTEST
        >>> from utool.util_gridsearch import *  # NOQA
        >>> import utool as ut
        >>> cfg_list = [{'f': 1, 'b': 1}, {'f': 2, 'b': 1}, {'f': 3, 'b': 1, 'z': 4}]
        >>> nonvaried_cfg, varied_cfg_list = partition_varied_cfg_list(cfg_list)
        >>> result = ut.repr4({'nonvaried_cfg': nonvaried_cfg,
        >>>                    'varied_cfg_list': varied_cfg_list}, explicit=1, nobr=True, nl=1)
        >>> print(result)
        nonvaried_cfg={'b': 1},
        varied_cfg_list=[{'f': 1}, {'f': 2}, {'f': 3, 'z': 4}],

    Example:
        >>> # ENABLE_DOCTEST
        >>> from utool.util_gridsearch import *  # NOQA
        >>> import utool as ut
        >>> cfg_list = [{'q1': 1, 'f1': {'a2': {'x3': 1, 'y3': 2}, 'b2': 1}}, {'q1': 1, 'f1': {'a2': {'x3': 1, 'y3': 1}, 'b2': 1}, 'e1': 1}]
        >>> print(ut.repr4(cfg_list, nl=1))
        >>> nonvaried_cfg, varied_cfg_list = partition_varied_cfg_list(cfg_list, recursive=True)
        >>> result = ut.repr4({'nonvaried_cfg': nonvaried_cfg,
        >>>                    'varied_cfg_list': varied_cfg_list}, explicit=1, nobr=True, nl=1)
        >>> print(result)
        nonvaried_cfg={'f1': {'a2': {'x3': 1}, 'b2': 1}, 'q1': 1},
        varied_cfg_list=[{'f1': {'a2': {'y3': 2}}}, {'e1': 1, 'f1': {'a2': {'y3': 1}}}],
    """
    import utool as ut
    if default_cfg is None:
        nonvaried_cfg = reduce(ut.dict_intersection, cfg_list)
    else:
        nonvaried_cfg = reduce(ut.dict_intersection, [default_cfg] + cfg_list)
    nonvaried_keys = list(nonvaried_cfg.keys())
    varied_cfg_list = [
        ut.delete_dict_keys(cfg.copy(), nonvaried_keys)
        for cfg in cfg_list]
    if recursive:
        # Find which varied keys have dict values
        varied_keys = list(set([key for cfg in varied_cfg_list for key in cfg]))
        varied_vals_list = [[cfg[key] for cfg in varied_cfg_list if key in cfg] for key in varied_keys]
        for key, varied_vals in zip(varied_keys, varied_vals_list):
            if len(varied_vals) == len(cfg_list):
                if all([isinstance(val, dict) for val in varied_vals]):
                    nonvaried_subdict, varied_subdicts = partition_varied_cfg_list(varied_vals, recursive=recursive)
                    nonvaried_cfg[key] = nonvaried_subdict
                    for cfg, subdict in zip(varied_cfg_list, varied_subdicts):
                        cfg[key] = subdict
    return nonvaried_cfg, varied_cfg_list